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?