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13.3: The One Factor ANOVA Model

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    In ANOVA, we calculate the variance two different ways: The mean square factor (\(\mathrm{MS}_{F}\)), also known as mean square between, measures the variability of the means between groups, while the mean square within (\(\mathrm{MS}_{E}\)), also known as mean square within, measures the variability within the population. Under the null hypothesis, the ratio of \(\mathrm{MS}_{F} / \mathrm{MS}_{E}\) should be close to 1 and has \(\mathrm{F}\) distribution.

    One Factor ANOVA model to compare the means of \(k\) independent populations

    Model Assumptions

    • The populations being sampled are normally distributed.
    • The populations have equal standard deviations.
    • The samples are randomly selected and are independent.

    Test Statistic

    • \(\mathrm{F}=\dfrac{\mathrm{MS}_{\text {Factor }}}{\mathrm{MS}_{\text {Error }}}\)
    • \(\mathrm{df}_{\text {num }}=k-1\)
    • \(\mathrm{df}_{\text{den}}=n-k\)

     

    This page titled 13.3: The One Factor ANOVA Model was last modified on Sat, 09 Apr 2022 19:01:17 GMT and is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Maurice A. Geraghty via source content that was edited to the style and standards of the LibreTexts platform.