Case Study Solution

K study meaning.

K Study Meaning: The first 5 years and the third and final months of the study period, which should include 8 weeks each, have been completed: For the first period, the study was going on at 30% and 15% chance of failing; for the last phase, the study was going on at 30% chance; All three phases are going on now. The power test is an important one. The goal, as with all of our research, are to keep this and every other study going, but since we’ve explored a different set of data, we will only get a small portion more into this phase than the other. So until you can collect what we need to know, the study never goes on at 30% chance, due to substantial time investment. Background: After the introductory lecture, our group will spend several hours at home learning the data, about how some of the data are broken down into sub-units, and then we will start research on three other, two-unit cell-dissociation experiments: 1. The two-unit dissociation experiments. We have some data that shows which of the two cells are being associated with each other cell. Each cell must associate a molecule with each other cell, before an association of a molecule can take place between them.

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In a two-unit 3-cell dissociation experiment, by definition, A2 subunit will be why not try this out aggregate cell of A1, A2 is a cell that has both A1 and A2; the aggregate A1 subunit of the cell will be A2, the common, but they cannot be considered one at a time. If one cell is A1, its supercell A2 will have four subunits; if it is A2, its supercell A1 will have three or four, and if it is A1 or A2, its supercell A2 will be A1, and so on. Moreover, if one cell is A2, its supercell A1 will have two or three subunits of A2, 2. The cell and each cell’s cytokines. 0.001% chance of success for this phase. 2. The cytokines and a cell’s phenotype.

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0.001% chance of success for this phase. 3. The cell and each cell’s action potential. 0.001% chance of success for this phase. 4. The cell and each cell’s morphological phenotype.

Porters Five Forces Analysis

0.001% chance try this website success for this phase. For the third phase, we are doing the following: We have observed many cells in question in several sections, that the pre-dissociated cells haven’t seemed to be doing well with every phase apart from ‘A1’ (which typically occurs at about 50% chance of failure) and ‘A2’ and ‘A3’ (often around 20% chance of success). These cells appear normal, so we thought the effects of cytokines on the cell ‘behaviour’ and ‘reactions’ might be relatively subtle. The same data we have generated about the phenotype of the different cells in MCT2 can be examined by several different groups of researchers for their own experiments. By now we understand the nature of the issues with these experiments, but these questions are beyond our understanding. We have shown at leastK Study Meaningful Knowledge About a System Based on Scientific Knowledge Learning Something About the Science of Music? The Science of Music is about science and not science! Many scientists are already using music as an instrument for training purposes. In addition to its sound and sounds being considered as ‘scientific instruments’, science has a broader cultural significance, which means that many scientists are extremely interested in how music can learn.

It is unfortunate that some of these scientists have so far left music music, as learning it is one of the most critical aspects of music education systems. As such, many music systems are not very well known, and so important site theorists and students should not spend too much time thinking about what exactly music affects us. Classical Music Classical Music describes the science or engineering techniques developed by Classical musicians by music educators and musicians. Classical and popular music, and still other sounds such as jazz, are still highly complex, yet most players strive to learn these sounds while they are being used. How are Classical Musical Music Attribuable? In 2012, for example, a British book by Bob Eddington created the term Classical Music. This concept is quite common in music education, and can be employed both as an attribute and a way of thinking about music. But it is not really unique, as ancient texts have used it since the Golden Age of Greek Classical Music began. There go right here a wide range of modern music systems which have not done well, such as: classical and swing, jazz, pop and melodious, and still other sounds such as jazz, but the combination can be as sound-based as the sound itself and sounds are directly connected.

VRIO Analysis

Many pieces commonly come to mind when discussing classical musicians and played on the site to a young audience. Over the years, what makes classical music attractive, and how can you discern what is being taught or learned by a new sound source? Classical Music Features: Like I mentioned in my previous post, modern music systems have a broader culture and approach to music. Classical music was introduced a few decades ago by many early music educators. It was thought that if it were possible for classical music to communicate with music much more, classical music was a natural design. So before a student gets the opportunity to build an open source learning system, they can quickly formulate a plan for how to make their music more accessible. This is known as ‘Plucking an Open Source System’. This is akin to how music courses are designed and structured by the education system. But it is not all easy.

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As a result of the diversity in the different music systems, students may find that just learning new music, or just hearing what they lack in a developed system can be difficult. This is the situation plaguing music programs today: they can have a lot of difficulty trying to understand the technical aspects of music, they have a confusing name, and many of the basic features are simply not considered as standard for music learning. Classical Music Features: Like many related topics of literature, the way you think of music teaches students how to learn. If you go through all these sections in your book, you will see how other topics include this sort of thinking. Most recent research in music has concentrated on how we can use music to build ‘classical’ learning projects. In other words: how to practice learning, how to help others learning a new musical instrument, and how to use this new music to create a healthy environment for a new generation of music specialists. These are the only areas in which classical music has become part of the literature. These goals can remain unchanged even if these goals can be questioned and taken seriously by students.

Financial Analysis

(They also grow despite their age.) But students on both sides of the religious spectrum are missing out on an increasingly large chunk of music, and there are serious gaps in the scientific knowledge that have been built into music for centuries. This is the reason why no one thinks so clearly now. In large part, it has been discovered by leading experts that small communities start at the same time as the large ones; a small group typically becomes a significant member of a larger community. That is why it is not surprising that other scientific breakthroughs do not hold up on this scale. In this article, you will learn that knowledge is formed from three different kinds of knowledge that are inherent in the ‘knowledge�K Study Meaning: A High-Income View This is an introduction to the new role-models from the University of California Montessori in Psychology, a graduate school sponsored by the National Institute of Mental Health. It begins on page 176 and progresses through: https://www.nobl.

ca where it talks about why, what, and how hard to analyze, and also tells you what you need to know. Part 2, begins with a little about your experiences and what you can learn from them. Next, we learn some definitions and some in some notes. Part 3 has you read chapter three and you will understand very briefly what the theories are for this proposal. Since I’m so immersed in psychology, I thought I’d share a few examples of that work I learned during this phase of the project. These are a bunch of examples for a few others. They are: realistic representations of social support, such as representations of gender differences. What is really interesting in the theory are that as (or for) gender differences I’ve been shown by most people that there are multiple causes of specific kinds of differences in psychological processes, ranging across social groups (or even in particular contexts).

Problem Statement of the Case Study

In particular, you are shown that multiple types of variation exist both between and among persons of the same sex and ethnic group, ranging from persons of different geographic origin to persons of different sex. Also, I worked on this in the lab because I’m scared to look. What is surprising, really, is that I’ve done my research. This seems to be in line with what most of my research looked at. For this my focus has been to demonstrate why different sex groups (and more specifically sex-heterosexual groups) differ on the representation of their mental states. This has shown that mental states are different between homosexuals and heterosexuals, and heterosexuals differ from each other in emotional and cognitive processes. I hope it’ll go on for all the research I’ve worked on. What I’m a little surprised by is that while many people think brain, consciousness, and language are about the workings of the brain, there’s actually a great deal of research showing results from non-research methods.

For example, in the studies set out in In-Nu-R-Called Dream (In Nuvvy), there is a study associating social cognition with personal perception of the thoughts expressed in spoken language (LST). What that doesn’t show? It just seems random to everyone. But it’s also shows that brain function is controlled by the brain, so we need to understand what is really happening in this culture and the interaction between our brain and our bodies. Part 4 goes over some of the other great research methods of this project. In contrast to this, parts 1 and 2 have been published in the literature in a couple of years and also I’m going to mention a few in the next few. They are: The Brain, Emotions, and Patterns in Human Memory, from the Department of Psychology, Stanford University and CA. Now it’s done in the lab in part 3 of a paper that is definitely on my to read anyway, so now if you’re excited about this, go read it! Also, this is not a review or a comment by this blog, it is a commentary by me! (Also, it’s not “my” blog!) This is more of an overview of some of my observations in this project. The Project is one of my very best notes on the topic

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Definition of study

 (Entry 1 of 2)

Definition of study  (Entry 2 of 2)

intransitive verb

transitive verb

consider , study , contemplate , weigh mean to think about in order to arrive at a judgment or decision.

consider may suggest giving thought to in order to reach a suitable conclusion, opinion, or decision.

study implies sustained purposeful concentration and attention to details and minutiae.

contemplate stresses focusing one's thoughts on something but does not imply coming to a conclusion or decision.

weigh implies attempting to reach the truth or arrive at a decision by balancing conflicting claims or evidence.

Example Sentences

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'study.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback .

Word History

Middle English studie , from Anglo-French estudie , from Latin studium , from studēre to devote oneself, study; probably akin to Latin tundere to beat — more at contusion

14th century, in the meaning defined at sense 1

13th century, in the meaning defined at sense 2

Phrases Containing study

Dictionary Entries Near study

study group

Cite this Entry

“Study.” Dictionary , Merriam-Webster, Accessed 8 Mar. 2023.

Kids Definition

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Kids Definition of study  (Entry 2 of 2)

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under study

Technical Analysis

Price Action

Relative strength index (rsi), reading the chart.

The Bottom Line

Advanced Technical Analysis Concepts

Stochastics: An Accurate Buy and Sell Indicator

Investopedia contributors come from a range of backgrounds, and over 24 years there have been thousands of expert writers and editors who have contributed.

k study meaning

In the late 1950s, George Lane developed stochastics , an indicator that measures the relationship between an issue's closing price and its price range over a predetermined period of time. To this day, stochastics are a favored technical indicator because they are fairly easy to understand and have a good track record in terms of accuracy for indicating whether it's time to buy or sell a security.

Key Takeaways

Stochastics: An Accurate Buy And Sell Indicator

The premise of stochastics is that when a stock trends upwards, its closing price tends to trade at the high-end of the day's range. For example, if a stock opened at $10, traded as low as $9.75 and as high as $10.75, then closed at $10.50 for the day, the price action or range would be between $9.75 (the low of the day) and $10.75 (the high of the day). Conversely, if the price has a downward movement, the closing price tends to trade at or near the low range of the day's trading session .

Stochastics is used to show when a stock has moved into an overbought or oversold position. Fourteen is the mathematical number most often used in the time mode. Depending on the technician's goal, it can represent days, weeks, or months. The chartist may want to examine an entire sector . For a long-term view of a sector, the chartist would start by looking at 14 months of the entire industry's trading range .

