35.8 Statistical validity conditions
- 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 35.4 (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)?