ANOVA Example: Maths Performance Dataset
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Questions and Answers

What is the total variance (SSTotal) in a two-way ANOVA?

  • The variability of the cell means around the grand mean
  • The variability of the interaction effects around the grand mean
  • The variability of each child's score around the grand mean, ignoring group membership (correct)
  • The variability of the marginal means for gender around the grand mean

    • What does the between-treatment variability (SSbetween treatment) represent in a two-way ANOVA?

  • The variability of the marginal means for gender around the grand mean
  • The variability of the interaction effects around the grand mean
  • The variability of each child's score around the grand mean
  • The variability of the cell means around the grand mean (correct)

    • What is represented by SSinteraction in a two-way ANOVA?

  • The variability of the marginal means for gender around the grand mean
  • The variability of the marginal means for class around the grand mean
  • The remaining variability after accounting for gender and class effects (correct)
  • The variability of the cell means around the grand mean

    • What is an assumption of homogeneity of variance in a two-way ANOVA?

    <p>The assumption that the variance of each group is equal</p> Signup and view all the answers

    What is typically presented in a two-way ANOVA summary table?

    <p>The sums of squares for each factor and interaction</p> Signup and view all the answers

    In a two-way ANOVA, what does the grand mean represent?

    <p>The overall mean of all observations</p> Signup and view all the answers

    What is the residual variance consists of?

    <p>The variance left after accounting for the interaction and main effects of IV1 and IV2</p> Signup and view all the answers

    What is the effect on the SSerror when extra factors and interaction terms are added to the analysis?

    <p>It shrinks the SSerror</p> Signup and view all the answers

    What is the purpose of checking for homogeneity of variance?

    <p>To determine if the groups have similar variances</p> Signup and view all the answers

    What does a two-way ANOVA summary table typically include?

    <p>The main effects of IV1 and IV2, and their interaction</p> Signup and view all the answers

    What type of effect is represented by non-parallel lines in a graph?

    <p>Interaction between IV1 and IV2</p> Signup and view all the answers

    What can be concluded if the p-value in a homogeneity of variance test is greater than 0.05?

    <p>The groups have similar variances</p> Signup and view all the answers

    What is the primary advantage of using factorial ANOVA over one-way ANOVA?

    <p>It enables the evaluation of the effect of multiple independent variables.</p> Signup and view all the answers

    What is the term for the variation in the dependent variable that can be attributed to the different levels of the independent variables?

    <p>Between-treatment Variability</p> Signup and view all the answers

    What is the term for the situation where the effect of one independent variable on the dependent variable depends on the level of another independent variable?

    <p>Interaction Effect</p> Signup and view all the answers

    What is the assumption that must be met for the validity of a two-way ANOVA?

    <p>Homogeneity of Variance</p> Signup and view all the answers

    What is the purpose of a two-way ANOVA summary table?

    <p>To summarize the results of a two-way ANOVA, including the main effects and interaction effects</p> Signup and view all the answers

    What is the term for an ANOVA where four independent variables have been manipulated?

    <p>Four-way ANOVA</p> Signup and view all the answers

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