Random factors for Fit General Linear Model

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

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.

Interpretation

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.

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.

Interpretation

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.

Variance

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

Interpretation

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.

% of Total (Variance)

The % of Total estimates the percentage of the total variance that is contributed by each random term in the model. It is calculated as the variance for each source divided by the total variation, then multiplied by 100 to express as a percentage.

If a variance component estimate is less than zero, Minitab displays zero for the percent of total variability.

Interpretation

Use the percentage of the total variance to assess the variation from each source.

StDev

StDev is the standard deviation for each random term in the Variance Components table. The standard deviation is equal to the square root of the variance for that source.

The standard deviation is a convenient measure of variation because it has the same units of measurement as the response variable.

% of Total (StDev)

The % of Total is the standard deviation for each source of variation, divided by the total standard deviation and multiplied by 100.

The percentage of the total standard deviation is the square root of the variance for each source. Thus, the variance percentages sum to 100, but the standard deviation percentages do not.

Interpretation

Use the percentage of the total standard deviation to compare the variation from each source to the total variation.

If a variance component estimate is less than zero, Minitab displays the negative estimate, but sets the estimate to zero in order to calculate the percent of total variability.

By using this site you agree to the use of cookies for analytics and personalized content.  Read our policy