# 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.

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

- 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.
- For each category, subtract the expected frequency from the actual (observed) frequency.
- Take the square of each of these results and divide each square by the expected frequency.
- 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 makes an adjustment to the chi-square test which reduces 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 unequal frequencies strength.