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# Factorial design

Explanations > Social Research > Design > Factorial design

## Description

For each variable (or factor) to be explored in an experiment, first identify the settings of each variable (or levels) that are to be tried out. To explore all combinations of factors and levels, the total number of experiments that are needed is the product of the numbers of levels.

Thus with two factors F1 and F2, and three levels for F1 (L11, L12, L13) and two factors for F2, (L21, L22), the number of experiments is 3 x 2 = 6 combinations of levels.

Each experiment may be done with the same group or different groups.

Factorial experiments often stick to two variables as it becomes geometrically more complex when there are more.

The results may be plotted by row or column (for 2 x 2 experiments) in a graph to show

## Example

An investigation into the factors that cause stress in the workplace seeks to discover the effect of various combinations of three levels of background noise and two levels of interruption. They apply the test to the same group at the same time of day and day of week over six weeks. The change in stress as measured with a standard instrument is as below:

Stress levels

 F1: Interruptions L11: Infrequent interruptions L12: Frequent interruptions
 F2: Background noise L21:Low noise L22: Moderate noise L23: High noise
 1 3 2 7 7 8

This is shown in the graphs below (different views of the same data), from which it may be noted (amongst other things) that medium background noise has a much greater effect on stress when there are frequent interruptions as compared with when interruptions are infrequent.

## Discussion

Definitions: Factors are major independent variables. Levels are sub-divisions of factors.

Factorial designs for the analysis of multiple variables at once, which can be very helpful when it is not sure which is more significant or how they interact.

The number of experiments that are required for a full analysis increases geometrically with the number of levels. For example an experiment with four factors and three levels each would need 34 = 81 experiments.

Factorial designs improve the 'signal-to-noise' ratio in an experiment by increasing the signal.

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