Analysis of Variance

Functions > Design of Experiments > Factor Screening > Analysis of Variance

• anova(A, Y, [“fac”/order])—Returns a table of statistics to examine the variance from the main factors, the blocking, and the error of an experiment that has its runs defined in the design matrix A and its results recorded in the matrix Y. You can use the optional arguments “fac” or order to specify the factors and interactions on which to report.

This function applies only to the following factorial designs in their coded form: full factorials or 2-level (+1/-1) fractional factorials.

The matrix returned by anova has the following columns:

Column	Description
0	Labels for each source reported upon—Each factor, each interaction, the blocking, and the error
1	• Sum of squares (SS) between groups for each factor, for each interaction, and for the blocking • SS within groups for the error • Total SS
2	Degrees of freedom
3	Mean squares (MS)—SS divided by the degrees of freedom
4	F-statistic—MS divided by the MS error
5	P-value—Probability of rejecting the factor, interaction, or blocking based on its F-statistic when in fact it is significant

For some design matrix resolutions, the anova function cannot compute all the interactions.

Arguments

• A is a design matrix.

• Y is a matrix of measured or simulated results with each row containing the results for each run defined in A. The matrix Y must have at least 2 columns and it should not contain NaNs for missing replicates. The elements of Y must have compatible units.

• “fac” (optional) is a string specifying the factors and interactions on which to report. For the separators, you can use a space, a comma, a colon, or a semicolon.

• order (optional) is an integer that specifies the order of the interactions on which to report. order ≥ 1.