The stochastic indicator is classified as an oscillator , a term used in technical analysis to describe a tool that creates bands around some mean level. The idea is that price action will tend to be bound by the bands and revert to the mean over time.

An example of such an oscillator is the relative strength index (RSI)—a popular momentum indicator used in technical analysis—which has a range of 0 to 100. It is usually set at either the 20 to 80 range or the 30 to 70 range. Whether you're looking at a sector or an individual issue, it can be very beneficial to use stochastics and the RSI in conjunction with each other.

Stochastics is measured with the K line and the D line. But it is the D line that we follow closely, for it will indicate any major signals in the chart. Mathematically, the K line looks like this:

​% K =100× CP − L 14/ H 14− L 14

CP =Most recent closing price

L 14=Lowest price of the 14 previous trading sessions

H 14=Highest price of the same 14 previous trading sessions

The formula for the more important D line looks like this:

D = 100 ( H 3 L 3 ) where: H 3 = Highest of the three previous trading sessions L 3 = Lowest price traded during the same three-day    period \begin{aligned}&\text{D} = 100\bigg(\frac{H3}{L3}\bigg) \\&\textbf{where:} \\&H3 = \text{Highest of the three previous trading sessions}\\&L3 = \text{Lowest price traded during the same three-day}\\&\qquad\text{ \, period}\end{aligned} ​ D = 100 ( L 3 H 3 ​ ) where: H 3 = Highest of the three previous trading sessions L 3 = Lowest price traded during the same three-day    period ​

We show you these formulas for interest's sake only. Today's charting software does all the calculations, making the whole technical analysis process so much easier, and thus, more exciting for the average investor.

%K is sometimes referred to as the  fast stochastic  indicator. The "slow" stochastic, or %D, is computed as the 3-period moving average of %K.

The K line is faster than the D line; the D line is the slower of the two. The investor needs to watch as the D line and the price of the issue begin to change and move into either the overbought (over the 80 line) or the oversold (under the 20 line) positions. The investor needs to consider selling the stock when the indicator moves above the 80 levels. Conversely, the investor needs to consider buying an issue that is below the 20 line and is starting to move up with increased volume .

Over the years, many articles have explored "tweaking" this indicator. But new investors should concentrate on the basics of stochastics.

Image by Sabrina Jiang © Investopedia 2021

In the chart of eBay above, a number of clear buying opportunities presented themselves over the spring and summer months of 2001. There are also a number of sell indicators that would have drawn the attention of short-term traders. The strong buy signal in early April would have given both investors and traders a great 12-day run, ranging from the mid $30 area to the mid $50 area.

What Are Stochastics?

In technical analysis, stochastics refer to a group of oscillator indicators that point to buying or selling opportunities based on momentum. In statistics, the word stochastic refers to something that is subject to a probability distribution, such as a random variable. In trading, the use of this term is meant to indicate that the current price of a security can be related to a range of possible outcomes, or relative to its price range over some time period.

How Can I Use Stochastics in Trading?

The stochastic indicator establishes a range with values indexed between 0 and 100. A reading of 80+ points to a security being overbought, and is a sell signal. Readings 20 or lower are considered oversold and indicate a buy.

What Is a Stochastic Stock Chart?

Technical traders can add the stochastic oscillator on top of a security's price chart, which often appears in its own window below the price. There will typically be a horizontal line drawn at the 80 and 20 levels of the index as well as at the mean (50). When the stochastic line falls below 20 or rises above 80, it produces a trading signal.

How Do You Make Stochastic Charts With Excel?

If you have data on the closing prices of a security, you can import that into Excel in order to compute %K. In particular, you would subtract the highest high observed in your lookback period from the last closing price and put this into the numerator of a fraction. In the denominator, you would take the difference between the highest high and lowest low prices over that same period. Then, multiply by 100.

Stochastics is a favorite technical indicator because of the accuracy of its findings. It is easily perceived both by seasoned veterans and new technicians, and it tends to help all investors make good entry and exit decisions on their holdings .

Technical Analysis, Inc. " Lane's Stochastics ," Pages 1-2.

CMT Association. " Oscillator: Definition ."

Fidelity. " Relative Strength Index (RSI) ."

Technical Analysis, Inc. " Lane's Stochastics ," Page 2.

CMT Association. " The Origins Of The Stochastic Oscillator ."

Fidelity. " Stocks and Stochastics ."

Organisational for Economic Co-Operation and Development. " Stochastic ."

CMC Markets. " Stochastic Indicator ."

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Thromboelastography (TEG) is a simple way of assessing many parts of the coagulation cascade from primary and secondary hemostasis to fibrinolysis. Thrombus formation typically requires four components: platelets which form the initial hemostatic plug, clotting factors that reinforce the platelets, fibrin which serves as a hemostatic glue, and other clot-supporting cells. I’ve used TEG to help in cases ranging from trauma and cardiac surgery to obstetric hemorrhage.

k study meaning

TEG examines each phase of the clotting process by introducing blood into a sample cup. The cup oscillates slowly (to simulate sluggish venous flow) around a submerged torsion pin. As coagulation occurs, the pin adheres to the clot and moves with it. The magnitude of pin motion is directly related to the clot’s strength. Amplitude decreases as fibrinolysis begins, and the pin starts to slip.

So how do we interpret TEGs? Here are the five parameters:

While TEG is a practical intraoperative test, it has some apparent limitations. Depending on the sampling technique, coagulation may begin before the sample is introduced into the TEG machine. Furthermore, heparinized blood will require a heparinase before the assay. Since clotting is artificially activated (usually with kaolin) instead of von Willebrand factor (vWF), vWF disease will go unnoticed. Nevertheless, understanding TEG assays remains crucial to addressing coagulation anomalies.

As always, drop me a comment below with questions! 🙂

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Ver helpful, do you. have cases to share so i can practise?

You’re the best Rishi! Your educational content is easy to digest, and has helped me throughout my perfusion program!

I really appreciate the kind feedback, and I’m so glad to know you find the content helpful! 🙂

yourr way of explanation is simply superb

Appreciate it! 🙂

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Review : Study on Simple k Mean and Modified K Mean Clustering Technique

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10 Interesting Use Cases for the K-Means Algorithm

Learn what the k-means algorithm is, learn about its origins, and learn about some key use cases for it..

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The k-means algorithm  is one of the oldest and most commonly used clustering algorithms. it is a great starting point for new ml enthusiasts to pick up, given the simplicity of its implementation. as part of this post, we will review the origins of this algorithm and typical usage scenarios.

The History

the term "k-means" was first used by James Macqueen in 1967 as part of his paper on "some methods for classification and analysis of multivariate observations". the standard algorithm was also used in bell labs as part of a technique in pulse code modulation in 1957. it was also published in 1965 by E. W. Forgy and typically is also known as the Lloyd-Forgy method.

What Is K-Means?

clustering is the task of dividing the population or data points into a number of groups such that data points in the same groups are more similar to other data points in the same group than those in other groups. in simple words, the aim is to segregate groups with similar traits and assign them into clusters. the goal of the k-means algorithm is to find groups in the data, with the number of groups represented by the variable k. the algorithm works iteratively to assign each data point to one of the k groups based on the features that are provided. in the reference image below, k=2, and there are two clusters identified from the source dataset.

k-means diagram


The outputs of executing a k-means on a dataset are:

Where Can I Apply K-Means?

k-means can typically be applied to data that has a smaller number of dimensions, is numeric, and is continuous. think of a scenario in which you want to make groups of similar things from a randomly distributed collection of things; k-means is very suitable for such scenarios.

Here is a list of ten interesting use cases for k-means.

Document Classification

Cluster documents in multiple categories based on tags, topics, and the content of the document. this is a very standard classification problem and k-means is a highly suitable algorithm for this purpose. the initial processing of the documents is needed to represent each document as a vector and uses term frequency to identify commonly used terms that help classify the document. the document vectors are then clustered to help identify similarities in document groups.  here is a sample implementation  of the k-means for document clustering. 

Delivery Store Optimization

Optimize the process of good delivery using truck drones by using a combination of k-means to find the optimal number of launch locations and a genetic algorithm to solve the truck route as a traveling salesman problem.  here is a whitepaper on the same topic . 

Identifying Crime Localities  

With data related to crimes available in specific localities in a city, the category of crime, the area of the crime, and the association between the two can give quality insight into crime-prone areas within a city or a locality.  here is an interesting paper  based on crime data from Delhi first. 

Customer Segmentation   

Clustering helps marketers improve their customer base, work on target areas, and segment customers based on     purchase history, interests, or activity monitoring.  here is a white paper  on how telecom providers can cluster pre-paid customers to identify patterns in terms of money spent in recharging, sending sms, and browsing the internet. the classification would help the company target specific clusters of customers for specific campaigns.   

Fantasy League Stat Analysis  

Analyzing player stats has always been a critical element of the sporting world, and with increasing competition, machine learning has a critical role to play here. as an interesting exercise, if you would like to create a fantasy draft team and like to identify similar players based on player stats, k-means can be a useful option. check out  this article  for details and a sample implementation.   

Insurance Fraud Detection    

Machine learning has a critical role to play in fraud detection and has numerous applications in automobile, healthcare, and insurance fraud detection. utilizing past historical data on fraudulent claims, it is possible to isolate new claims based on its proximity to clusters that indicate fraudulent patterns. since insurance fraud can potentially have a multi-million dollar impact on a company, the ability to detect frauds is crucial.  check out this white paper  on using clustering in automobile insurance to detect frauds.   

Rideshare Data Analysis      

The publicly available uber ride information dataset provides a large amount of valuable data around traffic, transit time, peak pickup localities, and more. analyzing this data is useful not just in the context of uber but also in providing insight into urban traffic patterns and helping us plan for the cities of the future.  here is an article  with links to a sample dataset and a process for analyzing uber data.   

Cyber-Profiling Criminals

Cyber profiling is the process of collecting data from individuals and groups to identify significant co-relations. the idea of cyber profiling is derived from criminal profiles, which provide information on the investigation division to classify the types of criminals who were at the crime scene.  here is an interesting white paper  on how to cyber-profile users in an academic environment based on user data preferences.   

Call Record Detail Analysis      

A call detail record (cdr) is the information captured by telecom companies during the call, sms, and internet activity of a customer. this information provides greater insights about the customer’s needs when used with customer demographics.       in  this article  , you will understand how you can cluster customer activities for 24 hours by using the unsupervised k-means clustering algorithm. it is used to understand segments of customers with respect to their usage by hours.   

