Storytelling and the use of language. A study of early childhood education asked kindergarten students to retell two fairy tales that had been read to them earlier in the week. The 10 children in the study included 5 high-progress readers and 5 low-progress readers. Each child told two stories. Story 1 had been read to them; Story 2 had been read and also illustrated with pictures. An expert listened to a recording of the children and assigned a score for certain uses of language. Here are the data:5
|
Child
|
Progress
|
Story 1
score
|
Story 2
score
|
|
1
|
high
|
0.55
|
0.80
|
|
2
|
high
|
0.57
|
0.82
|
|
3
|
high
|
0.72
|
0.54
|
|
4
|
high
|
0.70
|
0.79
|
|
5
|
high
|
0.84
|
0.89
|
|
6
|
low
|
0.40
|
0.77
|
|
7
|
low
|
0.72
|
0.49
|
|
8
|
low
|
0.00
|
0.66
|
|
9
|
low
|
0.36
|
0.28
|
|
10
|
low
|
0.55
|
0.38
|
Is there evidence that the scores of high-progress readers are higher than those of low-progress readers when they retell a story they have heard without pictures (Story 1)?
(a) Make Normal quantile plots for the 5 responses in each group. Are any major deviations from Normality apparent?
(b) Carry out a two-sample t test. State hypotheses and give the two sample means, the t statistic and its P-value, and your conclusion.
(c) Carry out the Wilcoxon rank sum test. State hypotheses and give the rank sum W for high- progress readers, its P-value, and your conclusion. Do the t and Wilcoxon tests lead you to different conclusions?