Data

In this section, we examine data that may arise as:

We will model the data in terms of g groups. The data often arise from completely randomised experiments with g treatments.

Model

The model that was used for 2 groups can be easily extended to to g > 2 groups, allowing different means and standard deviations in all groups.

Group i:   Y   ~   normal, σi)

However to develop a test for equal group means with g > 2 groups, we must make an extra assumption that the standard deviations in all groups are the same.

Group i:   Y   ~   normal, σ)

If there are g groups, this model has g + 1 unknown parameters — the g group means and the common standard deviation, σ. It is flexible enough to be useful for many data sets.

If the assumptions of a normal distribution and constant variance do not hold, a nonlinear transformation of the response may result in data for which the model is appropriate.