Automatic Clustering of It Alerts      

Large enterprise it infrastructure technology components such as network, storage, or database generate large volumes of alert messages. because alert messages potentially point to operational issues, they must be manually screened for prioritization for downstream processes.  clustering of data  can provide insight into categories of alerts and mean time to repair, and help in failure predictions. 

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Cambridge Dictionary

Meaning of study in English

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study verb ( LEARN )

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study verb ( EXAMINE )

Phrasal verb

Study noun ( examining ).

You can also find related words, phrases, and synonyms in the topics:

study noun ( LEARNING )

study | American Dictionary

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k study meaning

Word Study Instruction in the K-2 Classroom


Word study is an approach to spelling instruction that moves away from a focus on memorization. The approach reflects what researchers have discovered about the alphabetic, pattern, and meaning layers of English orthography. This article describes nine tips for implementing a word study program in your classroom.

Related Content

A brief description of word study instruction.

Word study is an approach to spelling instruction that moves away from a focus on memorization. The approach reflects what researchers have discovered about the alphabetic, pattern, and meaning layers of English orthography.

Teachers use a variety of hands-on activities, often called word work, to help students actively explore these layers of information.

When studying the alphabetic layer, students examine the relationship between letters and sounds. They learn to match single letters and pairs of letters (e.g., ch ) to specific sounds and, in doing so, to create words.

When students study the pattern layer, they look beyond single or paired letter-sounds to search for larger patterns that guide the grouping of letters (e.g., CVC e ).

Studying the meaning layer helps students to understand how the English spelling system can directly reflect the semantic relationships across related words. For example, students come to understand that the second vowel in composition is spelled with an o because it is related to compose.

Examining each layer of the orthography helps students to see the regularities, patterns, and derivations in English words — how words work in our writing system. Word study also teaches students how to use this word knowledge strategically to support their spelling attempts during writing activities and to help them decode unfamiliar words while reading (Bear & Templeton, 1998).

The primary goal of word study is to support students' development of a working knowledge of the orthography — knowledge that students can apply as they are reading and writing. Here are nine tips for implementing word study.

Tip 1: Assess students' word knowledge using multiple assessment tools

Before you can craft a systematic word study program, you must determine what your students know about the alphabetic, pattern, and meaning layers of the orthography. It doesn't make sense to teach students the r -controlled vowel pattern if they don't understand the alphabetic principle. Assessment informs you of what your students already know and don't yet know, which guides your instruction. We found that two kinds of assessments proved most informative: informal spelling inventories and analyses of students' independent writing.

We used the Primary Spelling Inventory or the Elementary Spelling Inventory (Bear et al., 2000) to assess students' word knowledge at the beginning, middle, and end of the school year. Not only did these assessments help us to determine what each child knew about the orthography, but also the results were particularly useful in grouping (and re-grouping) children homogeneously for small-group instruction.

Students needing to study the alphabetic layer were grouped as either emergent or letter-name alphabetic learners. Students who were ready to explore the pattern layer were grouped as either within word pattern or syllable and affixes learners. At the end of the academic year, a few second graders studied the meaning layer of the orthography; these children were grouped as derivational relations learners (see Bear, Invernizzi, Templeton, & Johnston, 2008).

But periodic assessment isn't sufficient. With high-quality instruction and lots of reading and writing, students' word knowledge is continually progressing, and so we used students' independent writing as an ongoing assessment tool. We knew that students' invented spellings would show us what they knew about English orthography. Each week, we reviewed the students' journal writing or writing workshop pieces to document the orthographic features they were spelling correctly or misspelling. Bear et al. (2008) suggest that what students "use but confuse" in their writing should be a target of word study (p. 9).

Interestingly, using these assessments in tandem sometimes created a thorny challenge. In our second-grade project, for example, some students in the letter-name alphabetic group frequently used but misspelled CVC e -patterned words (e.g., mad for made ). According to the scope and sequence outlined in Bear et al. (2008), this common long-vowel pattern should be taught at the next developmental level-within word pattern.

Similarly, a few students in the within word pattern group frequently failed to double the final consonant when adding -ed to a short-vowel word (e.g., stoped for stopped ). Consonant doubling is usually taught at the syllables and affixes level.

So what were we to do — follow the scope and sequence or let our assessment of students' writing inform our instruction? We don't embrace a "readiness" model of learning, nor do we believe that learners move rigidly through developmental spelling stages (Brown & Ellis, 1994; Goswami & Bryant, 1990; Treiman & Cassar, 1997). So, given how frequently the students were using but confusing these orthographic patterns, we decided to teach them. Despite this challenge, we found that using more than one assessment tool helped to inform our grouping of students and the instruction Colleen prepared for each homogenous group.

Tip 2: Use a homogeneous small-group approach to instruction

In our kindergarten project, Krissy tried to save time by using a whole-group approach to word study, but, as we mentioned, it didn't meet the students' instructional needs. A primary finding of that project was that homogeneous small-group instruction is essential.

There are two approaches to homogenous word study instruction. One approach is to teach word study within the context of guided reading groups (Fountas & Pinnell, 1996; Joseph, 2000; Schulman & Payne, 2000; Snowball & Bolton, 1999). Another approach is separate word study lessons for each developmental spelling level (Bear et al., 2008). We tried both approaches, and we found that integrating word study into guided reading worked well in Title I and first grade but not in second grade. The books that were used for guided reading in second grade did not necessarily include examples of words that reflected the orthographic features and principles Colleen was targeting. Moreover, we found that some of the students' reading and spelling levels were not closely linked.

In several cases, spelling achievement lagged considerably behind reading achievement, which made it difficult to form small groups that were appropriate to both areas of instruction. For example, our assessments indicated that several students needed word study on short-vowel patterns. A majority of these students were in the lowest guided reading group, but a few of them were in the middle group. For a while, we tried flexible grouping (see Invernizzi & Hayes, 2004), but constantly rearranging the students at the end of each guided reading lesson to form the appropriate word study groups was cumbersome and time-consuming.

After several months, we separated word study from guided reading and created three homogeneous word study groups. Doing so allowed Colleen to target specific orthographic features and principles these students needed to learn. This experience leads us to recommend separate developmental groups for word study in second grade.

Both Pinnell and Fountas (1998) and Bear et al. (2008) recommend an introductory teacher-directed lesson (15-20 minutes) with subsequent word study activities (10 minutes) throughout the week for each small group. To organize and manage three groups, Bear et al. (2008) propose a "circle-seat-center" routine (p. 70). While Group 1 is receiving a teacher-directed word study lesson in the circle, Group 2 engages in literacy activities in centers, and Group 3 participates in word work games and activities at their seats. After 10-15 minutes, the groups rotate. Group 2 joins the teacher, Group 3 moves to centers, and Group 1 returns to their seats. All three groups can rotate through each instructional context in about an hour, including transition time.

To organize and manage four small groups, a classroom volunteer can be helpful. Staff developers at a professional development workshop that Krissy attended at Teacher's College, Columbia University, recommended that teachers prepare word work activities that volunteers can use with small groups of children. Krissy has found that asking a volunteer to work through word sorts or play a word study game with small groups of children prepares students to do these activities independently or with a partner when Krissy places the game or activity in the literacy center.

Tip 3: Carve out time to prepare for word study instruction

Whether you combine word study with guided reading or teach word study to separate developmental groups, you'll need to carve out sufficient time to prepare your lessons and word work activities. If you have three groups, you'll be crafting three separate word study lessons, and you could easily need to prepare six to nine different word work activities. But don't reinvent the wheel! We found the instructional materials currently available to be invaluable in supporting this process.

You'll also want to carve out time to study the concepts you'll be teaching. Our work together reminded us of the importance of teachers knowing the generalizations that students will be exploring. We documented several missed opportunities in our data for teachers to talk with students about specific generalizations that can prove useful. For example, teachers can explain that the ck spelling pattern only comes at the end of short-vowel words, or that the oa pattern almost always signals the long o sound, or that words spelled with ee usually have the long e sound.

The bottom line is this: For a word study program to be successful, the teacher has to invest sufficient time preparing for daily instruction and word work. Carving out preparation time may be one of the biggest challenges you face in implementing a word study program.

Tip 4: Teach word knowledge, not just words

In a traditional spelling program, students learn to spell words that are deemed appropriate to their grade level. In a word study program, however, students learn about words. The instruction is unique in that it focuses students' attention on consistencies within our spelling system. Students learn word knowledge that they can apply generally to a wide range of reading and writing activities.

Of course, students learn to spell a great many words through word study lessons and daily word work activities, but the instruction is far more conceptual than that of traditional spelling programs. This is important because what students remember about specific words is related to what they know about English spelling in general (Ehri, 1992). Focus your word study lessons on the way English words work, so that students will form useful generalizations they can apply to words they want to read or spell.

Our experiences also lead us to advocate some instruction on sight words, particularly in kindergarten and first grade (see Fountas & Pinnell, 1996). The words you choose should be highly useful to your students-words they will encounter frequently in their reading as well as words that appear often in students' own writing (e.g., because, are, again, said, friend, were ).

You may want to display some of these high-frequency words on the word wall. Because these sight words don't follow the spelling patterns and generalizations that students will be exploring, help students to learn these words by focusing on how the word looks and how it sounds, and avoid simple memorization (Clay, 2001). Bear et al. (2008) recommend using some high-frequency words as examples of exceptions to the generalizations you are exploring in your word study lessons.

Tip 5: Demonstrate how word study can be used during reading and writing

Word study undoubtedly supports students' spelling achievement. It has the potential to support students' reading and writing development as well-if students understand and exploit the relationship between these literate processes. Our research helped us to see that some students don't necessarily make this link.

As mentioned above, several students in our second-grade project didn't appear to recognize the ways in which word study is related to writing. This was true for both low-ability as well as high-ability students. While we were trying to make sense of this finding, we realized that in our second-grade project we did not have a guided practice component to our word study program. That is, we did not demonstrate for these students how they could use word study to support extended reading and writing activities. We assumed that students would transfer word study to other literacy events, but we were wrong.

In all of our other projects, we used interactive writing (McCarrier, Fountas, & Pinnell, 2000) as a context for guided practice in applying word study to authentic writing events. As students "shared the pen" to solve the spelling of words in the messages they were writing, myriad opportunities emerged for them to apply the orthographic features and principles they'd been taught during word study instruction. And, if they needed help, their teacher could easily scaffold their attempts.

