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Covariate Pattern

A covariate pattern is a set of runs whose factor settings are all identical. In a design that means one design point, and in a replicated design it means the group of rows that repeat that point.

The term does not appear in any Quantum XL dialog or on any worksheet. It is the name this help uses for a grouping the software really does perform, and several reports are built on it.

How the grouping is made

Rows are grouped by a key built from each row, and rows that share the key are one group. The match is exact rather than within a tolerance, so two rows meant to be the same design point are only grouped together if their cells hold the same values.

There are two keys, not one, and neither is only the factor settings:

Grouping The key
The S-Hat groups the factor settings, plus the run's design point type (factorial, axial or centre), plus its block value. The block is left out only when the design blocks on replicates
Pure error every column of the regression's own design matrix, which is the model's columns including the blocking columns

Two consequences follow. In a blocked design, a design point repeated in two different blocks is two groups rather than one. And because pure error keys on the model's columns, rows that differ only in a factor the model does not contain are treated as repeats of each other.

The exact match is worth knowing when a design has been edited by hand. A setting typed as 10 in one row and 10.0 in another is the same number and groups normally, but a setting rounded differently in two rows is two groups of one rather than one group of two.

What is built on it

Report How it uses the grouping
The S-Hat model a standard deviation is computed within each group, and those become the response of a second regression
Pure error and lack of fit groups with two or more responses supply the pure error term. On a design with no repeated point the lack-of-fit block reads NA
S-bar on design-source charts the within-group standard deviations of the groups falling at that plotted setting, averaged
Cube plot from a design source a corner's value is the mean of the runs at that corner, and a corner with no runs stays blank
Binary logistic residuals the deletion measures ask what changes when all the runs at one pattern are removed, not one row

Y-bar does not use this grouping. On a design-source chart Y-bar is the average of every run whose plotted factor values match, whatever the other factors were set to, so it groups on the plotted factors alone.

Groups of one

A group with fewer than two responses contributes nothing to any of the above. It is not an error: a design with no replication has as many groups as runs, every group has one member, and the consequence is that the lack-of-fit block reads NA and the S-Hat model has nothing to fit.

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