Generate a Fractional Factorial Design

Generate a Factorial Design

This menu can be used to generate an efficient fractional factorial design using the minimum aberration algorithm of Laycock & Rowley (1995). To explain minimum aberration for a block design, we start by defining the resolution of a design as the largest integer r such that no interaction term with r factors is confounded with blocks. The aberration of the design is the number of interaction terms with r+1 factors that are confounded. A minimum aberration design is defined as a design with the smallest aberration out of the designs with the highest available resolution. So, essentially this minimizes the number of interactions with the minimum number of factors that are confounded. The fractional factorial is constructed by taking only one block from the block design, and the terms that were confounded with blocks in the block design become aliased in the fractional factorial.

Number of treatment factors

The number of treatment factors for the design. The names for each treatment factor can be specified using the treatment factor names option.

Treatment factor names

Provides a list of the treatment factor names to use in the generated design. The number of items in the list is controlled by the number of treatment factors option. To change a name either click or double-click on the name in the list and edit in the space provided.

Number of levels for all treatment factors

Each treatment factor must contain the same number of levels and this number is supplied using this option. The number of levels must be a prime number (e.g. 2, 3, 5, 7, 11) or 4.

Number of units in each block

Specifies the number of the units in each block; this must be a power of the number of levels.

Name of sub-block factor

Specifies the name for the identifier for the sub-blocks.

Pseudo-factors for ANOVA

Designs where the treatment factors have more than two levels may require pseudo-factors to be defined in order for them to be analysed by analysis of variance. This option can be used to specify the name of the pseudo-factors.

Number of block for fractional factorial

The number of the block to form the fractional factorial. Alternatively, a zero can be supplied to take a block at random.

Number of units in sub-blocks

Defines the size of the sub-blocks for a fractional factorial. This must be a power of the number of levels.

Options

Specifies additional options for randomizing and displaying the design.

Randomize design	When selected, the design will be randomized, otherwise the units will be in standard order. You can set the seed for the randomization using the randomization seed option.
Display design in a spreadsheet	When selected, the resulting design will be put into a spreadsheet window.

Action Buttons

Run	Generate the design.
Cancel	Close the menu without further changes.
Options	Opens a dialog where additional options and settings can be specified for the designs.
Defaults	Set the menu settings back to the default settings. Clicking the right mouse on this button produces a pop-up menu where you can choose to set the menu using the currently stored defaults or the GenStat default settings.