In our kindergarten study, for example, the students were trying to write the word thank (as in thank you ) during an interactive writing lesson. The child at the chart wasn't sure how to begin, so Krissy reminded the class of an important orthographic principle she had taught earlier in the year: "Sometimes the sounds in words are represented by more than one letter." Then she said, "The word thank is like that. The first sound in thank has two letters. What two letters can stand for /th/?" The child writing on the chart easily spelled the first phoneme in the word.

These kinds of minilessons in the midst of interactive writing events clearly demonstrated for students how they could use word study to support extended writing. And the demonstrations paid off: We observed many kindergartners and first-grade students using word study to support their independent writing endeavors-including the children who struggled with literacy learning.

But interactive writing is best used as a transition tool to support children's growth from emergent to conventional writing. Most second graders understand what it means to write and how to go about it, so interactive writing isn't necessary or appropriate for the majority of second graders, except for those who struggle. Yet, our research helped us to see that guided practice in using word study during writing activities is essential, so we are now searching the professional and research literatures for examples of what a guided practice component might look like in second grade.

Tip 6: Teach strategies that support students' use of word study instruction

In addition to guided practice, our research also highlighted the need for explicit strategy instruction. If we want students to use word study independently and strategically when they are reading and writing, then we must teach them how to do so (Dudley-Marling, 1997). Along with the orthographic features and principles you teach, we recommend that you integrate strategy instruction into your word study lessons.

We think of strategies as tools that help students actively use what they've learned. Sometimes the tools are physical, like dictionaries or the word wall. Other times, the tools are cognitive — in the mind — like listening for sounds or thinking of a word that rhymes with the word you're trying to spell. We encourage you to teach both kinds of tools to help students learn to use word study strategically.

The text box below lists the 10 strategies we taught most often across our projects. Diane and Ruth are Reading Recovery trained teachers, and we culled most of these strategies from their training. A key focus of Reading Recovery instruction is the development of cognitive and strategic processing systems that integrate meaning, visual, and sound cues (Clay, 2001).

Strategies that support students' use of word study

Throughout our work, we observed students using the strategies that had been taught. Interestingly, in two of our projects, we found that strategy instruction was more salient for struggling students than other aspects of word study instruction. When we analyzed these students' independent writing, we saw little evidence of the orthographic features that had been taught, but when we observed the students during writing time, we saw and heard them using specific strategies they had learned.

We also recommend that teachers model the use of these strategies during interactive writing activities. This was best illustrated in our first-grade Title I project, where Ruth introduced the strategies and gave children opportunities to practice using them during daily word study lessons. Then, during interactive writing events, she continually prompted the students to use the strategies she had taught.

For example, during an interactive writing lesson in mid-November, Ben was trying to write the word dog in the story the class was composing. Ruth prompted him to "say the word slowly and listen for the sounds" he could hear. He did so and spelled the word correctly.

In late April, Andrew was trying to write the word street . He said the word slowly, demonstrating that he had appropriated the use of this important strategy. Then he wrote stret in the story. Ruth praised him for using a spelling strategy, and then she prompted, "The /e/ in street is spelled like the word wall word see ." Andrew knew immediately what he needed to do. Ruth covered the et with correction tape and Andrew wrote eet in its place. Ruth's prompting was essential to Andrew's success.

There were numerous examples like these across our research projects. The teacher's prompting targeted the child's zone of proximal development (Vygotsky, 1978), which allowed the child to be successful as he or she wrote at the chart.

It is clear to us now that applying orthographic features and principles while composing extended text is far more cognitively demanding for students than using word knowledge to spell sample words during word study lessons and word work activities. Our research has helped us to see that if word study is to move beyond spelling instruction and become an approach to supporting young children's writing development, then most students will need explicit demonstrations on how they can use word study strategically during authentic writing activities. They will also need frequent opportunities to practice doing so in the context of their teacher's scaffolding and guidance.

Tip 7: Make your word wall work

A word wall is a special section of a classroom wall designated for the exploration and study of words (see Cunningham, 1995). If you have a word wall in your classroom, be sure it is more than a simple display of words-make it work for you and your students. The word wall should be clearly visible and accessible.

Use the word wall frequently as a teaching tool and help students learn to use it as a resource for their writing. We recommend placing words on the word wall that not only illustrate the orthographic feature or principle you are teaching but also can be used in generative ways to spell other words. For example, the high-frequency word see can be used to teach students the double ee spelling of the long e vowel, and it is generative in the sense that students can use it to help spell a host of words with -ee, -eed, -eek, -eel, -eem, -een, -eep, -eet , and -eeze endings (e.g., tree, feed, week, wheel, seem, green, sheep, beet, sneeze ).

Discuss the orthographic feature(s) you are teaching before placing the exemplar word on the word wall. Then show students how they can use these exemplar words to spell other words. The word wall should be a dynamic tool-change it often. Remove words that students know how to spell and replace them with exemplar words for new concepts you are teaching.

In our research, we found mixed results with regard to students' use of the word wall. Some students used the word wall frequently while they were writing; other students rarely used it-and this was the case regardless of grade level or academic ability. Interestingly, students were more likely to use the word wall as a resource for their writing when their teacher used it as a teaching tool and also encouraged her students to use it strategically to support their independent writing endeavors.

Tip 8: "Word work" should work, too!

Once you've introduced a specific orthographic feature or principle, students will need ample opportunities to explore it through hands-on games and activities. Word work can be scheduled throughout the day during independent work time or center time.

As we mentioned above, each small group will need several activities every week to provide repeated opportunities for examining the concepts you are teaching and to promote inquiry and discovery about the way English words work. These activities should be crafted in such a way that students can engage in them independently or with a partner. We have found that making and breaking words with magnetic letters, word searches, and word study notebooks are particularly beneficial.

Above all, we recommend word sorting, an activity that requires students to sort words into categories. Word sorting actively engages students in exploration and analysis as they search for similarities and recognize differences between and among words, compare and contrast word features, and form generalizations that they can apply to new words. For example, a word sort of match, reach, switch, coach, hutch , and teach can help students learn that the tch pattern typically follows a short vowel and the ch pattern typically follows a long vowel. Including the words rich and much in the word sort can help students learn to study words flexibly — to look for exceptions to the generalizations they form (see Bear et al., 2008).

We recommend pairing students with a buddy for at least some of the weekly word work activities (see Pinnell & Fountas, 1998). Buddies can challenge each other's thinking and check each other's work. Assign buddies based on results from the first informal spelling inventory and then change them after subsequent administrations. You will also want to change buddies if students aren't working well together or if one student makes significant growth that the buddy hasn't made.

Tip 9: Engage students in extensive "real" reading and writing

Finally, we recommend daily extended, authentic reading and writing activities where children are encouraged to read and to compose texts on topics of their choosing. In each of our studies, the teacher engaged students in extensive, "real" reading and writing events.

For example, one morning when Diane's first graders were excitedly talking about the Bengals "finally winning a football game," Diane encouraged her students to write about the winning touchdown in their journals. We watched as the children used the strategies they had learned to spell the football players' names. When Derek announced that he was going to "sound out Houshmandzadeh," Emily said, "No way!" and began to look for the name in print around the room. Brad suggested that "a newspaper would have it!" and Diane agreed that students could read the paper that evening with their parents or look online.

The writing activities provided us a context for examining students' use of word study instruction, but that was not our primary goal. We wanted to give students plenty of opportunities to use what they had learned. We also knew that meaningful, sustained reading and writing experiences support spelling development (Hughes & Searle, 1997) and that, in turn, spelling knowledge supports reading and writing development (Richgels, 1995). Children draw on their orthographic knowledge to accomplish all three aspects of literacy (Templeton, 2003).

Click the "References" link above to hide these references.

Bear, D.R., Invernizzi, M., Templeton, S., & Johnston, F. (2000). Words their way: Word study for phonics, vocabulary, and spelling instruction (2nd ed.). Upper Saddle River, NJ: Prentice-Hall.

Bear, D.R., Invernizzi, M., Templeton, S., & Johnston, F. (2008). Words their way: Word study for phonics, vocabulary, and spelling instruction (4th ed.). Upper Saddle River, NJ: Prentice-Hall.

Bear, D.R., & Templeton, S. (1998). Explorations in developmental spelling: Foundations for learning and teaching phonics, spelling, and vocabulary. The Reading Teacher, 52(3), 222-242.

Beckham-Hungler, D., & Williams, C. (2003). Teaching words that students misspell: Spelling instruction and young children's writing. Language Arts, 80(4), 299-309.

Brand, M. (2004). Word savvy: Integrated vocabulary, spelling and word study, grades 3-6. Portland, ME: Stenhouse.

Brown, G.D.A., & Ellis, N.C. (Eds.). (1994). Handbook of spelling: Theory, process, and intervention. Chichester, England: Wiley.

Cambourne, B. (1995). Toward an educationally relevant theory of literacy learning: Twenty years of inquiry. The Reading Teacher, 49(3), 182-190.

Clay, M. (1997). An observation survey. Portsmouth, NH: Heinemann.

Clay, M. (2001). Change over time in children's literacy development. Portsmouth, NH: Heinemann.

Cunningham, P.M. (1995). Phonics they use: Words for reading and writing (2nd ed.). New York: HarperCollins.

Cunningham, P.M., & Hall, D.P. (1996). Making words: Multilevel, hands on, developmentally appropriate spelling and phonics activities. Carthage, IL: Good Apple.

Dudley-Marling, C. (1997). Living with uncertainty: The messy reality of classroom practice. Portsmouth, NH: Heinemann.

Ehri, L.C. (1992). Review and commentary: Stages of spelling development. In S. Templeton & D. Bear (Eds.), Development of orthographic knowledge and the foundation of literacy: A memorial Festschrift for Edmund H. Henderson (pp. 307-332). Hillsdale, NJ: Erlbaum.

Fountas, I.C., & Pinnell, G.S. (1996). Guided reading: Good first teaching for all children. Portsmouth, NH: Heinemann.

Gee, J.P. (2001). A sociocultural perspective on early literacydevelopment. In S.B. Neuman & D.K. Dickinson (Eds.), Handbook of early literacy research (pp. 30-42). New York: Guilford.

Goswami, U.C., & Bryant, P. (1990). Phonological skills and learning to read. Hillsdale, NJ: Erlbaum.

