**Try these parameter values:**

**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

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.

**Adjust the observed and expected counts to the right:**

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