More than Two Categories (3 of 3)
Next section: Introduction to test of independence
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
- Make a table of expected and observed frequencies.
- Compute Chi Square using the formula:
.
- 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.
Assumptions
- 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