Q 536. Minitab has the ability to report 2 different Kappa values for Attribute Agreement Analysis - Cohen's Kappa and Fleiss Kappa. What is the difference between the two? Using an example highlight the situation where a researcher will look at Cohen's Kappa instead of Fleiss Kappa.

 

Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday. 

• All questions so far can be seen here - https://www.benchmarksixsigma.com/forum/lean-six-sigma-business-excellence-questions/
• Please visit the forum home page at https://www.benchmarksixsigma.com/forum/ to respond to the latest question open till the next Tuesday/ Friday evening 5 PM as per Indian Standard Time. Questions launched on Tuesdays are open till Friday and questions launched on Friday are open till Tuesday.
• When you respond to this question, your answer will not be visible till it is reviewed. Only non-plagiarised (plagiarism below 5-10%) responses will be approved. If you have doubts about plagiarism, please check your answer with a plagiarism checker tool like https://smallseotools.com/plagiarism-checker/ before submitting. 
• The best answer is always shown at the top among responses and the author finds honorable mention in our Business Excellence dictionary at https://www.benchmarksixsigma.com/forum/business-excellence-dictionary-glossary/ along with the related term

Below are the differences between Cohen's Kappa and Fleiss Kappa: -

·         Fleiss Kappa works for any number of raters whereas Cohen's Kappa only works for two raters

·         One of the important requirement of Fleiss Kappa is that each rater needs to rate different items, while Cohen's Kappa both raters need to rate identical items.

·         Fleiss Kappa can lead to paradoxical results namely that, even with nominal categories, reordering the categories can change the results. But Cohen's version lead to odd results when there are large differences in the occurrence of possible outcomes

 

Example 1: - Let’s us take a response variable (categorical scale) with three values: yes, maybe, no and there are two raters. Both the raters are used to judge all observations.

For Cohen’s Kappa there should be 2 raters and the same 2 raters judge all observations. So we in this scenario Cohens' kappa is suitable

Example 2: - In the same example above let say there were three raters and different raters judge all observations.

In Fleiss' kappa case, there should be 3 raters or more and the raters should be non-unique which is the above case so in this scenario Fleiss Kappa is suitable.

Kappa, one of many coefficients used to evaluate inter-rater and similar types of reliability, was developed in 1960 by Jacob Cohen. Kappa is denoted k, an index used to measure the level of consistency between two raters.

 

Kappa value used for?

 

The kappa is frequently used to test inter-rater reliability. The significance of rater reliability lies in the fact that it characterizes the extent to which the data collected in the study are correct representations of the variables measured.

 

What is a good kappa coefficient?

 

Usually, a kappa of less than 0.4 is reflected as poor (a Kappa of 0 means there is no difference between the observers and chance alone). Kappa values of 0.4 to 0.75 are measured as moderate to good and a kappa of > 0.75 shows excellent agreement.

 

What is Fleiss Kappa?

 

Fleiss' kappa named after Joseph L. Fleiss is a way of measuring, for assessing the reliability of agreement between a fixed numbers of raters. This helps us to test to measure the inter-rater agreement between two or more raters.

 

What is Cohen’s Kappa?

 

Cohen’s kappa measures the agreement between two raters whom each classifies mutually exclusive categories. The best way to think about this is that Cohen’s Kappa is a quantitative measure of reliability for two raters that are rating the same thing, corrected for how often the raters may agree by chance. Cohen's kappa is a metric regularly used to assess the agreement between two raters. Cohen’s can also be used to measure the performance of a classification model.

 

But before that, we need to understand the characteristics between reliability and validity

 

Validity and Reliability - Validity means we are concerned with the degree to which a test measures what it claims to measure or in other words, how accurate the test is. On the other side, reliability is disturbed more by the degree to which a test produces similar results under consistent conditions or to put it another way, the precision of a test.

 

Check this dartboard example of reliability and validity.

 

 

For the results of a useful experiment, good reliability is important. But, reliability can be broken down into different types, Intra-rater reliability and Inter-rater reliability.

 

·         Intra-rater reliability is associated with the degree of agreement between different measurements done by the same person.

·         Inter-rater reliability is connected to the degree of agreement between two or more raters.

 

Evaluating Cohen’s Kappa The value for kappa can be < 0 (negative). A score of 0 means that there is random agreement among raters, while a score of 1 means that there is the complete agreement between the raters. It’s essential that we acquaint ourselves with figure 2 to have a strong understanding.

 

Figure 2: N x N grid used to interpret results of raters, Now let's break down each grid to our understanding

 

A => The number of instances that both raters said were correct, and are in agreement.

B => The total number of cases that Rater 2 said was incorrect, but Rater 1 said were correct. This case is a disagreement.

C => The total number of occurrences that Rater 1 said was incorrect, but Rater 2 said were correct. This is also a disagreement.

D => The total number of occasions that both Raters said were incorrect. And are in agreement.

In order to work out the kappa value, we first need to know the probability of agreement (this explains why highlighted the agreement diagonal). This formula is derived by adding the number of tests to which the raters agree and then dividing it by the total number of tests.

