Question

In: Statistics and Probability

A study of reading comprehension in children compared three methods of instruction. The three methods of...

A study of reading comprehension in children compared three methods of instruction. The three methods of instruction are called Basal, DRTA, and Strategies. As is common in such studies, several pretest variables were measured before any instruction was given. One purpose of the pretest was to see if the three groups of children were similar in their comprehension skills. The READING data set described in the Data Appendix gives two pretest measures that were used in this study. Use one-way ANOVA to analyze these data and write a summary of your results.

Reading Data:

subject group   pre1    pre2    post1   post2   post3
1       B       4       3       5       4       41
2       B       6       5       9       5       41
3       B       9       4       5       3       43
4       B       12      6       8       5       46
5       B       16      5       10      9       46
6       B       15      13      9       8       45
7       B       14      8       12      5       45
8       B       12      7       5       5       32
9       B       12      3       8       7       33
10      B       8       8       7       7       39
11      B       13      7       12      4       42
12      B       9       2       4       4       45
13      B       12      5       4       6       39
14      B       12      2       8       8       44
15      B       12      2       6       4       36
16      B       10      10      9       10      49
17      B       8       5       3       3       40
18      B       12      5       5       5       35
19      B       11      3       4       5       36
20      B       8       4       2       3       40
21      B       7       3       5       4       54
22      B       9       6       7       8       32
23      D       7       2       7       6       31
24      D       7       6       5       6       40
25      D       12      4       13      3       48
26      D       10      1       5       7       30
27      D       16      8       14      7       42
28      D       15      7       14      6       48
29      D       9       6       10      9       49
30      D       8       7       13      5       53
31      D       13      7       12      7       48
32      D       12      8       11      6       43
33      D       7       6       8       5       55
34      D       6       2       7       0       55
35      D       8       4       10      6       57
36      D       9       6       8       6       53
37      D       9       4       8       7       37
38      D       8       4       10      11      50
39      D       9       5       12      6       54
40      D       13      6       10      6       41
41      D       10      2       11      6       49
42      D       8       6       7       8       47
43      D       8       5       8       8       49
44      D       10      6       12      6       49
45      S       11      7       11      12      53
46      S       7       6       4       8       47
47      S       4       6       4       10      41
48      S       7       2       4       4       49
49      S       7       6       3       9       43
50      S       6       5       8       5       45
51      S       11      5       12      8       50
52      S       14      6       14      12      48
53      S       13      6       12      11      49
54      S       9       5       7       11      42
55      S       12      3       5       10      38
56      S       13      9       9       9       42
57      S       4       6       1       10      34
58      S       13      8       13      1       48
59      S       6       4       7       9       51
60      S       12      3       5       13      33
61      S       6       6       7       9       44
62      S       11      4       11      7       48
63      S       14      4       15      7       49
64      S       8       2       9       5       33
65      S       5       3       6       8       45
66      S       8       3       4       6       42

Solutions

Expert Solution

Use Excel and enter the data as given in question:

Then use the following steps:

Click on Data Tab --> Data Analysis --> Anova: Single Factor -->In input range, select all the 5 column data containing pre1, pre2, post1, post2 and post3 columns --> Choose 'Columns' in Grouped by option --> Tick the labels checkbox -->Select output range and specify a cell where result should be displayed ---> Click ok

The result is:

Anova: Single Factor

SUMMARY

Groups

Count

Sum

Average

Variance

pre1

66

646

9.787879

9.123543

pre2

66

337

5.106061

4.89627

post1

66

533

8.075758

11.51725

post2

66

443

6.712121

6.94662

post3

66

2905

44.01515

44.13823

ANOVA

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

71493.16

4

17873.29

1166.33

2.6E-191

2.399432

Within Groups

4980.424

325

15.32438

Total

76473.59

329

As the p-value = 2.6 E-191 << 0.05, we reject H0 (the null hypothesis) and conclude that the results are significant. Hence, there is a significant difference between the three groups of children in terms of their comprehension skills.


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