Model for two groups
We now consider a model for two-group numerical data in which the data in each group is a random sample from a normal population,
Group 1: | Y ~ normal (µ1 , σ1) |
Group 2: | Y ~ normal (µ2 , σ2) |
To simplify this model, we assume that the standard deviations are equal in the two groups,
For data that can be assumed to arise from this model, the hypotheses of interest concern whether the group means are equal,
Equal means? | ![]() |
In the remainder of this section, we show that this model can be expressed as a general linear model and that equality of the group means can be tested with standard GLM methods.
Egg shell density and vitamin D
In a randomised experiment, 12 hens were given a diet supplemented with the leaves of a plant containing viramin D and 12 were given a normal diet. After 2 weeks, the shell density of the eggs produced by each hen was recorded.
The sliders under the diagram adjust the four parameters of the most general normal model. Click Best fit to set them to the sample mean and standard deviation in both groups.
Click the checkbox Equal st devn then click Best Fit again. With such small samples from each group, it is reasonable to assume that the standard deviations in the two groups are the same.
In the rest of this section, we consider whether the group means for this kind of data are equal too.