Exam 15: Random- and Mixed-Effects Analysis of Variance Models

If a given set of data were analyzed with both a two-factor fixed-effects model and a two-factor random-effects model, which F ratio will definitely stay unchanged?

MCP can be used to further examine

In a two-factor mixed-effects ANOVA, A (fixed factor) has 3 levels, and B (random factor) has 5 levels. Each cell has 5 observations. What is df_with?

Complete the following ANOVA summary table for a two-factor model, where there are three levels of factor A (random dosage effect) and four levels of factor B (random physician effect). Each cell of the design includes six patients ( $\alpha$ = .05). Source SS df MS F Critical Value Decision 25 - - - - - - - 15 - - - - - - - - - Within - - 1 Total 160 -

To examine development in the pedagogical content knowledge (PCK) of new teachers, 12 novice teachers are measured on their PCK at the beginning of their teaching career, at the end of the first semester, and at the end of the first school year. The scale that measures PCK ranges from 0 to 45 with higher scores reflecting greater levels of PCK. The data are shown below. Conduct a one-factor repeated measures ANOVA to determine the mean differences across time, using $\alpha$ = .05. Use the Bonferroni method to detect exactly where the differences are among the time points (if they are different). Subject Time 1 Time 2 Time 3 1 16 17 28 2 17 23 32 3 11 21 30 4 15 23 35 5 21 32 40 6 14 22 31 7 12 19 31 8 17 21 25 9 11 16 24 10 8 14 20 11 14 24 28 12 12 19 25

The denominator of the F ratio used to test the main effect of factor A in a two-factor ANOVA is MS_AB in which one of the following?

Gilbert wants to make generalizations about the class attendance rate in his district. He randomly samples four schools and collects data on the attendance rate of 50 classes (one class represents one observation). Which ANOVA model is most appropriate for analysis of these data?

Which of the following statements regarding a comparison of the fixed- effects and random-effects models is false?

Ravi conducts a study where randomly selected patients of a clinic are measured on their blood pressure each month over the course of one year. Which ANOVA model is most appropriate for analysis of these data?

In one-factor repeated measures model, scores are collected at three different time points (J = 3). The assumption of sphericity basically states that

In the table below, each cell represents one combination of factor levels. The actual experiment assigns participants only to the combinations represented by the shaded cells (the rows are randomly selected). This experiment is an example of which of the following designs?

In a one-factor random-effects model, suppose we find that the effect of factor A is significant at $\alpha$ = .05.

In two-factor mixed-effects ANOVA (A is the fixed-effects factor and B is the random-effects factor), which of the following statements is not always true?

How many hypotheses are tested in a two-factor split-plot ANOVA?

When testing the interaction effect of a two-factor design, which of the following models does not use MS_with as the denominator for that F ratio?

Which model(s) generally requires the assumption of sphericity?

In a two-factor split-plot ANOVA, A (between-subjects factor) has 3 levels, B (within-subjects factor) has 4 levels, and each cell has 5 observations. The F_A ratio has degrees of freedom equal to?

Complete the following ANOVA summary table for a two-factor model, where there are two levels of factor A (fixed program effect) and five levels of factor B (random school effect). Each cell of the design includes seven students ( $\alpha$ = .05). Source SS df MS F Critical Value Decision 100 - - - - - 210 - - - - - - - 20 - - - Within - - - Total 690

In which of the following models can the population variance of the residual errors ( $\sigma$ _{$\varepsilon$} ²) be estimated?

In the same study as described in Question 3, Gilbert randomly selected 25 classes from the four sampled schools. All selected classes participated in a program that aimed to increase attendance rate (the remaining classes were controls). Gilbert then collected data on the change of attendance rate to see whether the program made a difference. Which ANOVA model is most appropriate for analysis of these data?