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?