In a study to compare language development in hearing-impaired (HI) and hearing-normal (HN) children, a researcher obtained data on a sample of 20 HI and 20 HN children. There were five children at each of four age levels 12 months apart in each group. Their scores on a language development test are given below:
|
|
Age Level 1
|
Age Level 2
|
Age Level 3
|
Age Level 4
|
|
Hearing Impaired
|
2
2
3
1
2
|
4
3
1
2
5
|
3
7
5
4
6
|
12
9
8
10
11
|
|
Hearing
Normal
|
2
3
4
4
3
|
7
10
7
8
9
|
10
12
13
9
11
|
12
11
13
14
10
|
(a) Construct a plot of the means and describe the pattern of change across age levels in the two groups.
(b) Based on the plot, what hypothesis is of primary interest? Carry out the appropriate SPSS analysis, report the ANOVA table, and draw a conclusion, indicating what statistics you used in obtaining your answer.
(c) Report the results of all remaining statistical tests in the ANOVA table, indicating what hypothesis was tested and what conclusion you would draw (indicate which statistics you used).
(d) The researcher wants to determine if the average growth from Age Level 2 to 3 is the same as the average growth from Age level 3 to 4 for the hearing impaired children.
State this hypothesis as a contrast of the cell means. Report the estimate, standard error, Scheffe critical value, and 95% Scheffe confidence interval. Draw a specific and complete conclusion based on your results.