Statistics: Chi-Square Test

No Significant Difference

Color: O E
Red: 6 5
Blue: 6 6
Green: 3 3
Yellow: 3 5

Significant Difference

Color: O E
Red: 6 2
Blue: 6 6
Green: 3 3
Yellow: 3 9

Statistics: Chi-Square Test

The chi-square test is employed when one wishes to determine if a sample fits some theoretical distribution. The chi-square statistic is calculated as:

where are the observed, and are the expected counts.

Once calculated, the chi-square statistic is compared to a critical value, which is determined using the sample size, the chosen level of significance (typically a = 0.05), and a critical value table. If the statistic calculated is less than the critical value, the sample fits the theoretical distribution. Otherwise, there is a significant difference between the observed and expected.

Statistics: Chi-Square Test

Adjust the observed and expected counts to the right:

In this case the critical value doesn't change because the sample size remains constant.