STA221H1 Lecture Notes - Lecture 70: Factorial Experiment, Multiple Comparisons Problem, Analysis Of Variance
29 Apr 2018
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Textbook Exercises Set 52
10.95 Learning from picture book reading. Developmental Psychology published an article that
examined toddlers’ ability to learn from reading picture books. The experiment involved 36
children at each of three different ages: 18, 24, and 30 months. The children were randomly
assigned into one of three different reading book conditions: book with color photographs
(Photos), book with colored pencil drawings (Drawings), and book with no photographs or
drawing (Control). Thus, a 3 * 3 factorial experiment was employed (with age at three levels and
reading book condition at three levels). After a book-reading session, the children were scored
on their ability to reenact the target actions in the book. Scores ranged from 0 (low) to 3 (high).
An ANOVA of the reenactment scores is summarized in the following table:
a. Fill in the missing degrees-of-freedom (df) values in the table.
Age df = a – 1 = 3 – 1 = 2!
Book df = b – 1 = 3 – 1 = 2!
Age x Book df = (a – 1) (b – 1) = 4!
Error df = n – ab = 108 – 9 = 99!
Correct - 2 + 2 + 4 + 99 = 107 (= total df)!
b. How many treatments are investigated in this experiment? List them.
3 x 3 = 9 treatments (18 months / photos, 24 months / photos, 30 months / photos, 18 months /
drawings, 24 months / drawings, 30 months / drawings, 18 months / control, 24 months / control, 30
months / control)!
c. Conduct a test for Age * Book interaction at a = .05. Interpret the result practically.
We can conclude that the effect of age on average score (on ability to reenact actions in book)
depends on the type of book. That is, the mean difference in score between 18, 24 and 30 month
toddlers differ among different book types. (vice versa is also correct, where age and type of book are
swapped in the above statement.)!
d. On the basis of the test you conducted in part c, do you need to conduct tests for Age and
Book main effects? Explain.
No. We conduct tests for main effects only if the test for the interaction effect fails.!
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Document Summary
Developmental psychology published an article that examined toddlers" ability to learn from reading picture books. The experiment involved 36 children at each of three di erent ages: 18, 24, and 30 months. The children were randomly assigned into one of three di erent reading book conditions: book with color photographs (photos), book with colored pencil drawings (drawings), and book with no photographs or drawing (control). Thus, a 3 * 3 factorial experiment was employed (with age at three levels and reading book condition at three levels). After a book-reading session, the children were scored on their ability to reenact the target actions in the book. Scores ranged from 0 (low) to 3 (high). An anova of the reenactment scores is summarized in the following table: fill in the missing degrees-of-freedom (df) values in the table. Age df = a 1 = 3 1 = 2. Book df = b 1 = 3 1 = 2.
