Home / DOE / Create Designs / Define Replicates and Blocks
Define Replicates and Blocks¶
The page headed Enter number of replicates and number of blocks appears in the build sequence of every design type built in the Create Design builder, and again from QXL DOE New > Modify Design > Add/Remove Replicates or Change Blocking/Folding, which are two ribbon entries onto the same page. Custom Design and D-Optimal have their own dialogs and no such page.
Enter number of replicates and number of blocks sets how many times the run block is repeated and whether the runs are divided into blocks. The two controls are labelled Select number of replicates: and Select number of blocks:. The blocking list offers No blocking first, then one entry per possible block count, each marked either (block in design), meaning the blocks are generated from the design and confounded with a chosen term, or (block with replicate), meaning the replicates are divided among the blocks.
On the design types that support it, the page also carries Help Me Choose Power/Sample size for Quantitative Outputs, which opens the power calculation with the design's current run count already filled in.
Replicates¶
Select number of replicates: repeats the whole run block. Two replicates of an eight-run design is sixteen runs, the eight settings run twice.
Replicating is what makes a standard deviation estimable at each design point, which is what the S-Hat model is built from, and it is what the pure-error term in the ANOVA table comes from. With no replicated points the lack-of-fit block on the regression sheet is blank rather than zero. See The S-Hat Model and Sums of Squares.
Blocking¶
The blocking list always starts with No blocking. Every other entry is a number of blocks followed by one of two labels, and the label is the important part:
| Entry looks like | What it means |
|---|---|
| n (block in design) | the blocks are generated from the design itself, and the block effect is confounded with one or more terms. Which terms are confounded is reported in the alias table on the design sheet |
| n (block with replicate) | the replicates are divided among the blocks, replicate count divided by block count in each. No block generator is used and no blocking lines are produced |
Only three design types can be blocked in the design: the 2-level factorial, CCD and Box-Behnken. For the 3-level factorial, the N-level factorial, Plackett-Burman, Taguchi and custom designs the only blocking on offer is block-with-replicate, whose counts are the divisors of the replicate count above 1. With a single replicate those five types offer No blocking and nothing else.
Where in-design blocking is available, the counts come from what the design's own structure supports. Box-Behnken is the strictest case, with a fixed set per factor count. See Blocking for the counts and for the one case that raises Invalid number of blocks for the Box-Behnken Design.
Blocking has one effect on the analysis that is worth knowing before you choose it: the blocking term's sum of squares is taken out of SS Regression, and the degrees of freedom for regression drop by one per blocking column. See Blocking.
Folding, on the 2-level factorial page only¶
The 2-level factorial version of this page carries Fold design: as well, because folding only means something for a fractional factorial. An accepted fold appends a sign-flipped copy of the design below the original, so it doubles the run count. A fold that would not break any aliasing is refused with Cannot fold this design. rather than doubling the runs for nothing. See Folding.
Center points, on the 2-level factorial page only¶
The same page is also where a 2-level factorial gets its center points, in Number of center points per block:. Every other design type either asks on its own page (CCD and Box-Behnken) or does not offer them at all.
Center points sit at the middle setting of every quantitative factor, so a design whose factors are all categorical has no middle to sit at. In that case the label above the box is replaced by Center points are not available when all inputs are qualitative., and the box shows 0 and is greyed out.
Opened from Modify Design, this page has no center points box. It is hidden on that path, and center points are changed with Modify Design > Add/Remove Center Points instead.
Power and sample size¶
Help Me Choose Power/Sample size for Quantitative Outputs opens the power calculation with the design's current structure already loaded, so the power it reports is for the design as it stands. The wizard's version of the button is labelled Help Me Choose....
The button is not on every design's version of this page. It appears for the 2-level factorial, the 3-level factorial, the N-level factorial, Plackett-Burman and the Taguchi L4, L8, L12, L16 and L32 arrays. CCD, Box-Behnken and the other Taguchi arrays do not show it.
On the Create Design builder it is greyed out unless at least one output is quantitative. The wizard's version is never greyed out, because the wizard asks about outputs later in its sequence. See Power and Sample Size Calculation.