PSY 429 Experimental Psychology

Class Exercise #5

Analysis of Variance

Answers

1.An experiment examined the effects of caffeine on memory. Memory scores were compared between a group given caffeine and a group given a placebo.

a. How many independent variables are there?

1

b. Identify the independent variable(s) and the levels of each.

drug: caffeine and no caffeine (placebo) (2 levels)

c. Identify the dependent variable(s)?

memory scores

d. State the null hypothesis (if only 1) or hypotheses (if more than 1).

 There is only one hypothesis:

There will be no difference in memory scores as a function of the drug.

Stating it another way: Memory scores will not significantly differ between the two groups.

2. A study examined the effects of four doses of a new drug on symptoms of schizophrenia.

a. How many independent variables are there?

1

b. Identify the independent variable(s) and the levels of each.

new drug: dose 1, dose 2, dose 3, dose 4 (4 levels)

c. Identify the dependent variable(s)?

a measure of symptoms of schizophrenia

d. State the null hypothesis (if only 1) or hypotheses (if more than 1).

 There is only one hypothesis:

There will be no difference in symptoms of schizophrenia depending on the dose of the drug.

3. A study compared brain development (i.e. weight of cortex) of rats as a function of the effects of a positive, challenging, and diverse environment (called an enriched environment) with an environment that is relatively impoverished and isolated for two different species of rats, "hooded" rats and "Sprague-Dawley" rats.

a. How many independent variables are there?

2

b. Identify the independent variable(s) and the levels of each.

1) Type of environment: enriched environment and impoverished environment

2) The species of rat used: hooded rats and Sprague-Dawley rats

c. Identify the dependent variable(s)?

weight of cortex

d. State the null hypothesis (if only 1) or hypotheses (if more than 1).

 There are three hypotheses:

1) The type of environment, enriched versus impoverished, will make no difference in the weight of the cortex.

2) The type of rat used, hooded versus Sprague-Dawley rats, will make no difference in the weight of the cortex.

3) There will be no interaction between the type of environment and the species of rat.

4. An experiment was designed to examine the effects of a new antianxiety drug (versus a placebo) on male and female college students who were previously identified as either low or high in text anxiety.

a. How many independent variables are there?

3

b. Identify the independent variable(s) and the levels of each.

1) drug: drug and placebo (2 levels)

2) gender: male and female (2 levels)

3) test anxiety: low and high (2 levels)

c. Identify the dependent variable(s)?

measure of performance on a test

d. State the null hypothesis (if only 1) or hypotheses (if more than 1).

 There are 7 hypotheses:

1) There will be no difference in test scores between subjects given the drug versus those given a placebo.

2) There will be no difference in test scores between male and female.

3) There will be no difference in test scores between low and high anxiety subjects.

4) There will be no 2-way interaction between the drug and gender. In other words, scores on the test under the drug condition will not depend on whether subjects were male or female.

5) There will be no 2-way interaction between the drug and anxiety. In other words, scores on the test under the drug conditon will not depend on whether subjects were low or high anxious.

6) There will be no 2-way interaction between gender and anxiety. In other words, scores on the test for males (or females) will not depend on their level of anxiety.

7) There will be no 3-way interaction between drug, gender, and level of anxiety. In other words, scores on the test under the drug conditon will not depend on gender and level of anxiety.

5. Consider the following scores in an experiment involving three groups, A, B, and C, with five subjects in each group.

Without actually computing the sum of squares error term (SS-error), what must its value be? Why?

 0

SS-error is a measure of the variability within the groups. Since each subject's score is the same within a group, there is no variability within a group.

6. What does a mean square represent in analysis of variance?

 A mean square represents the mean of the x²s. The mean square between groups is an unbiased estimate of s² , the error variance, plus a term that can be zero only when there are no treatment effects at all. If, however, there are treatment effects, then the value of the sample mean square must be an estimate of s² plus any positive quantity reflecting treatment effects.

7. State the critical value of F that would be used to reject the null hypothesis for a one-way between-subjects analysis of variance at an alpha level of .05 under each of the following conditions: See F Table.

a. k = 3, n = 21 F = 3.15

b. k = 4, n = 20 F = 2.76

c. k = 3, n = 30 F = 3.15

d. k = 5, n = 75 F = 2.37

8. In a one-way between-subjects analysis of variance, what are the possible sources of between-groups variability?

 1) treatment effects

2) individual differences

3) error (experimental &/or random)

9. In a one-way between-subjects analysis of variance, what are the possible sources of within-groups variability?

 1) individual differences

2) error (experimental &/or random)

9. Under what circumstances will the F ratio, over the long run, approach 1.00? Under what circumstances will the F ratio, over the long run, be greater than 1.00?

 The F ratio will, over the long run, approach 1.00 when the null hypothesis is true and there is no difference between groups.

The F ratio will, over the long run, be greater than 1.00 when the null hypothesis is not true and there is a difference between groups.

10. Complete the missing entries in the ANOVA summary table for a one-way analysis of variance having 3 levels of the independent variable and n = 30 per group.

11. Complete the missing entries in the ANOVA summary table for a one-way analysis of variance having 4 levels of the independent variable.

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