What Factorial is
In statistics, Factorial is a mathematical operation that multiplies a sequence of consecutive numbers. It is expressed as an exclamation mark (!). For example, the factorial of 4 is expressed as 4!.
Steps for Factorial:
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Start with a positive integer (n)
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Multiply the integer by all positive integers that are less than it.
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The result is the factorial of the integer (n!).
For example, 4! = 4 x 3 x 2 x 1 = 24.
Examples
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Factorials are commonly used in permutation and combination analysis. For example, to calculate the number of possible outcomes of a survey with three rating levels (e.g. strongly agree, agree, disagree), the number of possible outcomes can be calculated using 3! (3 factorial).
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Factorials are used in the calculation of variance components in linear mixed models. For example, if there are two factors, Factor A and Factor B, with two levels each, the variance of Factor A can be calculated using 4! (4 factorial).
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Factorials are used in the calculation of repeated measures ANOVA. For example, if there are three measures of a trait taken at three different time points, the total number of possible combinations can be calculated using 3! (3 factorial).