Use balanced analysis of variance (ANOVA) to examine the effects of multiple factors on a continuous response. This procedure requires that the number of observations for each combination of the factor levels to be the same (balanced).

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

·    fixed - a fixed factor is a discrete variable that 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.

A textile manufacturer is interested in determining the factors that effect the breaking strength of a synthetic fiber. Researchers from the company sampled the output of four production machines and three operators selected at random in order to determine if these variables effect fiber strength. Two observations were obtained from each of the three operators while they worked at each of the four machines.

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