# Chi-square test of equal frequencies

The chi-square test of equal frequencies checks whether the frequencies (number of values) in each category or group are statistically different from each other.

Note: This statistical test is a fixed system operation and cannot be modified.

The following procedure describes how the chi-square value is calculated:

1. Determine the expected frequency. Because the frequency is expected to be the same for each category (equal frequencies), it is the average frequency or count. The average frequency is N/R, where N is the total frequency and R is the number of categories.
2. For each category, subtract the expected frequency from the actual (observed) frequency.
3. Take the square of each of these results and divide each square by the expected frequency.
4. Add up all the results.

The chi-square value is compared to a theoretical chi-square distribution to determine the probability of obtaining the value by chance.

• This probability is the significance value.
• If the significance value is less than the significance level, the frequencies are significantly different.
• For sparse tables, IBM® Cognos Analytics adjusts the chi-square test to reduce the contribution of cells with a small expected value, which would otherwise have a disproportionately large contribution to the statistic.

The effect size for this test is the strength of the unequal frequencies.