Parameters

A normal model for two groups has four unknown parameters (the mean and standard deviation for each normal distribution). These parameters give considerable flexibility and allow the model to be used for a variety of different data sets.

(If the standard deviations in the groups are assumed to be equal, the number of unknown parameters can be reduced to three, but we will not consider models of that form until a later section.)

Illustration

The following diagram shows the flexibility of this class of models

Use the four sliders to adjust the four parameters of the model. (Note that the relative heights of the normal curves change as the scale parameters are adjusted to maintain equal areas for the two normal curves.)

Click Take sample a few times to see typical data sets that arise from the model. The blue bands at the base of the normal distributions are at µ ± 2σ so they include about 95% of the sample values in each group.