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Options

This page is the control by control reference for the pages the Create Design builder shows for this design. What the design is and what it gives you is on Two Level Factorial Designs. How each number is produced is on Math Details.

Choosing the design

The first page is headed Select 2-level factorial design. and holds a grid. The number of factors runs along the top, 2 to 15, and the number of runs down the side, 4, 8, 16, 32, 64 and 128. Each cell that holds a design shows its resolution as a Roman numeral, and hovering a cell reports the factors, the runs and the resolution.

Under the grid two lines describe the design you have selected. For the 7-factor, 16-run cell they read:

1/8 Fractional Factorial Design, 7 Factors in 16 Runs.

Resolution: IV. Main effects are aliased with three-ways, and two-ways are aliased with two-ways.

The first line names the fraction as either Full Factorial Design or 1/n Fractional Factorial Design, where n is a power of two. It is not a word like half or quarter: this grid reports the fraction numerically, and n can reach 2048 in the widest cells.

The second line is the word Resolution, the resolution as a Roman numeral, and then a fixed description. These are the six the grid can produce, verbatim. A resolution II description also exists in the software, but no cell in this grid ever reaches it:

Resolution Description
Full There is no aliasing.
III Main effects are aliased with two-ways.
IV Main effects are aliased with three-ways, and two-ways are aliased with two-ways.
V Main effects are aliased with four-ways, and two-ways are aliased with three-ways.
VI Main effects are aliased with five-ways, and two-ways are aliased with four-ways.
VII Main effects are aliased with six-ways, and two-ways are aliased with five-ways.
VIII Main effects are aliased with seven-ways, and two-ways are aliased with six-ways.

Note that from resolution IV up, each description has a second clause about the two-way interactions, and that clause is the one that tells you whether the interactions can be separated from each other.

A full factorial reports the word Full where the Roman numeral would be, not a number, and its description is There is no aliasing.

The rest of the pages

Enter Factor Names and Coding takes the factor names and their low and high settings. See Factor Names and Coding.

Define outputs (responses) takes the responses. See Define outputs.

Enter number of replicates and number of blocks is the last page, and for this design type it carries four things rather than two: replicates, blocking, Fold design: and Number of center points per block:. Two-level factorials are the only designs that set center points and folding on this page. See Define Replicates and Blocks.

Folding

An accepted fold appends a copy of the design below the original, doubling the run count. Fold on all factors flips the sign of every factor in that copy; Fold on factor 'name' flips only that one factor's column and leaves the rest of the copy identical. Either way the run count doubles. A fold that would not shorten the defining relation is refused with Cannot fold this design. See Folding.

See Also