factorial

(noun)

The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 * 2 * 3 * 4 * 5 = 120.

Related Terms

Examples of factorial in the following topics:

  • Factorial Experiments: Two Factors

    • A full factorial design may also be called a fully crossed design.
    • For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2 by 2 factorial design.
    • A factorial experiment can be analyzed using ANOVA or regression analysis.
    • This table shows the notation used for a 2x2 factorial experiment.
    • This figure is a sketch of a 2 by 3 factorial design.

  • Two-Way ANOVA

    • Another term for the two-way ANOVA is a factorial ANOVA.
    • Factorial experiments are more efficient than a series of single factor experiments and the efficiency grows as the number of factors increases.
    • Consequently, factorial designs are heavily used.
    • We define a factorial design as having fully replicated measures on two or more crossed factors.
    • In a factorial design multiple independent effects are tested simultaneously.

  • ANOVA Design

    • Factorial ANOVA is used when the experimenter wants to study the interaction effects among the treatments.
    • When the experiment includes observations at all combinations of levels of each factor, it is termed factorial.
    • Factorial experiments are more efficient than a series of single factor experiments, and the efficiency grows as the number of factors increases.
    • Consequently, factorial designs are heavily used.
    • Differentiate one-way, factorial, repeated measures, and multivariate ANOVA experimental designs; single and multiple factor ANOVA tests; fixed-effect, random-effect and mixed-effect models

  • Exercises

    • What is better about conducting a factorial experiment than conducting two separate experiments, one for each independent variable?
    • An A(3) x B(4) factorial design with 6 subjects in each group is analyzed.
    • The following data are from an A(2) x B(4) factorial design.

  • Between- and Within-Subjects Factors

    • When all combinations of the levels are included (as they are here), the design is called a factorial design.
    • A concise way of describing this design is as a Gender (2) x Age (3) factorial design where the numbers in parentheses indicate the number of levels.

  • Experimental Design

    • Factorial experiments: Use of factorial experiments instead of the one-factor-at-a-time method.
    • A scale is emblematic of the methodology of experimental design which includes comparison, replication, and factorial considerations.
    • Outline the methodology for designing experiments in terms of comparison, randomization, replication, blocking, orthogonality, and factorial experiments

  • Analysis of Variance Designs

  • Experimental Designs

    • This design can be described as an Associate's Weight (2) x Associate's Relationship (2) factorial design.
    • The design was a factorial design because all four combinations of associate's weight and associate's relationship were included.
    • A factorial design allows this question to be addressed.
    • Factorial designs can have three or more independent variables.

  • Generating the exact null distribution and p-value

    • The expression $\binom{n}{k}$is read as n choose k, and the exclamation points represent factorials.

  • Randomized Design: Single-Factor

    • denotes factorial) possible run sequences (or ways to order the experimental trials).