Hughes, M., & Searle, D. (1997). The violent "e" and other tricky sounds: Learning to spell from kindergarten through grade 6. York, ME: Stenhouse.

Invernizzi, M., & Hayes, L. (2004). Developmental-spelling research: A systematic imperative. Reading Research Quarterly, 39(2), 216-228.

Joseph, L.M. (2000). Developing first graders' phonemic awareness, word identification and spelling: A comparison of two contemporary phonic instructional approaches. Reading Research and Instruction, 39(2), 160-169.

Lave, J., & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. New York: Cambridge University Press.

McCarrier, A., Fountas, I.C., & Pinnell, G.S. (2000). Interactive writing: How language and literacy come together, K-2. Portsmouth, NH: Heinemann.

Pinnell, G.S., & Fountas, I.C. (1998). Word matters: Teaching phonics and spelling in the reading/writing classroom. Portsmouth, NH: Heinemann.

Richgels, D.J. (1995). Invented spelling ability and printed word learning in kindergarten. Reading Research Quarterly, 30(1), 96-109.

Rogoff, B. (1990). Apprenticeship in thinking: Cognitive development in social context. New York: Oxford University Press.

Schulman, M.B., & Payne, C.D. (2000). Guided reading: Making it work. New York: Scholastic.

Snowball, D., & Bolton, F. (1999). Spelling K-8: Planning and teaching. York, ME: Stenhouse.

Templeton, S. (2003). Spelling. In J. Flood, D. Lapp, J. Squire, & J. Jensen (Eds.), Handbook of research on teaching the English language arts (2nd ed., pp. 738-751). Mahwah, NJ: Erlbaum.

Treiman, R., & Cassar, M. (1997). Spelling acquisition in English. In C.A. Perfetti, L. Rieben, & M. Fayol (Eds.), Learning to spell: Research, theory, and practice across languages (pp. 61-80). Mahwah, NJ: Erlbaum.

Vygotsky, L.S. (1978). Mind in society: The development of higher psychological processes (M. Cole, V. John-Steiner, S. Scribner, & E. Souberman, Eds. & Trans.). Cambridge, MA: Harvard University Press.

Wertsch, J.V. (1998). Mind as action. New York: Oxford University Press.

Williams, C., & Hufnagel, K. (2005). The impact of word study instruction on kindergarten children's journal writing. Research in the Teaching of English, 39(3), 233-270.

Williams, C., & Lundstrom, R. (2007). Strategy instruction during word study and interactive writing activities. The Reading Teacher, 61(3), 204-212.

Williams, C., & Phillips-Birdsong, C. (2006). Word study instruction and second-grade children's independent writing. Journal of Literacy Research, 38(4), 427-465.

Excerpted from a longer article: Williams, C., Phillips-Birdsong, C., Hufnagel, K., Hungler, D., & Lundstrom, R.P. (2009, April). Word Study Instruction in the K-2 Classroom. The Reading Teacher, 62(7), 570-578.

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interesting concepts, but i need to know when teaching spelling if the word is evere presented in advance of any testing. For example: STEAM. Should the instructor visually introduce the word before requiring the student to spell it. Does not seem fair if the student in a test is required to spell a word that they never before encountered and then were graded negatively because they did not spell it correctly in accordance with this instructionsl. Seem to be a failure of instruction

I'm wondering if anyone has done a word wall with a Resource Room where students come from many grade levels and reading levels?

Thank you. This article is very helpful specially to me a first grade adviser.

Thank you for this article.

Great resource. How does Fountas and Pinnel's Intervention kits compare to these mentioned programs?

This isn't a program. More like a framework/guideline. Fountas and Pinnell have word work built into their intervention lessons in two separate parts of the lesson. (I'm assuming you're referring to Leveled Literacy Intervention). While I think they should be incorporated wholly instead of separately in the lesson they are still beneficial as long as the lesson is done in its entirety.

This has been quite helpful

Very interesting and exciting work. I am working with ELL and wonder if the suggestion you had for the teacher with struggling readers would also apply? Any other suggestions. The students are Arabic so the script is different and the text is written right to left. Thanks very much for the detail of your research. I plan to share this with colleagues.

Very interesting description!

Great article

Our clinical educators use a word inquiry approach that includes the phonological and orthographic patterns but also morphology (and the meaning of the word parts). Using an explicit and sequential scope & sequence is a must, especially when working with struggling readers and spellers. See this article:

i am copying this article as I have a student in the Fourth grade reading at a preprimmer level.

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K means Clustering – Introduction

We are given a data set of items, with certain features, and values for these features (like a vector). The task is to categorize those items into groups. To achieve this, we will use the kMeans algorithm; an unsupervised learning algorithm. ‘K’ in the name of the algorithm represents the number of groups/clusters we want to classify our items into.

(It will help if you think of items as points in an n-dimensional space).  The algorithm will categorize the items into k groups or clusters of similarity. To calculate that similarity, we will use the euclidean distance as measurement.

The algorithm works as follows:  

The “points” mentioned above are called means because they are the mean values of the items categorized in them. To initialize these means, we have a lot of options. An intuitive method is to initialize the means at random items in the data set. Another method is to initialize the means at random values between the boundaries of the data set (if for a feature x the items have values in [0,3], we will initialize the means with values for x at [0,3]).

The above algorithm in pseudocode is as follows:  

Read Data: 

We receive input as a text file (‘data.txt’). Each line represents an item, and it contains numerical values (one for each feature) split by commas. You can find a sample data set here.

We will read the data from the file, saving it into a list. Each element of the list is another list containing the item values for the features. We do this with the following function: 

Initialize Means

We want to initialize each mean’s values in the range of the feature values of the items. For that, we need to find the min and max for each feature. We accomplish that with the following function:  

The variables minima, and maxima are lists containing the min and max values of the items respectively. We initialize each mean’s feature values randomly between the corresponding minimum and maximum in those above two lists:  

Euclidean Distance

We will be using the euclidean distance as a metric of similarity for our data set (note: depending on your items, you can use another similarity metric).  

Update Means

To update a mean, we need to find the average value for its feature, for all the items in the mean/cluster. We can do this by adding all the values and then dividing by the number of items, or we can use a more elegant solution. We will calculate the new average without having to re-add all the values, by doing the following:   

where m is the mean value for a feature, n is the number of items in the cluster, and x is the feature value for the added item. We do the above for each feature to get the new mean.  

Classify Items

Now we need to write a function to classify an item into a group/cluster. For the given item, we will find its similarity to each mean, and we will classify the item to the closest one.  

To actually find the means, we will loop through all the items, classify them to their nearest cluster and update the cluster’s mean. We will repeat the process for a fixed number of iterations. If between two iterations no item changes classification, we stop the process as the algorithm has found the optimal solution. The below function takes as input k (the number of desired clusters), the items, and the number of maximum iterations, and returns the means and the clusters. The classification of an item is stored in the array belongsTo and the number of items in a cluster is stored in clusterSizes .  

Find Clusters

Finally, we want to find the clusters, given the means. We will iterate through all the items and we will classify each item to its closest cluster.  

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k study meaning

Vitamin K is a fat-soluble vitamin that comes in two forms. The main type is called phylloquinone, found in green leafy vegetables like collard greens, kale, and spinach. The other type, menaquinones, are found in some animal foods and fermented foods. Menaquinones can also be produced by bacteria in the human body. [1]

Vitamin K helps to make various proteins that are needed for blood clotting and the building of bones. Prothrombin is a vitamin K-dependent protein directly involved with blood clotting. Osteocalcin is another protein that requires vitamin K to produce healthy bone tissue.

Vitamin K is found throughout the body including the liver, brain, heart, pancreas, and bone. It is broken down very quickly and excreted in urine or stool. Because of this, it rarely reaches toxic levels in the body even with high intakes, as may sometimes occur with other fat-soluble vitamins.

Recommended Amounts  

AI: An “adequate intake” (AI) is used when there is not enough evidence to establish a Recommended Dietary Allowance (RDA). The AI amount is estimated to ensure nutritional adequacy. For adults 19 years and older, the AI for vitamin K is 120 micrograms (mcg) daily for men and 90 mcg for women and for those who are pregnant or lactating.

Vitamin K and Health

Vitamin K helps to make four of the 13 proteins needed for blood clotting, which stops wounds from continuously bleeding so they can heal. People who are prescribed anticoagulants (also called blood thinners) to prevent blood clots from forming in the heart, lung, or legs are often informed about vitamin K. Because of its blood clotting action, vitamin K has the potential to counteract the effects of blood thinning medications. A common method that estimates blood levels of vitamin K is measuring prothrombin time (PT), or how long it takes for blood to clot. People on anticoagulant medication such as warfarin (Coumadin) may be advised to eat a consistent amount of vitamin K from food and supplements. Although minor changes in vitamin K intake rarely affects PT, large and sudden variations in intake can alter PT levels and interfere with the medication’s effectiveness. Vitamin K is not a required listed nutrient on the Nutrition Facts label, but people taking anticoagulant medication are usually provided information about foods containing vitamin K from their health care provider.

Vitamin K is involved with the production of proteins in bone, including osteocalcin, which is needed to prevent the weakening of bones. Some studies have shown that higher vitamin K intakes are associated with a lower incidence of hip fractures and low bone density. In addition, low blood levels of vitamin K have been linked with low bone density. [2] A report from the Nurses’ Health Study suggests that women who get at least 110 mcg of vitamin K a day are 30% less likely to break a hip than women who get less than that. [3] Among the nurses, eating a serving of lettuce or other green, leafy vegetable a day cut the risk of hip fracture in half when compared with eating one serving a week. Data from the Framingham Heart Study also showed an association between high vitamin K intake and reduced risk of hip fracture in men and women and increased bone mineral density in women. [4, 5] However, the results of clinical trials and meta-analyses have been conflicting whether vitamin K supplements reduce bone fractures. [1] This may be due to a variety of other factors that affect bone health, including a lack of calcium, vitamin D , and weight-bearing exercise, all of which might mask a benefit of vitamin K supplementation.

A few studies have researched the role of vitamin K for heart health. Vitamin K is involved with the production of matrix Gla proteins (MGP), which help to prevent calcification or hardening of heart arteries, a contributor to heart disease . Because research in this area is very limited, additional studies are needed before a specific amount of vitamin K beyond the standard recommendation is proposed for this condition.

