Chapter 7 - Module 13 & 14

Question 1

Why do we use designs with three or more levels of an independent variable ?

Answer 1

First, it allows them to compare multiple treatments. Second, it allows them to compare multiple treatments to no treatment (the control group). Third, more complex designs allow researchers to compare a placebo group to control and experimental groups. Another advantage of comparing more than two kinds of treatment in one experiment is that it reduces both the number of experiments conducted and the number of subjects needed.

Question 2

What is one way of counteracting the increased chance of a type 1 error?

Answer 2

The Bonferroni adjustment:
A means of setting a more stringent alpha level in order to minimize Type I errors. (But not the best method!!) ANOVA is the way that we counteract this error.

Question 3

What is the main point of using more than two groups in an experiment?

Answer 3

Using more than two groups in an experiment also allows researchers to determine whether each treatment is more or less effective than no treat- ment (the control group). In summary, adding levels to the independent variable allows us to determine more accurately the type of relationship that exists between the variables.

Question 4

What is a ANOVA?

Answer 4

An inferential parametric statistical test for comparing the means of three or more groups.

Question 5

What is a one-way between subjects ANOVA?

Answer 5

An inferential statistical test for comparing the means of three or more groups using a between-subjects design. The term one-way indicates that the design uses only one indepen- dent variable.

Question 6

What happens when you reject the HO in a ANOVA? What happens when you fail to reject the HO in a ANOVA?

Answer 6

When a researcher rejects H0 using an ANOVA, it means that the indepen- dent variable affected the dependent variable to the extent that at least one group mean differs from the others by more than would be expected based on chance. Failing to reject H0 indicates that the means do not differ from each other more than would be expected based on chance. In other words, there is not enough evidence to suggest that the sample means represent at least two different populations

Question 7

What is error variance and how is it estimated?

Answer 7

The amount of variability among the scores caused by chance or uncontrolled variables. The amount of error variance can be estimated by looking at the amount of variability within each condition.

Question 8

What is within-group variance?

Answer 8

The variance within each condition; an estimate of the population error variance.

Question 9

What happens when the IV has no effect or an effect? (In terms of variance)

Answer 9

If there were no effect of the independent variable, then the variance between groups would be due to error (means close to the grand mean). If the independent vari- able (rehearsal type) had an effect, we would expect some of the group means to differ from the grand mean but changes are due to the independent variable.

Question 10

Between group variance

Answer 10

In sum, be- tween-groups variance is an estimate of systematic variance (the effect of the independent variable and any confounds) and error variance]

Question 11

What is an f-ratio? What does the f-ratio formula mean?

Answer 11

The ratio of between groups variance to within groups variance.

F = Between group variance / within group variance

F = (systemic variance + error variance) / error variance

In sum, be- tween-groups variance is an estimate of systematic variance (the effect of the independent variable and any confounds) and error variance.

Question 12

What are the two points to remember about F-ratios?

Answer 12

First, in order for an F-ratio to be significant (show a statis- tically meaningful effect of an independent variable), it must be substantially greater than 1 (we will discuss exactly how much larger than 1 in the next module). Second, if an F-ratio is approximately 1, then the between-groups variance equals the within-groups variance and there is no effect of the inde- pendent variable.

Question 13

Null hypothesis and Alternative hypothesis for the one way ANOVA:

Answer 13

HO: The independent variable had no effect—the samples all represent the same population

HA: The independent variable had an effect—at least one of the samples represents a different population than the others

Question 14

What are the total sum of squares for a one-way anova?

Answer 14

The sum of the squared deviations of each score from the grand mean. In other words, we determine how much each individual subject varies from the grand mean, square that deviation score, and sum all of the squared deviation scores.

Question 15

What is the within-groups sum of squares?

Answer 15

The sum of the squared deviations of each score from its group mean. (compare each score in each condition to the mean of that condition)

Question 16

What is the between-groups sum of squares?

Answer 16

The sum of the squared deviations of each group’s mean from the grand mean, multiplied by the number of subjects in each group. The basic idea behind the between-groups sum of squares is that if the independent variable had no effect (if there were no differences between the groups), then we would expect all the group means to be about the same. If all the group means were similar, they would also be approximately equal to the grand mean and there would be little variance across conditions. If, however, the independent variable caused changes in the means of some con- ditions (caused them to be larger or smaller than other conditions), then the condition means not only will differ from each other but will also differ from the grand mean, indicating variance across conditions.

Question 17

What is a mean square?

Answer 17

An estimate of either variance between groups
or variance within groups

Question 18

What is eta-squared?

Answer 18

An inferential statistic for measuring effect size with an ANOVA. indicates how accurately the differences in scores can be pre- dicted using the levels (conditions) of the independent variable.

Question 19

Assumptions of a one-way ANOVA?

Answer 19

1. The data are on an interval-ratio scale.
2. The underlying distribution is normally distributed.
3. The variances among the populations being compared are
   homogeneous

Because ANOVA is a robust statistical test, violations of some of these as- sumptions do not necessarily affect the results. Specifically, if the distribu- tions are slightly skewed rather than normally distributed, it does not affect the results of the ANOVA. In addition, if the sample sizes are equal, the as- sumption of homogeneity of variances can be violated. However, it is not ac- ceptable to violate the assumption of interval-ratio data. If the data collected in a study are ordinal or nominal in scale, other statistical procedures must be used. These procedures are discussed in later modules.

Question 20

What is a post-hoc test?

Answer 20

When used with an ANOVA, a means of comparing all possible pairs of groups to determine which ones differ significantly from each other. A post hoc test is designed to permit multiple comparisons and still maintain alpha (the probability of a Type I error) at .05.

Question 21

CRITICAL THINKING: MODULE 14 QUESTION 1: Of the following four F-ratios, which appears to indicate that the independent variable had an effect on the dependent variable?
1.25/1.11
b. 0.91/1.25
c. 1.95/0.26
d. 0.52/1.01

Answer 21

The F-ratio 1.95/0.26 5 7.5 suggests that the independent variable had an effect on the depen- dent variable.

Question 22

CRITICAL THINKING MODULE 14 QUESTION 2: The following ANOVA summary table represents the results from
a study on the effects of exercise on stress. There were three conditions in the study: a control group, a moderate exercise group, and a high exercise group. Each group had 10 subjects and the mean stress levels for each group were Control 5 75.0, Moderate Exercise 5 44.7, and High Exercise 5 63.7. Stress was measured

Answer 22

The resulting F-ratio is less than 1 and thus not sig- nificant. Although stress levels differed across some of the groups, the difference was not large enough to be significant.