 

The formula for Cohen’s Kappa is the probability of agreement taken away from the probability of random agreement divided by 1 minus the probability of random agreement.

 

 

Things to keep in mind when using Cohen’s

 

1.             Cohen’s kappa is more useful than overall accuracy when working with unbalanced data.

2.             The same simulation will give you lower values of Cohen’s kappa for unbalanced than for balanced test data.

 

Lastly, When to Use Cohen’s over Fleiss?

 

Fleiss' k works for any number of raters, however, Cohen's k only works for two raters; in addition, Fleiss' k permits each rater to be rating different items, while Cohen's k will only admit that both raters are rating identical items. However, Fleiss' k can lead to inconsistent results that, even with nominal categories, reordering the categories can change the results. But Cohen's version has its own problems and can lead to odd results when there are large differences in the occurrence of possible outcomes.

Cohen's Kappa and Fleiss Kappa are two different measures of agreement between two or more raters. Cohen's Kappa is used when there are two raters, while Fleiss Kappa is used when there are three or more raters.

Cohen's Kappa is a measure of agreement between two raters that takes into account the possibility of agreement occurring by chance. It is calculated by subtracting the expected proportion of agreement from the observed proportion of agreement and dividing the result by one minus the expected proportion of agreement.

Fleiss Kappa is a measure of agreement on multi-rater items. It is calculated by subtracting the average observed chance agreement from the observed agreement among the raters, and dividing the result by one minus the average observed chance agreement.

Fleiss Kappa takes into account the number of raters involved and the number of levels or categories present. Both Cohen's Kappa and Fleiss Kappa are used to measure and quantify the amount of agreement between two or more ratings or observations of the same group of persons or things. They are both used to assess the reliability and accuracy of ratings given by different persons. While both measures provide a numeric score that indicates the level of agreement between raters, Fleiss Kappa tends to be more accurate when there are more than two raters and more than two categories.

Cohen's kappa is used for two raters considering same items will be rated by both raters while  Fleiss Kappa used for multiple raters with a possibility of rating different items 

example: when in a study no of raters will be two and all the raters will rate for all the data points or observations like taste score (good , bad , neutral) then we can use Cohen's kappa

 

 

 

Fleiss' Kappa	Cohen's Kappa
This is a way to measure agreement between 3 or more raters. Used for nominal data (e.g. likert scale). Therefore this measures agreement between 3 or more dependent categorical samples	Similar to Fleiss’s Kappa This is a way to measure inter rater reliability but for below scenarios: -          2 raters rate same trial once each or -          1 rater rates 2 trials (measures agreement of new method with old or over time),
Can be used for any number of raters	Can be used for only 2 raters
Allows for scenario where each rater is rating different items also	Only works for scenario where raters are rating identical items
Assumption includes that raters are chosen independently from larger set	Assumption includes that raters are chosen deliberately and are fixed
Scenarios for use: 5 raters randomly picked from a pool asked to give pass/fail by picking samples randomly from pool (e.g. destructive tests)	Scenarios for use: 2 raters asked to give pass/fail for 20 interview candidates Have 2 machines for measuring pass/fail of an item’s attribute
Condition of random sampling among raters means this is not suitable if all raters are reqd to rate all samples	Conversely not suitable if all samples cant be rated because of cost of test or if its destructive in nature

Cohen Kappa Is an inter observer correlation measurement for a single factor with more than one observer evaluation. It is used to provide the user with calculable benchmark of the degree of agreements vis-à-vis all observers. As such, it is used to know how recurrent there is agreement in the observer’s interpretation. In a normal scenario where a yes/no answer is involved, the outcome is weak as it does account for chance. This is why Kappa which take into consideration the removal of chance to be much more preferable as a measurable statistical tool.

 

Results of Kappa can range from -1 to 1. A Kappa 0 indicates that the agreed results are equal while expecting a chance. When Kappa value is 1, the agreed results are perfect. When Kappa is less than zero, the agreed result are less weighted with respect to chance. A good Kappa result can range  from 0.75 to 0.90.

 

Fleiss Kappa is a mathematically derived statistic to know how reliable is an agreement in relation to constant number of observers. It is relevant when observers label a rating when the items are classified or to the amount of ratings. Fleiss Kappa is a Fleiss Kappa for greater than 2 people who rates the agreements. However compared to Cohen Kappa, Fleiss Kappa are random people who are selected for rating an agreement while in Cohen Kappa, those who rate are known and fixed.

 

A researcher will obviously look for Cohen Kappa when the values classified are of nominal order that is there is the results as no, bad, false, true, good, yes, crispy or nor crispy etc. however for ordinal values, a researcher will take Kendall coefficient into account.

Fleiss’s Kappa and Cohen’s kappa both are used for checking agreements within and between appraisers. While Kappa value can be calculated for any number of appraiser and trial numbers, Cohen's kappa can only be calculated under some specific conditions (e.g. only 2 raters). Also the assumption with Cohen’s kappa is that the appraisers are deliberately chosen and fixed, while with Fleiss’ kappa, the appraisers are chosen at random from a larger pool.

 

The best answer has been provided by Anupam Goswami.