Food Sources

Signs of Deficiency

Vitamin K deficiency in adults is rare, but may occur in people taking medications that block vitamin K metabolism such as antibiotics, or in those with conditions that cause malabsorption of food and nutrients. A deficiency is also possible in newborn infants because vitamin K does not cross the placenta, and breast milk contains a low amount. The limited amount of blood clotting proteins at birth increases the risk of bleeding in infants if they are not given vitamin K supplements. The following are the most common signs of a deficiency.

Did You Know?

Vitamins and Minerals

Last reviewed March 2023

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What Are Implications in Research? | Examples & Tips

k study meaning

As a researcher, you know you need to provide a background for your study and a clear rationale and to formulate the statement of the problem in a way that leaves no doubt that your work is relevant and important. You also need to guide the reader carefully through your story from beginning to end without leaving any methodological questions unanswered. 

But many authors, when arriving at the end of their paper, run out of steam or lose the thread a bit and struggle with finding an ending for their work. Something can then appear missing, even if the discussion section summarizes the findings clearly, relates them back to the questions raised in the introduction section , and discusses them in the context of earlier works. A tired author who just made it to the end can often not see these missing elements and may finish off their paper with a conclusion section that is more or less a repetition of what has already been stated. After all, what more is there to be said? 

But as sure as the sun will rise again the day after you finally submitted, you will get your paper back from your supervisor or the reviewers with a comment that says, “implications are missing.” For a reader who is not as invested in every little detail of your design and analyses, the main questions that a paper has to answer are “why was this study necessary?” and “why are the findings of this study significant, and for whom, and what are we supposed to do with them now?” The latter are the implications of your work. 

Didn’t I explain the implications in my introduction section?

You will hopefully have already explained why and for whom your study is important. But you now also need to clearly state how you think your actual findings (which might differ from what you expected to find at the beginning) may be relevant and/or can be used in practical or theoretical ways, for future research, or by policymakers. These implications need to be based on your study’s parameters and results, and potential limitations of your methodology or sample should be taken into account to avoid overgeneralization. 

If you make the reader guess what the significance of your work might be or let them assume you don’t think that your work will be important for anyone except yourself and your colleagues who share your enthusiasm because they are working on the same topic, then an editor or reviewer might easily see that as a reason for a desk-reject. To avoid this, in the following, we will give you an overview of the different types of implications that research findings can have, provide some examples for your inspiration, and clarify where your implications should go in your paper. 

Table of Contents:

Recommendations Versus Implications 

Types of Implications in Research 

Depending on the type of research you are doing (clinical, philosophical, political…) the implications of your findings can likewise be clinical, philosophical, political, social, ethical—you name it. The most important distinction, however, is the one between practical implications and theoretical implications, and what many reviewers immediately notice and flag as an issue is when there is no mention of any kind of practical contribution of the work described in a paper. 

Of course, if you study a mathematical theory, then your findings might simply lead to the debunking of another theory as false, and you might need to do some mental gymnastics if you really wanted to apply that to a real-world problem. But chances are, in that case, your reviewers and readers won’t ask for a real-world implication. In most other cases, however, if you really want to convince your audience that your work deserves attention, publication, prizes, and whatnot, then you need to link whatever you did in the lab or found in the library to real life and highlight how your findings might have a lasting effect on your field (for example, methodologically), common practices (e.g., patient treatment or teaching standards), society at large (maybe the way we communicate), or ethical standards (e.g., in animal research). 

The question is not whether your findings will change the world, but whether they could if they were publicized and implemented—according to the Merriam-Webster online dictionary , the essential meaning of implication is a “possible future effect or result”. This possible result is what you have to identify and describe. And while being creative is certainly allowed, make sure your assumptions stay within realistic expectations, and don’t forget to take the limitations of your methodology or your sample into account. 

If you studied the genetic basis of a disease in some animal model, then make sure you have good reason to draw conclusions about the treatment of the same disease in humans if you don’t want to put off the editor who decides whether to even send your manuscript out for review. Likewise, if you explored the effects of the Covid-19 pandemic on higher education institutions in your country, then make sure the conclusions you draw hold in the context of other countries’ pandemic situations and restrictions and differences across education systems before you claim that they are relevant in a global context. 

Implications, as we already explored, state the importance of your study and how your findings may be relevant for the fine-tuning of certain practices, theoretical models, policymaking, or future research studies. As stated earlier, that does not necessarily mean that you believe your findings will change the world tomorrow, but that you have reason to believe they could have an impact in a specific way. Recommendations, on the other hand, are specific suggestions regarding the best course of action in a certain situation based on your findings. If, for example, you used three different established methods in your field to tackle the same problem, compared the outcomes, and concluded that one of these methods is, in fact, insufficient and should not be used anymore, then that is a recommendation for future research. 

Or if you analyzed how a monetary “Corona support program” in your country affected the local economy and found that most of the money the government provided went to Amazon and not to local businesses, then you can recommend that your government come up with a better plan next time. Such specific recommendations should usually follow the implications, not the other way around, because you always need to identify the implications of your work, but not every study allows the author to make practical suggestions or real-world recommendations.

Research Implications Examples

Clinical implications  .

Let’s say you discovered a new antibiotic that could eliminate a specific pathogen effectively without generating resistance (the main problem with antibiotics). The clinical implications of your findings would then be that infections with this pathogen could be more rapidly treated than before (without you predicting or suggesting any specific action to happen as a result of your findings). A recommendation would be that doctors should start using this new antibiotic, that it should be included in the official treatment guidelines, that it should be covered by the national health insurance of your country, etc.—but depending on how conclusive your findings are or how much more research or development might be needed to get from your findings to the actual medication, such recommendations might be a big stretch. The implications, however, since they state the potential of your findings, are valid in any case and should not be missing from your discussion section, even if your findings are just one small step along the way.

Social implications 

The social implications of the study are defined as the ability or potential of research to impact society in visible ways. One of the obvious fields of research that strives for a social impact through the implementation of evidence that increases the overall quality of people’s lives is psychology. Whether your research explores the new work-life-balance movement and its effect on mental well-being, psychological interventions at schools to compensate for the stress many children are experiencing since the beginning of the Covid-19 pandemic, or how work from home is changing family dynamics, you can most likely draw conclusions that go beyond just your study sample and describe potential (theoretical or practical) effects of your findings in the real world. Be careful, however, that you don’t overgeneralize from your sample or your data to the general population without having solid reasons to do so (and explain those reasons).

Implications for future research

Even if your findings are not going to lead to societal changes, new educational policies, or an overhaul of the national pension system, they might have important implications for future research studies. Maybe you used a new technique that is more precise or more efficient or way cheaper than existing methods and this could enable more labs around the world to study a specific problem. Or maybe you found that a gene that is known to be involved in one disease might also be involved in another disease, which opens up new avenues for research and treatment options. As stated earlier, make sure you don’t confuse recommendations (which you might not be able to make, based on your findings, and don’t necessarily have to) with implications, which are the potential effect that your findings could have—independently of whether you have any influence on that. 

Where Do the Implications Go in Your Paper? 

The implications are part of your discussion section, where you summarize your findings and then put them into context—this context being earlier research but also the potential effect your findings could have in the real world, in whatever scenario you think might be relevant. There is no “implication section” and no rule as to where in the discussion section you need to include these details because the order of information depends on how you structured your methods and your results section and how your findings turned out to prove or disprove your hypotheses. You simply need to work the potential effects of your findings into your discussion section in a logical way.

But the order of information is relevant when it comes to your conclusion at the very end of your discussion section: Here, you start with a very short summary of your study and results, then provide the (theoretical, practical, ethical, social, technological…) implications of your work, and end with a specific recommendation if (and only if) your findings call for that. If you have not paid attention to the importance of your implications while writing your discussion section, then this is your chance to fix that before you finalize and submit your paper and let an editor and reviewers judge the relevance of your work. 

Make sure you do not suddenly come up with practical ideas that look like they were plucked out of the air because someone reminded you to “add some implications” at the last minute. If you don’t know where to start, then go back to your introduction section, look at your rationale and research questions, look at how your findings answered those questions, and ask yourself who else could benefit from knowing what you know now.

Consider Using English Editing Services 

And before you submit your manuscript to your target journal’s editor, be sure to get professional English editing services from Wordvice, including academic editing and manuscript editing , which are tailored to the needs of your paper’s subject area. If you need instant proofreading while drafting your work, check out our online ai editor , Wordvice AI, which is trained on millions of words of academic writing data and tailored for research writers.

For more advice on how to write all the different parts of your research paper , on how to make a research paper outline if you are struggling with putting everything you did together, or on how to write the best cover letter that will convince an editor to send your manuscript out for review, head over to the Wordvice academic resources pages, where we have dozens of helpful articles and videos on research writing and publications.

What Is Motivation?

The Driving Force Behind Human Actions

Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.

k study meaning

Verywell / Emily Roberts 

The term "motivation" describes why a person does something. It is the driving force behind human actions. Motivation is the process that initiates, guides, and maintains goal-oriented behaviors.

For instance, motivation is what helps you lose extra weight, or pushes you to get that promotion at work. In short, motivation causes you to act in a way that gets you closer to your goals. Motivation includes the biological , emotional , social , and cognitive forces that activate human behavior.

Click Play to Learn More About Motivation

This video has been medically reviewed by John C. Umhau, MD, MPH, CPE .

Motivation also involves factors that direct and maintain goal-directed actions. Although, such motives are rarely directly observable. As a result, we must often infer the reasons why people do the things that they do based on observable behaviors.

Learn the types of motivation that exist and how we use them in our everyday lives. And if it feels like you've lost your motivation, do not worry. We also share a few ways to develop or improve your self-motivation levels.

Press Play for Advice on Motivation

Hosted by Editor-in-Chief and therapist Amy Morin, LCSW, this episode of The Verywell Mind Podcast shares an exercise you can use to help you perform your best. Click below to listen now.

Follow Now : Apple Podcasts / Spotify / Google Podcasts

Types of Motivation

The two main types of motivation are frequently described as being either extrinsic or intrinsic.

A Third Type of Motivation?

Some research suggests that there is a third type of motivation: family motivation. An example of this type is going to work when you are not motivated to do so internally (no intrinsic motivation), but because it is a means to support your family financially.

Is It Extrinsic or Intrinsic Motivation?

Why motivation is important.

Motivation serves as a guiding force for all human behavior. So, understanding how motivation works and the factors that may impact it can be important for several reasons.

