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Publication date: 07/30/2020

The Analysis of Variance Report

The Analysis of Variance report partitions the total variation of a sample into two components. The ratio of the two mean squares forms the F ratio. If the probability associated with the F ratio is small, then the model is a better fit statistically than the overall response mean.

Note: If you specified a Block column, then the Analysis of Variance report includes the Block variable.


Lists the three sources of variation. These sources are the model source, Error, and C. Total (corrected total).


Records an associated degrees of freedom (DF for short) for each source of variation:

The degrees of freedom for C. Total are N - 1, where N is the total number of observations used in the analysis.

If the X factor has k levels, then the model has k - 1 degrees of freedom.

The Error degrees of freedom is the difference between the C. Total degrees of freedom and the Model degrees of freedom (in other words, N - k).

Sum of Squares

Records a sum of squares (SS for short) for each source of variation:

The total (C. Total) sum of squares of each response from the overall response mean. The C. Total sum of squares is the base model used for comparison with all other models.

The sum of squared distances from each point to its respective group mean. This is the remaining unexplained Error (residual) SS after fitting the analysis of variance model.

The total SS minus the error SS gives the sum of squares attributed to the model. This tells you how much of the total variation is explained by the model.

Mean Square

Is a sum of squares divided by its associated degrees of freedom:

The Model mean square estimates the variance of the error, but only under the hypothesis that the group means are equal.

The Error mean square estimates the variance of the error term independently of the model mean square and is unconditioned by any model hypothesis.

F Ratio

The model mean square divided by the error mean square. If the hypothesis that the group means are equal (there is no real difference between them) is true, then both the mean square for error and the mean square for model estimate the error variance. Their ratio has an F distribution. If the analysis of variance model results in a significant reduction of variation from the total, the F ratio is higher than expected.


Probability of obtaining (by chance alone) an F value greater than the one calculated if, in reality, there is no difference in the population group means. Observed significance probabilities of 0.05 or less are often considered evidence that there are differences in the group means.

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