# Kendall's coefficients for Attribute Agreement Analysis

Find definitions and interpretation guidance for Kendall's coefficients.

## Coef

Use Kendall's coefficient of concordance (Coef) to assess the association between appraisers when ratings are ordinal and you have 3 or more levels of ratings.

Kendall's coefficient accounts for the order of scores, but kappa statistics do not. For example, Kendall's coefficient accounts for the fact that the consequences of misclassifying a perfect item (rating = 5) as bad (rating = 1) are more serious than misclassifying the item as very good (rating = 4).

### Interpretation

Kendall's coefficient of concordance can range from 0 to 1. The higher the value of Kendall's, the stronger the agreement.

## Chi-Sq

The approximate chi-square statistic that is used to determine the p-value in a chi-square test.

## DF

The degrees of freedom (DF) are used with the chi-square value to determine the p-value. DF = N–1.

## P

The p-value is a probability that measures the evidence against the null hypothesis. Lower p-values provide stronger evidence against the null hypothesis.

Use the p-value for Kendall's coefficient of concordance to determine whether to reject or fail to reject the null hypothesis.
• H0: The appraiser agreement is due to chance.
• H1: The appraiser agreement is not due to chance.

Minitab uses the chi-square value to determine the p-value.

### Interpretation

To determine whether ratings are associated, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates that the risk of concluding that the ratings are associated–when, actually, they are not–is 5%.
P-value ≤ α: The appraiser agreement is not due to chance (Reject H0)
If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that the appraiser ratings are associated with one another.
P-value > α: The appraiser agreement is due to chance (Fail to reject H0)
If the p-value is larger than the significance level, you fail to reject the null hypothesis because there is not enough evidence to conclude that the appraiser ratings are associated.
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