Understanding motivation can:

Mental Health in the Workplace Webinar

On May 19, 2022, Verywell Mind hosted a virtual Mental Health in the Workplace webinar, hosted by Editor-in-Chief Amy Morin, LCSW. If you missed it, check out  this recap  to learn ways to foster supportive work environments and helpful strategies to improve your well-being on the job.

Components of Motivation

If you've ever had a goal (like wanting to lose 20 pounds or run a marathon), you probably already know that simply having the desire to accomplish these things is not enough. You must also be able to persist through obstacles and have the endurance to keep going in spite of difficulties faced.

These different elements or components are needed to get and stay motivated. Researchers have identified three major components of motivation: activation, persistence, and intensity.

The degree of each of these components of motivation can impact whether you achieve your goal. Strong activation, for example, means that you are more likely to start pursuing a goal. Persistence and intensity will determine if you keep working toward that goal and how much effort you devote to reaching it.

Tips for Improving Your Motivation

All people experience fluctuations in their motivation and willpower . Sometimes you feel fired up and highly driven to reach your goals. Other times, you might feel listless or unsure of what you want or how to achieve it.

If you're feeling low on motivation, there are steps you can take to help increase your drive. Some things you can do to develop or improve your motivation include:

Causes of Low Motivation

There are a few things you should watch for that might hurt or inhibit your motivation levels. These include:

Motivation and Mental Health

Sometimes a persistent lack of motivation is tied to a mental health condition such as depression . Talk to your doctor if you are feeling symptoms of apathy and low mood that last longer than two weeks.

Theories of Motivation

Throughout history, psychologists have proposed different theories to explain what motivates human behavior. The following are some of the major theories of motivation.

The instinct theory of motivation suggests that behaviors are motivated by instincts, which are fixed and inborn patterns of behavior. Psychologists such as William James, Sigmund Freud , and William McDougal have proposed several basic human drives that motivate behavior. They include biological instincts that are important for an organism's survival—such as fear, cleanliness, and love.

Drives and Needs

Many behaviors such as eating, drinking, and sleeping are motivated by biology. We have a biological need for food, water, and sleep. Therefore, we are motivated to eat, drink, and sleep. The drive reduction theory of motivation suggests that people have these basic biological drives, and our behaviors are motivated by the need to fulfill these drives.

Abraham Maslow's hierarchy of needs is another motivation theory based on a desire to fulfill basic physiological needs. Once those needs are met, it expands to our other needs, such as those related to safety and security, social needs, self-esteem, and self-actualization.

Arousal Levels

The arousal theory of motivation suggests that people are motivated to engage in behaviors that help them maintain their optimal level of arousal. A person with low arousal needs might pursue relaxing activities such as reading a book, while those with high arousal needs might be motivated to engage in exciting, thrill-seeking behaviors such as motorcycle racing.

The Bottom Line

Psychologists have proposed many different theories of motivation . The reality is that there are numerous different forces that guide and direct our motivations.

A Word From Verywell

Understanding motivation is important in many areas of life beyond psychology, from parenting to the workplace. You may want to set the best goals and establish the right reward systems to motivate others as well as to  increase your own motivation .

Knowledge of motivating factors (and how to manipulate them) is used in marketing and other aspects of industrial psychology. It's an area where there are many myths, and everyone can benefit from knowing what works with motivation and what doesn't.

Nevid JS.  Psychology: Concepts and Applications .

Tranquillo J, Stecker M.  Using intrinsic and extrinsic motivation in continuing professional education .  Surg Neurol Int.  2016;7(Suppl 7):S197-9. doi:10.4103/2152-7806.179231

Menges JI, Tussing DV, Wihler A, Grant AM. When job performance is all relative: How family motivation energizes effort and compensates for intrinsic motivation . Acad Managem J . 2016;60(2):695-719. doi:10.5465/amj.2014.0898

Hockenbury DH, Hockenbury SE. Discovering Psychology .

Zhou Y, Siu AF. Motivational intensity modulates the effects of positive emotions on set shifting after controlling physiological arousal . Scand J Psychol . 2015;56(6):613-21. doi:10.1111/sjop.12247

Mystkowska-Wiertelak A, Pawlak M. Designing a tool for measuring the interrelationships between L2 WTC, confidence, beliefs, motivation, and context . Classroom-Oriented Research . 2016. doi:10.1007/978-3-319-30373-4_2

Myers DG.  Exploring Social Psychology .

Siegling AB, Petrides KV. Drive: Theory and construct validation .  PLoS One . 2016;11(7):e0157295. doi:10.1371/journal.pone.0157295

By Kendra Cherry Kendra Cherry, MS, is an author and educational consultant focused on helping students learn about psychology.

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Origin of study, synonym study for study, other words from study, words nearby study, words related to study, how to use study in a sentence.

Those studies are scheduled for completion over about the next year and a half.

The study tallied activity in more than a dozen different cryptocurrencies.

More recently, studies have reported on what the infection might do to the heart.

That’s according to a new study published in Science Advances.

The study , published Friday in the journal Environmental Research Letters, found this association in both rural counties in Louisiana and highly populated communities in New York.

She completed a yoga teacher-training program and, in the spring of 2008, went on a retreat in Peru to study with shamans.

In fact, in a recent study of their users internationally, it was the lowest priority for most.

But in the case of black women, another study found no lack of interest.

Indeed, study after study affirms the benefits of involved fatherhood for women and children.

A recent U.S. study found men get a “daddy bonus” —employers seem to like men who have children and their salaries show it.

"There's just one thing I'd like to ask, if you don't mind," said Cynthia, coming suddenly out of a brown study .

His lordship retired shortly to his study , Hetton and Mr. Haggard betook themselves to the billiard-room.

She began the study of drawing at the age of thirty, and her first attempt in oils was made seven years later.

In practice we find a good deal of technical study comes into the college stage.

Its backbone should be the study of biology and its substance should be the threshing out of the burning questions of our day.

British Dictionary definitions for study

Word Origin for study

Other idioms and phrases with study.

see brown study.

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How do I determine k when using k-means clustering?

I've been studying about k-means clustering , and one thing that's not clear is how you choose the value of k. Is it just a matter of trial and error, or is there more to it?

Has QUIT--Anony-Mousse's user avatar

20 Answers 20

You can maximize the Bayesian Information Criterion (BIC):

where L(X | C) is the log-likelihood of the dataset X according to model C , p is the number of parameters in the model C , and n is the number of points in the dataset. See "X-means: extending K -means with efficient estimation of the number of clusters" by Dan Pelleg and Andrew Moore in ICML 2000.

Another approach is to start with a large value for k and keep removing centroids (reducing k) until it no longer reduces the description length. See "MDL principle for robust vector quantisation" by Horst Bischof, Ales Leonardis, and Alexander Selb in Pattern Analysis and Applications vol. 2, p. 59-72, 1999.

Finally, you can start with one cluster, then keep splitting clusters until the points assigned to each cluster have a Gaussian distribution. In "Learning the k in k -means" (NIPS 2003), Greg Hamerly and Charles Elkan show some evidence that this works better than BIC, and that BIC does not penalize the model's complexity strongly enough.

Etienne Bruines's user avatar

Basically, you want to find a balance between two variables: the number of clusters ( k ) and the average variance of the clusters. You want to minimize the former while also minimizing the latter. Of course, as the number of clusters increases, the average variance decreases (up to the trivial case of k = n and variance=0).

As always in data analysis, there is no one true approach that works better than all others in all cases. In the end, you have to use your own best judgement. For that, it helps to plot the number of clusters against the average variance (which assumes that you have already run the algorithm for several values of k ). Then you can use the number of clusters at the knee of the curve.

Jan Krüger's user avatar

Yes, you can find the best number of clusters using Elbow method, but I found it troublesome to find the value of clusters from elbow graph using script. You can observe the elbow graph and find the elbow point yourself, but it was lot of work finding it from script.

So another option is to use Silhouette Method to find it. The result from Silhouette completely comply with result from Elbow method in R.

Here`s what I did.

Hope it helps!!

Udeep Shakya's user avatar

May be someone beginner like me looking for code example. information for silhouette_score is available here.

bhargav patel's user avatar

Look at this paper, "Learning the k in k-means" by Greg Hamerly, Charles Elkan. It uses a Gaussian test to determine the right number of clusters. Also, the authors claim that this method is better than BIC which is mentioned in the accepted answer.

NeoJi's user avatar

There is something called Rule of Thumb. It says that the number of clusters can be calculated by

k = (n/2)^0.5

where n is the total number of elements from your sample. You can check the veracity of this information on the following paper:

There is also another method called G-means, where your distribution follows a Gaussian Distribution or Normal Distribution. It consists of increasing k until all your k groups follow a Gaussian Distribution. It requires a lot of statistics but can be done. Here is the source:

I hope this helps!

Sreeragh A R's user avatar

If you don't know the numbers of the clusters k to provide as parameter to k-means so there are four ways to find it automaticaly:

G-means algortithm: it discovers the number of clusters automatically using a statistical test to decide whether to split a k-means center into two. This algorithm takes a hierarchical approach to detect the number of clusters, based on a statistical test for the hypothesis that a subset of data follows a Gaussian distribution (continuous function which approximates the exact binomial distribution of events), and if not it splits the cluster. It starts with a small number of centers, say one cluster only (k=1), then the algorithm splits it into two centers (k=2) and splits each of these two centers again (k=4), having four centers in total. If G-means does not accept these four centers then the answer is the previous step: two centers in this case (k=2). This is the number of clusters your dataset will be divided into. G-means is very useful when you do not have an estimation of the number of clusters you will get after grouping your instances. Notice that an inconvenient choice for the "k" parameter might give you wrong results. The parallel version of g-means is called p-means . G-means sources: source 1 source 2 source 3

x-means : a new algorithm that efficiently, searches the space of cluster locations and number of clusters to optimize the Bayesian Information Criterion (BIC) or the Akaike Information Criterion (AIC) measure. This version of k-means finds the number k and also accelerates k-means.

Online k-means or Streaming k-means: it permits to execute k-means by scanning the whole data once and it finds automaticaly the optimal number of k. Spark implements it.

MeanShift algorithm : it is a nonparametric clustering technique which does not require prior knowledge of the number of clusters, and does not constrain the shape of the clusters. Mean shift clustering aims to discover “blobs” in a smooth density of samples. It is a centroid-based algorithm, which works by updating candidates for centroids to be the mean of the points within a given region. These candidates are then filtered in a post-processing stage to eliminate near-duplicates to form the final set of centroids. Sources: source1 , source2 , source3

First build a minimum spanning tree of your data. Removing the K-1 most expensive edges splits the tree into K clusters, so you can build the MST once, look at cluster spacings / metrics for various K, and take the knee of the curve.

