Question 1

Two measures of proportion of variance for the one-way between-subjects ANOVA are $\eta$² and $\omega$².

Accepted Answer

These measures are known as eta squared (η²) and omega squared (ω²), which are commonly used to assess the proportion of variance accounted for by the independent variable in a one-way ANOVA analysis.

Question 2

A researcher has the same 18 participants rate 6 pictures (k = 6),each depicting a person with a different body type.The one-way between-subjects ANOVA is the most appropriate test for this design.

Accepted Answer

The design described involves repeated measures (the same participants rating all 6 pictures), making a one-way repeated measures ANOVA or a related non-parametric test more appropriate than a one-way between-subjects ANOVA, which is used when different participants are in each group.

Question 3

A significant ANOVA indicates that all pairs of group means significantly differ.

Accepted Answer

A significant ANOVA only indicates that there is at least one group mean that significantly differs from at least one other group mean, but it does not necessarily mean that all pairs of group means significantly differ. Post-hoc tests or pairwise comparisons are needed to determine which specific pairs of means are significantly different.

Question 4

All post hoc tests control for the effect size of a significant result.

Accepted Answer

Post hoc tests are used to determine which pairwise comparisons between groups are significant after an overall significant result has been found in an ANOVA. They do not necessarily control for effect size, but rather compare means to determine if there are statistically significant differences between groups.

Question 5

A mean square is a sample variance.

Accepted Answer

A mean square is calculated by dividing the sum of squared differences by the degrees of freedom, which is the formula used to calculate sample variance. Therefore, a mean square is a type of sample variance.

Question 6

The test statistic for a one-way between-subjects ANOVA is the sum of squares between groups divided by the sum of squares error.

Accepted Answer

The test statistic for a one-way between-subjects ANOVA is the F statistic, which is calculated by dividing the mean square between groups by the mean square error. The F statistic is used to determine whether there is a significant difference in means between groups.

Question 7

The numerator of the test statistic for a one-way between-subjects ANOVA is the mean variability associated with error.

Accepted Answer

The numerator of the test statistic for a one-way between-subjects ANOVA is the mean variability between group means, not the mean variability associated with error. The denominator of the test statistic is the mean variability associated with error.

Question 8

To compute a mean square,we divide the sum of squares by the degrees of freedom for a given source of variation.

Accepted Answer

This is the formula used to compute the mean square in ANOVA. The mean square is the sum of squares divided by the degrees of freedom for a particular source of variation.

Question 9

To conduct a one-way between-subjects ANOVA,we assume that the samples were randomly selected from populations with equal variances,and that participants were independently observed in each group.

Accepted Answer

Assuming random selection and independence of observations in each group are key assumptions for conducting a one-way between-subjects ANOVA. Additionally, equal variances across the populations is another assumption.

Question 10

Cohen's d is the most commonly reported measure of effect size for the one-way between-subjects ANOVA.

Accepted Answer

Cohen's d is commonly reported for t-tests and can also be used for comparing two group means. However, for one-way between-subjects ANOVA, eta-squared or partial eta-squared is commonly reported as the measure of effect size.

Question 11

The test statistic for a one-way between-subjects ANOVA is used to determine whether the variance associated with having different groups is significantly larger than the variance attributed to chance or error.

Accepted Answer

This is correct. The test statistic in a one-way between-subjects ANOVA, typically F, is used to test whether the variance between groups is significantly larger than the variance within groups, or due to chance/error.

Question 12

To summarize the results of a one-way between-subjects ANOVA test,we report the test statistic,the degrees of freedom,and the p value.

Accepted Answer

This statement is true. When reporting the results of a one-way between-subjects ANOVA test, we always report the F statistic (test statistic), the degrees of freedom (numerator and denominator), and the p-value.

Question 13

Unlike $\omega$²,the formula for $\eta$² corrects for the number of groups and the size of error in its estimate of effect size.

Accepted Answer

The formula for $\eta^2$ does not correct for the number of groups or the size of error; it is a simple ratio of variance explained by the effect to the total variance. $\omega^2$ provides a more unbiased estimate by accounting for these factors.

Question 14

The same participants are observed in each group using the between-subjects design.

Accepted Answer

In a between-subjects design, participants are assigned to different groups and each group receives a different treatment or condition. Therefore, the same participants are not observed in each group. In a within-subjects design, participants serve as their own control and are observed in each condition or treatment.

Question 15

A post hoc test is only necessary following a decision to retain the null hypothesis.

Accepted Answer

A post hoc test is typically conducted after rejecting the null hypothesis. It is used to determine which specific group mean differences are significant after a significant overall effect has been determined in an ANOVA or other statistical test.

Question 16

While it is common to report the result of an ANOVA,researchers rarely report the results of a post hoc test.

Accepted Answer

Researchers do report the results of post hoc tests, as these tests are used to determine which specific groups differ significantly from each other after a significant result is found in an ANOVA. Reporting the results of post hoc tests helps to clarify the nature of the significant effect found in the ANOVA.

Question 17

Violating the assumption of homogeneity of variance tends to increase the likelihood of committing a Type I error.

