35.8 Statistical validity conditions
As usual, these results hold under certain conditions to be met. The conditions for which the test is statistically valid are the same as for correlation (Sect. 34.4.3):
- The relationship is approximately linear.
- The variation in the response variable is approximately constant for all values of the explanatory variable.
- The sample size is at least 25.
The sample size of 25 is a rough figure here, and some books give other values.
In addition to the statistical validity condition, the test will be
- internally valid if the study was well designed; and
- externally valid if the the sample is a simple random sample from the population.
Example 35.6 (Statistical validity) For the red deer data,
the relationship is approximately linear,
and the variation in molar weight appears to be somewhat constant for various ages
(Fig. 33.2),
so regression is appropriate.
The sample size is \(n=78\).
The results from the hypothesis test should be statistically valid.
Think 35.5 (Statistical validity) Are the conditions for statistically validity met for the cyclones data
(Fig. 35.2)?
Example 35.7 (Emergency department patients) In Example 35.4, the scatterplot (Fig. 35.9) shows that the relationship is approximately linear, that the variation in ED patients seems reasonably constant for different numbers of days after distribution, and the sample size is larger than 30.
The test (Example. 35.4) and the CI (Example. 35.5) should be statistically valid.