Fixed Effects (in ANOVA)

The term fixed effects in the context of analysis of variance is used to denote factors in an ANOVA design with levels that are deliberately arranged by the experimenter, rather than randomly sampled from an infinite population of possible levels (those factors are called random effects). For example, if one were interested in conducting an experiment to test the hypothesis that higher temperature leads to increased aggression, one would probably expose subjects to moderate or high temperatures and then measure subsequent aggression. Temperature would be a fixed effect in this experiment, because the levels of temperature of interest to the experimenter were deliberately set, or fixed, by the experimenter.

A simple criterion for deciding whether or not an effect in an experiment is random or fixed is to ask how one would select (or arrange) the levels for the respective factor in a replication of the study. For example, if one wanted to replicate the study described in this example, one would choose the same levels of temperature from the population of levels of temperature. Thus, the factor "temperature" in this study would be a fixed factor. If instead, one's interest is in how much of the variation of aggressiveness is due to temperature, one would probably expose subjects to a random sample of temperatures from the population of levels of different temperatures. Levels of temperature in the replication study would likely be different from the levels of temperature in the first study, thus temperature would be considered a random effect.

For more information, see the description of the Analysis of Variance and the Variance Components and Mixed Model ANOVA/ANCOVA method of analysis.