A design created by adding an identical but complementary fraction to an original fraction of a factorial design in statistical experiments. The new design has twice the number of runs and has an additional column highlighting the differences between the initial design and the replicate.
Foldover Design Details
When you fold over a design, you take the original design's factors and reverse them to create an identical but reversed design. Foldover techniques increase the resolution of the original statistical design. For example, if your initial plan has a resolution III, its foldover design will have a resolution IV.
Switching the sign of one factor in your initial design will de-alias your factor's main effects and its interactions. In statistical studies, most of your experiments are not a one-time thing. You continuously add variables to your system the more you learn more about your investigation.
When your data factors are sequential in statistical research, you might have difficulty adding data sets to your already designed experiment. Foldover designs come in handy at this point. You carry out the small analysis first, then proceed in stages to the more extensive investigations. To create foldover designs, you use statistical analysis software. There are a number of these to choose from. They include:
- Minitab 18
- SPSS Statistics
- GNU Octave
- TIMi Suite
A Hypothetical Example of a Foldover Design
Think about a 1/8 fraction of a 2^6 factorial design with the following factors source: A, B, C, D, E, and F. Let's say in your original column, your values for the A column are: -1,-1,-1,-1, 1, 1, 1 and 1. The complementary (reversed) values in the A column of your foldover design will be 1, 1, 1, 1,-1,-1,-1, and -1.
From the foldover example above, you can see that column A in the foldover design is the reversed version of column A in the original version. Folding over means you only remove the (-) sign from the numbers in the original column and add the same character to the numbers without the foldover column.
When you combine the original design with the foldover design, you get a replicated setup. For instance, in the original design, you have eight observations in a column. The replicate resulting from folding over has 16 observations in one column.
Significance of Folded Designs
When you fold over a statistical spreadsheet design, you create a mirror image of the initial design. During a test analysis, the variables in your folded design will change slightly. For instance, folding over will convert a bare number in the initial format to a negative number.
Firstly, folding over a design changes the size of the spreadsheet. For example, your six-factor design will transform into a twelve-factor design. The upside of folded structures is it separates your confounded interactions. Therefore, folding over will remove the confounding factors (variables). Confounding variables are a source of bias when analyzing an experiment.
Secondly, by folding over an initial design, you increase the resolution of a plan. The resolution of a design is the degree to which the main effects confound with the different interactions. The higher the resolution, the less the confounding. 'Resolution III, IV, and IV designs are the most common' according to Minitab. Therefore, you can distinguish sampled signals from the original signals.