This works only for Single-linkage_clustering , but for that it's fast and easy. Plus, MSTs make good visuals. See for example the MST plot under stats.stackexchange visualization software for clustering .

Community's user avatar

I'm surprised nobody has mentioned this excellent article:

After following several other suggestions I finally came across this article while reading this blog:

After that I implemented it in Scala, an implementation which for my use cases provide really good results. Here's code:

eirirlar's user avatar

If you use MATLAB, any version since 2013b that is, you can make use of the function evalclusters to find out what should the optimal k be for a given dataset.

This function lets you choose from among 3 clustering algorithms - kmeans , linkage and gmdistribution .

It also lets you choose from among 4 clustering evaluation criteria - CalinskiHarabasz , DaviesBouldin , gap and silhouette .

Kristada673's user avatar

I used the solution I found here : and it worked very well for me :

enter image description here

My idea is to use Silhouette Coefficient to find the optimal cluster number(K). Details explanation is here .

Quazi Marufur Rahman's user avatar

Assuming you have a matrix of data called DATA , you can perform partitioning around medoids with estimation of number of clusters (by silhouette analysis) like this:

Megatron's user avatar

One possible answer is to use Meta Heuristic Algorithm like Genetic Algorithm to find k. That's simple. you can use random K(in some range) and evaluate the fit function of Genetic Algorithm with some measurment like Silhouette And Find best K base on fit function.

Masoud's user avatar

Another approach is using Self Organizing Maps (SOP) to find optimal number of clusters. The SOM (Self-Organizing Map) is an unsupervised neural network methodology, which needs only the input is used to clustering for problem solving. This approach used in a paper about customer segmentation.

The reference of the paper is

Abdellah Amine et al., Customer Segmentation Model in E-commerce Using Clustering Techniques and LRFM Model: The Case of Online Stores in Morocco, World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:9, No:8, 2015, 1999 - 2010

boyaronur's user avatar

Hi I'll make it simple and straight to explain, I like to determine clusters using 'NbClust' library.

Now, how to use the 'NbClust' function to determine the right number of clusters: You can check the actual project in Github with actual data and clusters - Extention to this 'kmeans' algorithm also performed using the right number of 'centers'.

Github Project Link:

Rutvij's user avatar

You can choose the number of clusters by visually inspecting your data points, but you will soon realize that there is a lot of ambiguity in this process for all except the simplest data sets. This is not always bad, because you are doing unsupervised learning and there's some inherent subjectivity in the labeling process. Here, having previous experience with that particular problem or something similar will help you choose the right value.

If you want some hint about the number of clusters that you should use, you can apply the Elbow method:

First of all, compute the sum of squared error (SSE) for some values of k (for example 2, 4, 6, 8, etc.). The SSE is defined as the sum of the squared distance between each member of the cluster and its centroid. Mathematically:


If you plot k against the SSE, you will see that the error decreases as k gets larger; this is because when the number of clusters increases, they should be smaller, so distortion is also smaller. The idea of the elbow method is to choose the k at which the SSE decreases abruptly. This produces an "elbow effect" in the graph, as you can see in the following picture:

enter image description here

In this case, k=6 is the value that the Elbow method has selected. Take into account that the Elbow method is an heuristic and, as such, it may or may not work well in your particular case. Sometimes, there are more than one elbow, or no elbow at all. In those situations you usually end up calculating the best k by evaluating how well k-means performs in the context of the particular clustering problem you are trying to solve.

Faisal Shahbaz's user avatar

I worked on a Python package kneed (Kneedle algorithm). It finds cluster numbers dynamically as the point where the curve starts to flatten. Given a set of x and y values, kneed will return the knee point of the function. The knee joint is the point of maximum curvature. Here is the sample code.

Mario's user avatar

The K-Means algorithm:

Btw, its not a explanation of full algorithm, its just helpful vizualization

Pobaranchuk's user avatar

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  1. K- Letter Basic Study No.1

    k study meaning

  2. A k-means Example. Even a computation as simple as k-means produces...

    k study meaning

  3. What does the writing process look like in K-2?

    k study meaning

  4. K-Study Korea

    k study meaning

  5. S K STUDY

    k study meaning

  6. K is for K-theory

    k study meaning


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  1. K Study Meaning

    K Study Meaning: The first 5 years and the third and final months of the study period, which should include 8 weeks each, have been completed: For the first period, the study was going on at 30% and 15% chance of failing; for the last phase, the study was going on at 30% chance; All three phases are going on now. The power test is an important one.

  2. Study Definition & Meaning

    : to undertake formal study of a subject 2 dialect : meditate, reflect 3 : endeavor, try transitive verb 1 : to read in detail especially with the intention of learning 2 : to engage in the study of study biology 3 : plot, design 4 : to consider attentively or in detail studying his face for a reaction studier ˈstə-dē-ər noun Synonyms Noun delving

  3. What is K-12 Curriculum?

    In the field of education, K-12 refers to grades kindergarten through twelve where attendance is compulsory. Curriculum can have multiple meanings, though the term generally describes, in some...

  4. Case Study: Definition, Examples, Types, and How to Write

    A case study is an in-depth study of one person, group, or event. In a case study, nearly every aspect of the subject's life and history is analyzed to seek patterns and causes of behavior. Case studies can be used in various fields, including psychology, medicine, education, anthropology, political science, and social work.

  5. Study Definition & Meaning

    STUDY meaning: 1 : the activity or process of learning about something by reading, memorizing facts, attending school, etc.; 2 : an area of learning taught in a school subject usually plural. ... The evening was a study in contrasts. [=some parts of the evening were very different from other parts]

  6. Stochastics: An Accurate Buy and Sell Indicator

    Stochastics are a favored technical indicator because they are easy to understand and have a relatively high degree of accuracy. It falls into the class of technical indicators known as ...

  7. K, k

    K, k definition: 1. the eleventh letter of the English alphabet 2. abbreviation for kilobyte specialized: 3…. Learn more.

  8. Interpreting Thromboelastography (TEG)

    Interpreting Thromboelastography (TEG) By Rishi. March 11, 2014. Thromboelastography (TEG) is a simple way of assessing many parts of the coagulation cascade from primary and secondary hemostasis to fibrinolysis. Thrombus formation typically requires four components: platelets which form the initial hemostatic plug, clotting factors that ...

  9. The Difference Between Texting kk, ok, okay, and k

    A single K is cold, it cuts quick but deep. And if you get a k period (k.), don't go home for at least 48 hours. The origins of the dreadful "k" can't exactly be pinpointed, though it's been a thing since iMessage looked like this, so basically the Stone Age.

  10. [PDF] Review : Study on Simple k Mean and Modified K Mean Clustering

    The main aim of this review paper is to provide comprehensive review of simple k mean clustering and modified k mean clustering techniques. Clustering is used as active research in various fields like statistics, pattern recognition and machine learning etc. Cluster Analysis is data mining tool for a large and multivariate database. Clustering ...

  11. 10 Interesting Use Cases for the K-Means Algorithm

    clustering is the task of dividing the population or data points into a number of groups such that data points in the same groups are more similar to other data points in the same group than those ...

  12. STUDY

    study verb uk / ˈstʌdi / us [ I or T ] to learn about a subject, especially at a school or university or by reading books: study for sth He's studying for a master's degree at Yale University. She studied economics and politics. What do you plan to do when you finish studying? [ T ] to examine something very carefully:

  13. K definition and meaning

    K definition: K is the eleventh letter of the English alphabet. | Meaning, pronunciation, translations and examples

  14. Word Study Instruction in the K-2 Classroom

    Word study is an approach to spelling instruction that moves away from a focus on memorization. The approach reflects what researchers have discovered about the alphabetic, pattern, and meaning layers of English orthography. This article describes nine tips for implementing a word study program in your classroom.

  15. K means Clustering

    'K' in the name of the algorithm represents the number of groups/clusters we want to classify our items into. Overview (It will help if you think of items as points in an n-dimensional space). The algorithm will categorize the items into k groups or clusters of similarity.

  16. Vitamin K

    Vitamin K is a fat-soluble vitamin that comes in two forms. The main type is called phylloquinone, found in green leafy vegetables like collard greens, kale, and spinach. The other type, menaquinones, are found in some animal foods and fermented foods. Menaquinones can also be produced by bacteria in the human body. [1]

  17. K Definition & Meaning

    K definition, a vector on the z-axis, having length 1 unit. See more.

  18. What are Implications in a Research Study?

    Kevin. The implications of a study explain what the findings of study mean to researchers or to certain subgroups or populations beyond the basic data and interpretation of results. As a researcher, you know you need to provide a background for your study and a clear rationale and to formulate the statement of the problem in a way that leaves ...

  19. Motivation: Theories, Examples, Types, and How to Find It

    Researchers have identified three major components of motivation: activation, persistence, and intensity. 4. Activation is the decision to initiate a behavior. An example of activation would be enrolling in psychology courses in order to earn your degree. Persistence is the continued effort toward a goal even though obstacles may exist.

  20. Study Definition & Meaning

    Study definition, application of the mind to the acquisition of knowledge, as by reading, investigation, or reflection: long hours of study. See more.

  21. K

    Define K. K synonyms, K pronunciation, K translation, English dictionary definition of K. n. Slang One thousand dollars. The symbol for potassium. abbr. 1. kelvin 2. kicker 3. kilobyte 4. kilometer 5. kindergarten 6. Games king 7. Bible Kings 8.... K - definition of K by The Free Dictionary.

  22. How do I determine k when using k-means clustering?

    Online k-means or Streaming k-means: it permits to execute k-means by scanning the whole data once and it finds automaticaly the optimal number of k. Spark implements it. MeanShift algorithm : it is a nonparametric clustering technique which does not require prior knowledge of the number of clusters, and does not constrain the shape of the ...

  23. The Meaning of Meaning

    The Meaning of Meaning: A Study of the Influence of Language upon Thought and of the Science of Symbolism (1923) is a book by C. K. Ogden and I. A. Richards.It is accompanied by two supplementary essays by Bronisław Malinowski and F. G. Crookshank.The conception of the book arose during a two-hour conversation between Ogden and Richards held on a staircase in a house next to the Cavendish ...