Question 1

If the results of an experiment using a one-factor between-subjects analysis of variance were reported as F(4, 70) = 2.96, p < .05, then you can determine that.

Accepted Answer

F(4, 70) = 2.96 indicates that the observed F-value was 2.96. The significance level (p-value) is less than .05, which means that the observed F-value is statistically significant. The critical F-value would depend on the alpha level chosen for the test, but we cannot determine it from the information given. The total number of subjects is not given by this information.

Question 2

For a one-factor between-subjects analysis of variance, η2 is obtained by dividing SSA by .

Accepted Answer

η^2 (eta squared) is calculated by dividing the sum of squares between groups (SSA) by the total sum of squares (SSTotal) to measure the effect size in an ANOVA.

Question 3

If the results of an experiment using a one-factor between-subjects analysis of variance were summarized as F(2, 12) = 2.24, p > .05, then you know that the experiment used subjects and the Fobs was.

Accepted Answer

The notation F(2, 12) indicates that there were 2 degrees of freedom between groups and 12 degrees of freedom within groups, which suggests there were 15 subjects in total (since degrees of freedom within groups are calculated based on the total number of subjects minus the number of groups). The F observed (Fobs) value of 2.24 with a p-value greater than .05 indicates that the result is nonsignificant, meaning there is not enough evidence to suggest a difference between the groups.

Question 4

The value of q for the Tukey HSD test depends upon the level of alpha, the number of means involved in the comparisons, and.

Accepted Answer

The value of q for the Tukey HSD test depends on the level of alpha, the number of means involved in the comparisons, and the degrees of freedom for the Mean Square Error (MSError), which is used to estimate the variability within groups.

Question 5

When computed from a one-factor between-subjects analysis of variance, η2 is defined as the sums of squares associated with the independent variable divided by the sums of squares for.

Accepted Answer

η2 is defined as the ratio of the sums of squares associated with the independent variable (i.e., the numerator) to the total sums of squares (i.e., the denominator). Therefore, the correct choice is A, which represents the total sums of squares only.

Question 6

Eta squared for a one-factor between-subjects analysis of variance is a measure of the.

Accepted Answer

Eta squared is a measure of the strength of effect of an independent variable in a one-factor between-subjects analysis of variance. It tells us how much of the variability in the dependent variable can be attributed to the independent variable.

Question 7

If SSTotal is 100, SSA is 20 and SSError is 80 for a one-factor between-subjects analysis of variance, then η2 is.

Accepted Answer

The answer of If SSTotal is 100, SSA is 20...

Question 8

If the results of an experiment using the one-factor between-subjects analysis of variance were summarized as F(2, 30) = 2.46, p > .05, then you would know that the number of levels of factor A was.

Accepted Answer

The notation F(2, 30) indicates that there are 2 degrees of freedom for the factor (between groups) and 30 degrees of freedom for the error (within groups). The degrees of freedom for the factor are calculated as the number of levels of the factor minus 1. Therefore, if there are 2 degrees of freedom for the factor, it means there were 3 levels of factor A (2 + 1 = 3).

Question 9

Post hoc comparisons for a one-factor between-subjects analysis of variance may be made using the.

Accepted Answer

The most commonly used post hoc comparison test for a one-factor between-subjects ANOVA is the Tukey HSD (Honestly Significant Difference) test. This test is designed to control for Type I error inflation and allows for pairwise comparisons between all groups while adjusting for the overall error rate. Therefore, the correct answer is C (Tukey HSD test).

Question 10

The probability of making at least one Type I error when performing multiple comparisons is called the rate in an experiment.

Accepted Answer

The probability of making at least one Type I error when performing multiple comparisons is referred to as the error rate in an experiment.

Question 11

If the critical difference for the Tukey test equals 3 for α equal to .05, then a difference between means of 10 and 5 for two groups is ,.

Accepted Answer

The Tukey test is used to determine if there are statistically significant differences between the means of multiple groups. The critical difference is the minimum amount that the means of two groups must differ by in order to be considered statistically significant. In this case, the critical difference is 3 for α = .05. Since the difference between the means of the two groups (10 - 5 = 5) is greater than 3, the difference is statistically significant with p < .05. Therefore, the correct answer is D, statistically significant; p < .05.

Question 12

The error rate in an experiment is the probability of making at least one in the statistical tests conducted on the data.

Accepted Answer

The error rate described in the statement is the probability of making a Type I error, which is rejecting a true null hypothesis.

Question 13

Eta squared represents the proportion of total variation in scores accounted for by.

Accepted Answer

Eta squared is a measure of effect size used in ANOVA to determine the proportional reduction of variability in the dependent variable due to the effect of the independent variable. Therefore, the best choice is B - the independent variable.

Question 14

In which of the following instances is a post hoc test needed?

Accepted Answer

When a statistically significant Fobs is obtained in an experiment with multiple levels of an independent variable, a post hoc test is needed to determine which specific levels differ significantly from each other. In this case, the experiment has four levels of an independent variable, so a post hoc test would be necessary.

Question 15

If the results of an experiment using a one-factor between-subjects analysis of variance were summarized as F(3, 32) = 4.06, p < .05, then you would know that the number of levels of factor A was .

Accepted Answer

The notation F(3, 32) indicates an F statistic where the first number (3) represents the degrees of freedom for the factor (which is one less than the number of levels), and the second number (32) represents the degrees of freedom for error. Since the degrees of freedom for the factor is 3, it means there were 4 levels of factor A (3 + 1).

Question 16

If the critical difference for the Tukey test equals 3 for α equal to .05, then a difference between means of 10 and 8 for two groups is ,.

Accepted Answer

The critical difference is 3, which means that any difference between means that is less than 3 is not statistically significant at the α level of .05. The difference between means of 10 and 8 is 2, which is smaller than the critical difference of 3. Therefore, the difference is nonsignificant and p > .05.

Question 17

Post hoc comparisons are.

Accepted Answer

Post hoc comparisons are conducted if Fobs is significant in a multilevel analysis of variance. It is done to determine which specific group means differ from each other.

Question 18

If the results of an experiment using the one-factor between-subjects analysis of variance were summarized as F(2, 30) = 2.46, p > .05, then you would know that the total number of subjects used (N) was and the null hypothesis was .

Accepted Answer

The degrees of freedom for the total number of subjects is calculated as the sum of the degrees of freedom for the groups and the error term: (2 + 30 + 1 = 33). Since p > .05, the null hypothesis was not rejected.

Question 19

If Fobs for a one-factor between-subjects design with two levels of the independent variable equals 4.00, then the value of tobs that would be obtained on the same set of scores is.

Accepted Answer

In a one-factor between-subjects design with two levels, the F-ratio (Fobs) is the square of the t-value (tobs) when comparing two means. Therefore, if Fobs = 4.00, then tobs = sqrt(4.00) = 2.00.

Quiz 10: One-Factor Between-Subjects Analysis of Variance