Key Concepts Study Tool: Chapter 15

Key Concepts Study Tool: Chapter 15

Click on each concept below to check your understanding.

ANOVA (ANalysis Of VAriance)

  • A little like a t-test, but for comparing differences across more than two groups.
  • Calculate Ndifferent (or the number of discordant pairs)
  • Compares three things:
    1. Differences between means
    2. Differences in values within samples
    3. Differences in values across samples
  • Each observation is different from the grand mean. There are two sources of this difference:
    1. The independent variable
    2. Random unexplained error
  • ANOVA compares the variation around the mean within groups to the variation across or between groups.

2. Equations Needed to Calculate ANOVA

  • Total sum of squares(SStotal): to determine whether there is more variation within groups than across groups, we need to identify the total variation available to be distributed between and across groups, which is equal to the total variation of all observations from the grand mean.

    sstotal

  • Equation for the sum of squares within groups:

    sswithin

  • Equation for the sum of squares between groups:

    ssbetween

  • Mean Square: standardized sum of squares, used so that values can be compared regardless of sample size.
  • Equation for the mean square within groups:

    mswithin

  • Equation for the mean square between groups:

    between

    Where: k = the number of groups you are comparing.

3. The F-Distribution

  • To assess values against the F-distribution, a test statistic must be calculated first. This is known as the F-ratio and is calculated using the following equation:

    fobserved

  • Once the F-statistic is computed, it can be assessed against the F-distribution, by looking at both the within-group and between-group degrees of freedom to identify the critical value.

4. How to Compute ANOVA: The Steps/strong>

  1. Find the grand mean and the mean for each group.
  2. Find group sums, sum of squared scores.
  3. Find SStotal, SSwithin, SSbetween
  4. Find dfbetween, and dfwithin(if you encounter degrees of freedom values that do not perfectly coincide with the provided values, always use the lower value).
  5. Find msbetween and mswithin

    anova

  6. Obtain the F-ratio.
  7. Obtain the F-ratio.
  8. Compare fobserved to fcritical.
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