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,
Age of audience
| ||||
participant | one | three | six | adult |
1 | 199.12 | 183.79 | 186.83 | 188.83 |
2 | 179.79 | 180.44 | 188.42 | 179.40 |
3 | 190.47 | 183.58 | 179.28 | 181.63 |
4 | 198.98 | 195.52 | 194.40 | 201.07 |
5 | 189.90 | 187.86 | 196.79 | 202.48 |
6 | 186.66 | 186.50 | 189.31 | 195.92 |
7 | 185.61 | 180.87 | 183.76 | 186.25 |
8 | 181.91 | 173.73 | 176.59 | 184.93 |
9 | 190.29 | 174.56 | 180.01 | 190.57 |
10 | 176.57 | 167.66 | 172.77 | 181.54 |
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.
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.