Question 1

When participant responding is not consistent,the one-way within-subjects ANOVA can actually have less power to detect an effect than the one-way between-subjects ANOVA.

Accepted Answer

This is true. When there is inconsistency in participant responding, the within-subjects ANOVA may have greater error variance, which will decrease the power of the test to detect true differences between conditions. In contrast, the between-subjects ANOVA assumes that each subject represents a unique level of the independent variable, and therefore individual variability is not confounded with the effects of the independent variable. This can result in a more powerful test, particularly if the individual differences are large enough that they obscure the effects of the independent variable in the within-subjects design.

Question 2

The test statistic for a one-way within-subjects ANOVA is mean square between groups divided by mean square error.

Accepted Answer

In a one-way within-subjects ANOVA, the test statistic is indeed calculated by dividing the mean square between groups (MSB) by the mean square error (MSE), which quantifies the variability between the different conditions relative to the variability within the conditions.

Question 3

Mean square error is the denominator for all one-way ANOVA tests.

Accepted Answer

In one-way ANOVA tests, mean square error is used as the denominator when calculating the F-ratio.

Question 4

The Bonferroni test is not an appropriate post hoc test following a significant one-way within-subjects ANOVA.

Accepted Answer

The Bonferroni test can be used as a post hoc test following a significant one-way within-subjects ANOVA to control for Type I error across multiple comparisons, although it is conservative and may reduce statistical power.

Question 5

$\eta$² is a more conservative measure of proportion of variance than partial $\eta$².

Accepted Answer

"Conservative" in statistical terms means tending to underestimate the true value. A more conservative measure of proportion of variance would give a smaller value than the actual proportion of variance. In comparison, partial measures tend to be less conservative and more accurate. Therefore, the statement in the question is true.

Question 6

As mean square error decreases,power decreases.

Accepted Answer

Mean square error (MSE) is a measure of the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. A decrease in MSE indicates an improvement in the accuracy of the estimates. Power, in statistical terms, refers to the probability that the test correctly rejects a false null hypothesis (i.e., detects an effect when there is one). The power of a test is influenced by several factors, including the sample size, the effect size, and the significance level, but not directly by the mean square error of the estimates.

Question 7

To summarize the one-way within-subjects ANOVA,we report the test statistic,the degrees of freedom,and the critical values.

Accepted Answer

In reporting the results of a one-way within-subjects ANOVA, we typically include the test statistic (F-value), degrees of freedom (df), and the p-value, not the critical values. Critical values are used during analysis to determine significance, but p-values are reported to indicate whether the results are statistically significant.

Question 8

Partial estimates of proportion of variance are used for a one-way between-subjects ANOVA.

Accepted Answer

Partial estimates of proportion of variance, such as partial eta squared, are used in factorial ANOVA designs, not in a one-way between-subjects ANOVA. In a one-way ANOVA, the total variance is partitioned into between-group and within-group variance.

Question 9

To report the results of a post hoc test,identify which post hoc test was computed and the p value for significant results.

Accepted Answer

To report the results of a post hoc test, it is necessary to identify which post hoc test was used and the corresponding p value for significant results. This is important as it allows for interpretation of the significance of the differences found between groups after controlling for Type I error.

Question 10

The mean square for each source of variation is a measure of the mean distance that scores deviate from their mean.

Accepted Answer

The mean square for each source of variation is a measure of variance within groups or between groups, not a measure of the mean distance that scores deviate from their mean.

Question 11

The formula for partial $\eta$² and partial $\omega$² removes the sum of squares within groups from the total sum of squares.

Accepted Answer

The formula for partial F-tests in the context of statistical analysis typically involves comparing the reduction in the residual sum of squares (RSS) when additional predictors are included in a model. It does not directly involve removing the sum of squares within groups from the total sum of squares; instead, it focuses on the improvement in model fit by including additional variables.

Question 12

The between-persons variation is measured in the one-way within-subjects ANOVA.

Accepted Answer

The answer of The between-persons variation is measured in the...

Question 13

If participant responding is consistent between groups,then the one-way within-subjects ANOVA will have higher power to detect an effect compared with the one-way between-subjects ANOVA.

Accepted Answer

Within-subjects ANOVA has higher power than between-subjects ANOVA because it controls for individual differences and reduces error variability. When participant responding is consistent between groups, within-subjects ANOVA can use this consistency as a baseline to detect smaller effects. In contrast, between-subjects ANOVA treats participants as independent, and any variability between participants is included in the error term, reducing power to detect an effect.

Question 14

The Bonferroni test controls for testwise alpha.

Accepted Answer

The Bonferroni test is a multiple comparison correction method that adjusts the alpha level to control for the probability of making one or more type I errors when conducting multiple statistical tests. It does this by dividing the original alpha level by the number of comparisons being made, resulting in a more conservative alpha level for each individual test. This method helps to control for testwise alpha, as it reduces the risk of falsely rejecting the null hypothesis in any single test.

Question 15

With a small number of comparisons,the Bonferroni test is an appropriate post hoc test following a significant one-way within-subjects ANOVA.

Accepted Answer

The Bonferroni test is a commonly used post hoc test that is appropriate for controlling the family-wise error rate (i.e., the probability of making at least one type I error) following a significant one-way within-subjects ANOVA. Additionally, the Bonferroni test requires a small number of comparisons to be effective, which makes it a popular choice for post hoc testing in many research studies. Therefore, the statement is true.

Question 16

The Bonferroni test controls for experimentwise alpha.

