4 Repeated measures ANOVA

For this exercise, we will use another set of fictional data to test another observation about child-directed speech. We observe that caregivers use a wider pitch-range, and particularly higher pitch contour while talking to children. We would like to test this observation for speech directed to children at three different stages: age one, three, and six, as well as to adults. As a result, our predictor is an ordered categorical variable with four levels. We record speech from 10 participants directed to all four groups.

The response variable is the maximum value of the fundamental frequency (F₀, in Hertz) of caregivers’ speech during the relevant recording.²

Here is our data,

You can get the data in two different formats: wide format or one column per variable. You will need to switch back-and-forth between these different formats during the following exercises.

For all statistical significance questions use α = 0.05.

Exercise 4.1. Produce a box plot of the response variable for each age group. Does the box plots show indications of

1. violation of assumption of normality
2. violation of homogeneity of variance
3. violation of sphericity

Exercise 4.2. Assuming the observations were independent, perform a one-way ANOVA using ‘age’ as the predictor.

1. Is the homogeneity assumption violated?
2. Is the main ANOVA result significant?
3. Are there any statistically significant differences between any pair of the means after Bonferroni correction?

Exercise 4.3. Now analyze the data using repeated measures ANOVA. Make sure to specify post-hoc comparisons using Bonferroni correction, test for sphericity, and effect size calculations.

1. Is the main ANOVA result statistically significant?
2. Is the sphericity assumption violated?
3. What is the effect size?
4. Are there any statistically significant differences between any pair of the means after Bonferroni correction?

Exercise 4.4. Run an independent-measures factorial ANOVA using both age and the subject as predictors. Don’t panic: it is normal that you did not get F and p values.

1. Compare the mean squares (variances) found in the current analysis with the repeated measures ANOVA (only check the values with ‘sphericity assumed’). Which variances are the same? Why?
2. Why does SPSS not calculate the F ratio?

Note: this question is a bit tricky. However, if you make the effort you will understand the logic of RM ANOVA and it’s relation to the (independent measures) factorial ANOVA better.