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Random Effects Model

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When the factor(s) in an experiment have a large number of levels of which a few are randomly selected for study, the resulting experimental design and analysis are performed using the technique of random effects analysis, also known as variance components analysis. This technique allows the researcher to draw inferences beyond the particular levels of the Factors used in the study.

The Random Effects model splits the overall variance into two components: one component due to the factor under study and the other due to random error.


A manufacturer of injection molded parts suspects that the batches of raw material coming from the supplier differ in terms of their moisture content, leading to higher rates of defects. A large number of batches are available at any given time, so six batches are randomly selected for the study and five determinations of moisture content made from each. Here the interest is not in the particular batches chosen, but in the entire population of raw material batches, hence Batches is a random variable.


The results can be generalized to all levels of the factor not included in the study.

If the factor effect is significant, we can only estimate the amount of variation it represents of the total. We cannot make comparisons among the levels to see where the difference lies, because they are not the only levels of interest.

See Also

Fixed Effects Model

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