Random factors for Balanced ANOVA

Find definitions and interpretation guidance for every statistic that is provided for random factors.

Variance component

Variance components estimate the amount of variation in the response that is attributable to each random term in an ANOVA table.


Use to assess how much of the variation in the study can be attributed to each random term. Higher values indicate that the term contributes more variability to the response. You can calculate the percentage that each random term contributes by taking the variance component for each source , dividing by the total variation, and then multiplying that by 100 to express it as a percentage.

Error term

The error term is the denominator used in each F-test. If a term has no exact F-test, Minitab uses the expected mean squares to solve for the error term and construct an approximate F-test. This type of test is called a synthesized test.


You can examine the error term to determine the denominator value that Minitab used to calculate the F-value. Minitab uses the F-test to calculate p-values.

Expected mean squares

In models that include random terms, expected mean squares describe how each source of variation consists of a linear combination of variances.


Minitab uses the linear combinations to solve for the variance components and the error term for synthesized tests. Usually, you interpret the variance components and the p-values from the synthesized tests instead of the expected mean squares.

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