More than Two Categories (3 of 3)


Reporting Results
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.

Summary of Computations
  1. Make a table of expected and observed frequencies.

  2. Compute Chi Square using the formula:


  3. Degrees of freedom = number of categories minus one.

The correction for continuity is not used when there are more than two categories. Some authors claim it should be used whenever an expected cell frequency is below 5. Research in statistics has shown that this practice is not advisable.

  1. Observations are sampled randomly and independently.

  2. 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.