Unit 8 of 12

Several Groups and Variability

  • 5 lessons
  • Videos 56 to 60

Several groups need more than a string of two-group tests. This unit covers analysis of variance, factorial designs, multiple comparisons, rank tests for several groups and inference about spread.

One-way ANOVA compares the variation between group means with the variation within groups to test whether several population means are equal, and Welch's version allows unequal variances. Factorial designs separate main effects from interactions, and blocking compares treatments within groups of similar units. Testing many true null hypotheses raises the chance of at least one false rejection, so Bonferroni, Holm and Tukey methods control the family-wise error rate, while the Benjamini-Hochberg procedure targets the false discovery rate.

Every lesson will be one video. The videos are coming soon, and each lesson page already has the definitions and an example for every key term.

Comparing Several Means

  1. One-Way ANOVA and Welch ANOVA

    How one-way ANOVA splits variation into between-group and within-group sums of squares, forms mean squares and an F statistic to test equal means, and when Welch ANOVA is used instead.

    Video 56

  2. Factorial Designs, Blocking and Interactions

    How a factorial design crosses factors, how cell means give simple effects, main effects and interactions, why genuine replication is needed, and how a randomized block design compares treatments within blocks.

    Video 57

  3. Planned Contrasts, Post-Hoc Comparisons and Multiple Testing

    How planned contrasts differ from post-hoc comparisons, how Bonferroni, Holm and Tukey methods control the family-wise error rate, and how the Benjamini-Hochberg procedure controls the false discovery rate.

    Video 58

Comparing Distributions and Spread

  1. Kruskal-Wallis Tests and Comparing Several Distributions

    How the Kruskal-Wallis test compares several independent groups through pooled ranks, what its identical-distribution null and omnibus conclusion mean, how ties are corrected, and when the chi-square approximation is reliable.

    Video 59

  2. Inference for Variance and Comparing Spread

    How the chi-square pivot gives confidence intervals for a variance and a standard deviation, how the F test and the Levene and Brown-Forsythe tests compare spread, and how much each one depends on normality.

    Video 60