Next section: Introduction to test of independence

The results of this experiment could be described as follows:

The proportions of subjects falling into the three outcome categories (better, worse, the same) were 0.45, 0.25, 0.30 respectively. These proportions differed significantly from the expected 0.333, 0.333, 0.333 proportions, χ²(2, N = 100) = 6.50, p = 0.039.As shown, the Chi Square statistic is reported with its degrees of freedom and sample size.

- Make a table of expected and observed frequencies.

- Compute Chi Square using the formula:

.

- Degrees of freedom = number of categories minus one.

- Observations are sampled randomly and independently.

- The formula for chi square yields a statistic that is only approximately distributed as Chi Square. For the Chi Square approximation to be sufficiently accurate, the total number of subjects should be at least 20.

Next section: Introduction to test of independence