Assignment 14b -------------- Two-factor ANOVA Subjects are given sentences to read, and the time needed for reading is recorded. Four sorts of sentences are investigated: a. Subject relative, animate NP: 'Dat is de man die de vrouwen zag' That's the man who saw the wormen b. Object relative, animate NP: 'Dat zijn de vrouwen die de man zag' Those are the women who the man saw. c. Subject relative, inanimate NP: 'Dat is de man die de stoelen zag' That's the man who saw the chairs. d. Object relative, inanimate NP: 'Dat zijn de stoelen die de man zag' Those are the chairs which the man saw. Sentences are organized in groups of four, and each sentence type is represented in each group. The order in which sentences are presented is varied, however. Four orders are used: abcd, bcda, cdab en dabc. Each order is called a 'list', so there are four lists. Reaction times are recorded for 16 groups of four subjects each and these are presented in the table below. (Source: Edith Kaan en Lau- rie Stowe, Developing an Experiment, 1995. Techniques and Design, Klapper vakgroep Taalwetenschappen, Rijksuniversiteit Groningen): ----------------------------- Sentence Type ----------------------------- List a b c d ----------------------------- 1 461 789 478 646 245 368 336 564 846 901 753 827 976 948 653 824 2 567 890 639 987 318 431 302 357 567 489 371 598 689 543 782 334 3 432 937 480 789 658 698 352 599 478 498 447 955 571 389 434 578 4 578 486 307 778 769 777 543 659 389 447 787 680 518 324 349 448 The data must be entered by hand. Define three columns and use as suitable variable names. a. ANOVA requires that the populations are distributed normally and that their standard deviations are roughly the same. Drawing all of the 16 normal quantile plots is normally required, but we will skip the step here to use laboratory time more effectively. b. Compute the means and standard deviations of the four observations in each of the groups (list/stype). What is the relation between the smallest and the largest standard deviation? Can we apply the two-factor ANOVA? c. Formulate H_0 and H_a for the main effect of sentence type. d. Formulate H_0 and H_a for the main effect of list. e. Formulate H_0 and H_a for the interaction sentence-type*list. f. Compute the two-factor ANOVA-table. Report which of the main effects (c, d) above are significant, whether there is a significant interaction between the main effects (e), and therefore which alternative hypotheses are confirmed. g. We investigate further the possible interaction between sentence type and list. Create a graphic in which the averages are shown. Two successive points must be connected by a straight line. The x-axis shows the lists and the y-axis shows the reaction time. The graphic shows the average reaction time for sentence type a, b, c, and d. What does the graphic show about the averages?