Laboratory Exercise 5: ANOVA ---------------------------- One-way ANOVA (ANOVA-table, Contrast) Examining the reading skills of children in the U.S., three methods of education were compared. Several variables were measured before the lessons started. One of the goals of the pretest was to see whether the three groups of children had similar cognitive capacities. One of its variables gave an indication of the "ability of reading garbled sentences", which measures a certain kind of text comprehension. The data for the 22 subjects are given below. The three types of education are called (B)asal, (D)irected Reading as Thinking Activity en (S)trategies. (Source: research done by Jim Baumann and Leah Jones from the School of Education of Purdue University.) Group B D S ---------------- 4 7 11 6 7 7 9 12 4 12 10 7 16 16 7 15 15 6 14 9 11 12 8 14 12 13 13 8 12 9 13 7 12 9 6 13 12 8 4 12 9 13 12 9 6 10 8 12 8 9 6 12 13 11 11 10 14 8 8 8 7 8 5 9 10 8 a. Draw for each group a boxplot. An ANOVA test compares averages, boxplots show medians. If the two distributions are nearly symmetric, both central measures will display nearly the same values. However, if the number of observations is low, and the variables values are not very diverse, boxplots are not very accurate. b. Give a one-way ANOVA table. Formulate H_0 and H_a. What is your conclusion? c. Give for each group (B, D, and S) the mean and the standard deviation. What is the ratio between the biggest and the smallest standard deviation? Are the results from the ANOVA table reliable? d. Analyse the contrasts '(D and S) vs. B' (contrast1) and 'D vs. S' (contrast 2). Check with contrast1 whether (D and S) have higher average scores than B. Check with contrast2 whether the average scores of D are not equal to the average scores of S. Give for both contrasts H_0 and H_a, the t-value, the p-value, and the conclusion. e. Perform a Bonferri-test with alfa=0.05. Of which groups-pairs are the members significantly different?