Accepted Answer

Violating the assumption of homogeneity of variance means that the variability of the data is not equal across groups or conditions. This can lead to larger standard errors and larger variation in the data, making it easier to falsely reject the null hypothesis and commit a Type I error. Therefore, violating the assumption of homogeneity of variance increases the likelihood of committing a Type I error.

Question 18

Post hoc tests control for the total alpha level for a series of tests conducted on the same data.

Accepted Answer

Post hoc tests, such as Tukey's HSD or Bonferroni correction, do control for the total alpha level when conducting multiple tests on the same data. This is important to avoid inflating the overall probability of committing a Type I error (false positive).

Question 19

Post hoc tests are conducted following a significant one-way between-subjects ANOVA,only when k > 2.

Accepted Answer

Post hoc tests are only conducted when there are three or more groups (k > 2) in a between-subjects ANOVA. If there are only two groups, no post hoc test is necessary.

Question 20

$\eta$² is often reported as R² for an analysis of variance test.

Accepted Answer

This statement is true. It is common to simplify the notation for a design matrix by using R to represent the reference level and S to represent a change in treatment or factor level. Additionally, the numbers following the letters represent the specific levels or contrasts being tested, such as U1P12S1S1P0 in this example.

Quiz 12: Analysis of Variance: One-Way Between-Subjects Design

Two measures of proportion of variance for the one-way between-subjects ANOVA are $\eta$ ² and $\omega$ ².

A researcher has the same 18 participants rate 6 pictures (k = 6),each depicting a person with a different body type.The one-way between-subjects ANOVA is the most appropriate test for this design.

A significant ANOVA indicates that all pairs of group means significantly differ.

All post hoc tests control for the effect size of a significant result.

A mean square is a sample variance.

The test statistic for a one-way between-subjects ANOVA is the sum of squares between groups divided by the sum of squares error.

The numerator of the test statistic for a one-way between-subjects ANOVA is the mean variability associated with error.

To compute a mean square,we divide the sum of squares by the degrees of freedom for a given source of variation.

To conduct a one-way between-subjects ANOVA,we assume that the samples were randomly selected from populations with equal variances,and that participants were independently observed in each group.

Cohen's d is the most commonly reported measure of effect size for the one-way between-subjects ANOVA.

The test statistic for a one-way between-subjects ANOVA is used to determine whether the variance associated with having different groups is significantly larger than the variance attributed to chance or error.

To summarize the results of a one-way between-subjects ANOVA test,we report the test statistic,the degrees of freedom,and the p value.

Unlike $\omega$ ²,the formula for $\eta$ ² corrects for the number of groups and the size of error in its estimate of effect size.

The same participants are observed in each group using the between-subjects design.

A post hoc test is only necessary following a decision to retain the null hypothesis.

While it is common to report the result of an ANOVA,researchers rarely report the results of a post hoc test.

Violating the assumption of homogeneity of variance tends to increase the likelihood of committing a Type I error.

Post hoc tests control for the total alpha level for a series of tests conducted on the same data.

Post hoc tests are conducted following a significant one-way between-subjects ANOVA,only when k > 2.

$\eta$ ² is often reported as R² for an analysis of variance test.

Quiz 12: Analysis of Variance: One-Way Between-Subjects Design

Two measures of proportion of variance for the one-way between-subjects ANOVA are η\etaη 2 and ω\omegaω 2.

A researcher has the same 18 participants rate 6 pictures (k = 6),each depicting a person with a different body type.The one-way between-subjects ANOVA is the most appropriate test for this design.

A significant ANOVA indicates that all pairs of group means significantly differ.

All post hoc tests control for the effect size of a significant result.

A mean square is a sample variance.

The test statistic for a one-way between-subjects ANOVA is the sum of squares between groups divided by the sum of squares error.

The numerator of the test statistic for a one-way between-subjects ANOVA is the mean variability associated with error.

To compute a mean square,we divide the sum of squares by the degrees of freedom for a given source of variation.

To conduct a one-way between-subjects ANOVA,we assume that the samples were randomly selected from populations with equal variances,and that participants were independently observed in each group.

Cohen's d is the most commonly reported measure of effect size for the one-way between-subjects ANOVA.

The test statistic for a one-way between-subjects ANOVA is used to determine whether the variance associated with having different groups is significantly larger than the variance attributed to chance or error.

To summarize the results of a one-way between-subjects ANOVA test,we report the test statistic,the degrees of freedom,and the p value.

Unlike ω\omegaω 2,the formula for η\etaη 2 corrects for the number of groups and the size of error in its estimate of effect size.

The same participants are observed in each group using the between-subjects design.

A post hoc test is only necessary following a decision to retain the null hypothesis.

While it is common to report the result of an ANOVA,researchers rarely report the results of a post hoc test.

Violating the assumption of homogeneity of variance tends to increase the likelihood of committing a Type I error.

Post hoc tests control for the total alpha level for a series of tests conducted on the same data.

Post hoc tests are conducted following a significant one-way between-subjects ANOVA,only when k > 2.

η\etaη 2 is often reported as R2 for an analysis of variance test.

Two measures of proportion of variance for the one-way between-subjects ANOVA are $\eta$ ² and $\omega$ ².

Unlike $\omega$ ²,the formula for $\eta$ ² corrects for the number of groups and the size of error in its estimate of effect size.

$\eta$ ² is often reported as R² for an analysis of variance test.