Laboratory Exercise 5: ANOVA
----------------------------

One-way ANOVA

(ANOVA-table, Contrasts, Bonferonni)

In a "lexical decision task" subjects are shown words and non-words
on a computer screen.  The subject must decide whether a string of
letters he is shown is or is not a word.  The time needed is the 
reaction time, also known as the lexical decision time.  The subjects
were divided into groups depending on their age: six, eight and
ten years old.  Each group comprised nine subjects.  The table 
below shows the reaction times. 

              
Age      6      8     10
        -----------------
        710    710    700
        899    850    800
        860    760    720
        900    722    650
        752    726    780
        785    800    800
        850    690    820
        850    750    820
        920    825    700

The data may be found in z:\public\share\heeringa\lexi.txt. Read this
file in, define two columns and use the column names 'age' and 'time'.

a. ANOVA assumes that the populaties are roughly normal and that
   the standard deviations are approximately the same.  Draw a 
   normal-quantile plot for each group.  Are they roughly normal?

b. Give for each group (6, 8, and 10) 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?

c. Formulate H_0 and H_a.  Produce a one-way ANOVA table. What is your
   conclusion?

d. Analyse the contrast '(8 and 10) vs. 6'.  Test whether eight- and
   ten-year olds lower average reaction times than six-year olds.
   Formulate H_0 and H_a, and report the t-value, the p-value, and the
   conclusion.

e. Analyse the contrasts '8 vs. 10.  Test whether eight- and
   ten-year olds have roughly the same average reaction times.
   Formulate H_0 and H_a, and report the t-value, the p-value, and the
   conclusion.

f. Perform a Bonferri-test with alfa=0.05. For which age-group pairs are
   the members significantly different?