Use the general linear model command to perform analysis of variance (ANOVA), analysis of covariance, and regression analysis on balanced or unbalanced data.

Using the general linear model procedure to conduct an ANOVA tests the hypothesis that the means of several populations are equal. In this case, the general linear model procedure requires the following:

·    a response, or measurement taken from the units sampled.

·    one or more factors.

Factors for the general linear model can be one of two types:

·    fixed - a fixed factor is a discrete variable for which is altered systematically.

·    random - a random factor is a discrete variable for which the values are selected at random from a larger population of values.

The different values represented for each factor variable are called levels of the factor. Each level of the factor in the analysis corresponds to a larger population with its own mean. The sample mean is an estimate of the level mean for the whole population.

·    For fixed factors, the ANOVA examines whether the factor level means are the same or different.

·    For random factors, the ANOVA examines whether the variance of the factor is zero.

In addition to helping you evaluate whether all the level means are the same, Minitab also provides output to help you determine which level means are different when differences exist.

A sociologist randomly sampled 45 professors who taught an evening course at a large metropolitan university. The data collected includes:

·    Subject - the subject matter of the course: humanities (1), social sciences (2), engineering (3), or management (4)

·    Degree - the highest degree that the professor posses: bachelor's (1), master's (2), or Ph.D. (3)

·    Salary - the amount of payment received for teaching the course (in thousands of dollars).

The sociologist was interested in examining the effects of degree and subject on salary. The data are unbalanced, so the sociologist chose to use the general linear models (GLM) procedure to analyze them.

Data: Professor.MTW (available in the Sample Data folder).