Accepted Answer

The answer of The Bonferroni test controls for experimentwise alpha....

Question 17

We make two hypothesis tests using the one-way within-subjects ANOVA: one for the between-groups effect and one for the within-groups effect.

Accepted Answer

The one-way within-subjects ANOVA only allows for testing the within-groups effect, as it compares the variation within each group to the variation between the groups. There is no separate test for the between-groups effect.

Question 18

A one-way within-subjects ANOVA would be an appropriate statistical test when n participants are observed k times.

Accepted Answer

A one-way within-subjects ANOVA is used when the same group of participants is observed or measured multiple times under different conditions or treatments. It is appropriate when there are repeated measures or dependent samples. Therefore, when n participants are observed k times, a one-way within-subjects ANOVA would be an appropriate statistical test.

Question 19

Partial $\eta$² is a more conservative measure of proportion of variance than $\eta$².

Accepted Answer

Partial $\eta$² is not more conservative; it typically gives a larger estimate of effect size compared to $\eta$² because it accounts for variance explained by other factors in the model.

Question 20

Consistency refers to the extent to which the dependent measure changes in an identifiable or predictable pattern across groups.

Accepted Answer

Consistency refers to a consistent pattern of changes in the dependent measure that can be identified and predicted across different groups or conditions. In other words, if the same test, task or measure is repeated with different individuals or groups, the results should show a consistent pattern or trend that is predictable and reliable.

Quiz 13: Analysis of Variance: One-Way Within-Subjects Repeated-Measuresdesign

When participant responding is not consistent,the one-way within-subjects ANOVA can actually have less power to detect an effect than the one-way between-subjects ANOVA.

The test statistic for a one-way within-subjects ANOVA is mean square between groups divided by mean square error.

Mean square error is the denominator for all one-way ANOVA tests.

The Bonferroni test is not an appropriate post hoc test following a significant one-way within-subjects ANOVA.

$\eta$ ² is a more conservative measure of proportion of variance than partial $\eta$ ².

As mean square error decreases,power decreases.

To summarize the one-way within-subjects ANOVA,we report the test statistic,the degrees of freedom,and the critical values.

Partial estimates of proportion of variance are used for a one-way between-subjects ANOVA.

To report the results of a post hoc test,identify which post hoc test was computed and the p value for significant results.

The mean square for each source of variation is a measure of the mean distance that scores deviate from their mean.

The formula for partial $\eta$ ² and partial $\omega$ ² removes the sum of squares within groups from the total sum of squares.

The between-persons variation is measured in the one-way within-subjects ANOVA.

If participant responding is consistent between groups,then the one-way within-subjects ANOVA will have higher power to detect an effect compared with the one-way between-subjects ANOVA.

The Bonferroni test controls for testwise alpha.

With a small number of comparisons,the Bonferroni test is an appropriate post hoc test following a significant one-way within-subjects ANOVA.

The Bonferroni test controls for experimentwise alpha.

We make two hypothesis tests using the one-way within-subjects ANOVA: one for the between-groups effect and one for the within-groups effect.

A one-way within-subjects ANOVA would be an appropriate statistical test when n participants are observed k times.

Partial $\eta$ ² is a more conservative measure of proportion of variance than $\eta$ ².

Consistency refers to the extent to which the dependent measure changes in an identifiable or predictable pattern across groups.

Quiz 13: Analysis of Variance: One-Way Within-Subjects Repeated-Measuresdesign

When participant responding is not consistent,the one-way within-subjects ANOVA can actually have less power to detect an effect than the one-way between-subjects ANOVA.

The test statistic for a one-way within-subjects ANOVA is mean square between groups divided by mean square error.

Mean square error is the denominator for all one-way ANOVA tests.

The Bonferroni test is not an appropriate post hoc test following a significant one-way within-subjects ANOVA.

η\etaη 2 is a more conservative measure of proportion of variance than partial η\etaη 2.

As mean square error decreases,power decreases.

To summarize the one-way within-subjects ANOVA,we report the test statistic,the degrees of freedom,and the critical values.

Partial estimates of proportion of variance are used for a one-way between-subjects ANOVA.

To report the results of a post hoc test,identify which post hoc test was computed and the p value for significant results.

The mean square for each source of variation is a measure of the mean distance that scores deviate from their mean.

The formula for partial η\etaη 2 and partial ω\omegaω 2 removes the sum of squares within groups from the total sum of squares.

The between-persons variation is measured in the one-way within-subjects ANOVA.

If participant responding is consistent between groups,then the one-way within-subjects ANOVA will have higher power to detect an effect compared with the one-way between-subjects ANOVA.

The Bonferroni test controls for testwise alpha.

With a small number of comparisons,the Bonferroni test is an appropriate post hoc test following a significant one-way within-subjects ANOVA.

The Bonferroni test controls for experimentwise alpha.

We make two hypothesis tests using the one-way within-subjects ANOVA: one for the between-groups effect and one for the within-groups effect.

A one-way within-subjects ANOVA would be an appropriate statistical test when n participants are observed k times.

Partial η\etaη 2 is a more conservative measure of proportion of variance than η\etaη 2.

Consistency refers to the extent to which the dependent measure changes in an identifiable or predictable pattern across groups.

$\eta$ ² is a more conservative measure of proportion of variance than partial $\eta$ ².

The formula for partial $\eta$ ² and partial $\omega$ ² removes the sum of squares within groups from the total sum of squares.

Partial $\eta$ ² is a more conservative measure of proportion of variance than $\eta$ ².