Find definitions and interpretation guidance for every statistic that is provided with the measures of association.

Fisher's exact test is a test of independence. Fisher's exact test is useful when the expected cell counts are low and the chi-square approximation is not very good.

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

Use the p-value to determine whether to reject or fail to reject the null hypothesis, which states that the variables are independent.

To determine whether variables are independent, 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 a 5% risk of concluding that an association between the variables exists when there is no actual association.

- P-value ≤ α: The variables have a statistically significant association (Reject H
_{0}) - If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that there is a statistically significant association between the variables.
- P-value > α: Cannot conclude that the variables are associated (Fail to reject H
_{0}) - 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 variables are associated.

For more information, go to What is Fisher's exact test?.

Use McNemar's test to determine whether paired proportions are different.

- Estimated difference
- Minitab calculates the difference between the marginal proportions.
- 95% CI
- Minitab calculates the 95% confidence interval for the difference between the marginal probabilities.
- P
- Minitab calculates the p-value to test the null hypothesis.

For more information, go to Why should I use McNemar's test?.

Use the CMH test to test the conditional association of two binary variables in the presence of a third categorical variable.

Minitab calculates a common-odds ratio across the tables and a p-value to assess its significance.

- Common-odds ratio
- Minitab calculates the common-odds ratio, which indicates the strength of association.
- CMH statistic
- The CMH statistic is used to indicate whether the association is statistically significant.
- DF
- The CMH statistic is compared with a chi-square percentile with one degree of freedom.
- P-value
- Minitab calculates the p-value to test the null hypothesis.

For more information, go to What is the Cochran-Mantel-Haenszel test?.

Cramer's V^{2} measures association between two variables (the row variable and the column variable). Cramer's V^{2} values range from 0 to 1. Larger values for Cramer's V^{2} indicate a stronger relationship between the variables, and smaller value for V^{2} indicate a weaker relationship. A value of 0 indicates that there is no association. A value of 1 indicates that there is a very strong association between the variables.

Kappa measures the degree of agreement of the nominal or ordinal assessments that are made by multiple appraisers when assessing the same samples. When you have ordinal ratings, such as defect severity ratings on a scale of 1-5, the concordance measures for ordinal categories, which take ordering into consideration, are usually more appropriate statistics to determine association than kappa alone.

Kappa values range from -1 to +1. The higher the value of kappa, the stronger the agreement.

When:

- Kappa = 1, perfect agreement exists.
- Kappa = 0, agreement is the same as would be expected by chance.
- Kappa < 0, agreement is weaker than expected by chance; this rarely occurs.

Goodman-Kruskal lambda (λ) and tau (τ) measure the strength of association based on the ability to correctly guess or predict the value of one variable when you know the value of the other. Lambda is based on modal probabilities, while tau is based on random category assignment.

- Lambda (λ)
- Lambda measures the percentage improvement in probability of the dependent variable (column or row variable) given the value of other variables (row or column variables).
- Tau (τ)
- Tau measures the percentage improvement in predictability of the dependent variable (column or row variable) given the value of other variables (row or column variables). Goodman-Kruskal tau is the same as Goodman-Kruskal lambda except the calculations of the tau statistic are based on assignment probabilities specified by marginal or conditional proportions.

For more information, go to What are the Goodman-Kruskal statistics?.

- Number of concordant and discordant pairs
- Use concordant and discordant pairs to describe the relationship between pairs of observations. To calculate the concordant and discordant pairs, the data are treated as ordinal, so ordinal data should be appropriate for your application. The number of concordant and discordant pairs are used in calculations for Kendall's tau, which measures the association between two ordinal variables.
- Goodman-Kruskal Gamma (γ)
- Goodman-Kruskal gamma (γ) shows how many more concordant than discordant pairs exist divided by the total number of pairs excluding ties. Use the Goodman-Kruskal gamma to measure the association between the ordinal variables.
- Somers' D
- Somers' D measures the strength and direction of the relationship between pairs of variables. Somers' D values range from -1 (all pairs disagree) to 1 (all pairs agree).
- Kendall's Tau-b
- Kendall's tau-b is used in cross tabulation to measure the association between two ordinal variables.

The test of concordance is a test of independence. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis. Use the p-value to determine whether to reject or fail to reject the null hypothesis, which states that the categorical variables are independent.

If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that there is a statistically significant association between the variables. 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 variables are associated.

Use Pearson's r and Spearman's rho to assess the association between two variables that have ordinal categories. Ordinal categories have a natural order, such as small, medium, and large.

The coefficient can range in value from -1 to +1. The larger the absolute value of the coefficient, the stronger the relationship between the variables. An absolute value of 1 indicates a perfect relationship, and a value of zero indicates the absence of an ordinal relationship. Whether an intermediate value is interpreted as a weak, medium, or strong correlation depends on your goals and requirements.

For more information, go to What are Spearman's rho and Pearson's r for ordinal categories?.