31.7 Statistical validity conditions
As usual, these results hold under certain conditions. The test above is statistically valid if
- All expected counts are at least five.
Some books may give other (but similar) conditions.
In addition to the statistical validity condition, the test will be
- internally valid if the study was well designed; and
- externally valid if the sample is a simple random sample and is internally valid.
The statistical validity condition refers to the expected (not the observed) counts. SPSS tells us if a problem exists with the expected count condition, underneath the first output table in Fig. 25.3. In jamovi, the expected counts must be explicitly requested to see if this condition is satisfied (Fig. 31.3).
For the student-eating data, the smallest observed count is 2 (living with parents; most meals off-campus), but the smallest expected count is 7.67, which is greater than five. The size of the expected counts is important for the statistical validity condition.