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 (µi , 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 (µi , 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.