Question 1

Posttests are only needed if H₀ is rejected in an ANOVA comparing more than two treatments.

Accepted Answer

The answer of Posttests are only needed if H₀ is...

Question 2

The distribution of F-ratios is negatively skewed.

Accepted Answer

The distribution of F-ratios is positively skewed, meaning it has a long tail to the right of the distribution.

Question 3

In analysis of variance,large sample variances reduce the likelihood of rejecting the null hypothesis.

Accepted Answer

Large sample variances increase the error term in the analysis of variance and decrease the power of the test, making it less likely to reject the null hypothesis.

Question 4

After an ANOVA,a researcher computes ² to evaluate effect size and ² = 0.50.If the ANOVA had SS_total = 100,then $\text { SSwithin }$ = $S S _ { \text {between } }$ = 50.

Accepted Answer

The effect size (ꞃ²) can be calculated as:

ꞃ² = SSbetween / SStotal

We are given that ꞃ² = 0.50 and SStotal = SSwithin + SSbetween.

Substituting these values, we get:

0.50 = SSbetween / (SSwithin + SSbetween + SSwithin)

0.50 = SSbetween / (2*SSwithin + SSbetween)

0.50(2*SSwithin + SSbetween) = SSbetween

1.00SSwithin + 0.50SSbetween = SSbetween

0.50SSbetween = 1.00SSwithin

So, SSwithin and SSbetween are equal to 50 each. Therefore, the answer is A.

Question 5

An ANOVA is used to determine whether any significant difference exists between treatment means,and posttests are used to determine exactly which treatment means are significantly different.

Accepted Answer

An ANOVA is used to test for overall significant differences among treatment means, while posttests (such as Tukey's HSD or Bonferroni tests) are used to determine which specific pairs of means are significantly different from each other.

Question 6

If an analysis of variance produces a value of F = 0,then all the samples have the same mean.

Accepted Answer

If the value of F is 0, it means there is no significant difference between the means of the samples, which implies that all the samples have the same mean.

Question 7

If an analysis of variance produces a value of F = 1.00,then all the samples have the same mean.

Accepted Answer

A value of F = 1.00 suggests that there is no significant difference between the means of the samples, but it does not necessarily mean that they are all the same. There could still be minor variations between them.

Question 8

$\text { SSwithin }$ measures the size of the sample variances.

Accepted Answer

$\text{SS}_{\text{within}}$ refers to the sum of squares within groups, which measures the variability of individual observations within each group, essentially reflecting the size of the sample variances within those groups.

Question 9

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments.If the t statistic has df = 12,then an ANOVA evaluating the same data would produce an F-ratio with df = 1,11.

Accepted Answer

The answer of A researcher uses an independent-measures t test...

Question 10

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.The research study used a total of 31 participants.

Accepted Answer

The degrees of freedom for the between-groups factor in an independent-measures ANOVA is equal to the number of groups minus 1. In this case, there were 4 groups, so the degrees of freedom should be 3. However, the degrees of freedom listed in the report (3,28) actually refer to the degrees of freedom for the error term and the total number of participants plus groups (n-1). Therefore, there were more than 31 participants in the study.

Question 11

Effect size for analysis of variance is measured by ²,which equals $S S _ { \text {between } }$ divided by $\text { SSwithin }$ .

Accepted Answer

Effect size for analysis of variance (ANOVA) is typically measured by $\eta^2$ (eta squared), which equals $SS_{\text{between}}$ divided by $SS_{\text{total}}$, not $SS_{\text{within}}$.

Question 12

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.If all the samples were the same size,then each sample had n = 7 participants.

Accepted Answer

The answer of A research report presents the results of...

Question 13

A researcher conducts an ANOVA to evaluate the mean difference between two treatments using the data from an independent-measures study and obtains F = 4.00.If the researcher had used an independent-measures t test,then t would be t = 2.00.

Accepted Answer

This is true. The F value in an ANOVA is equal to the square of the t value in an independent-measures t test. Therefore, F = t^2, and in this case, F = 4.00 and t = 2.00.

Question 14

An ANOVA comparing two treatment conditions produces $\text { SSwithin }$ = 80 and $S S _ { \text {between } }$ = 50.For these data,²= 25/80.

Accepted Answer

The formula for calculating $F$ in an ANOVA is $F = \frac{MS_{between}}{MS_{within}}$, where $MS_{between} = \frac{SS_{between}}{df_{between}}$ and $MS_{within} = \frac{SS_{within}}{df_{within}}$. The given formula $?²= 25/80$ does not represent the calculation of an F-ratio for ANOVA.

Question 15

The larger the differences among the sample means,the larger the numerator of the F-ratio will be.

Accepted Answer

The numerator of the F-ratio measures the variability among the sample means, so the larger the differences among the sample means, the larger the numerator will be.

Question 16

A research report presents the results of an independent-measures ANOVA as follows:
F(3,28)= 5.36,p < .01.The research study compared three treatments.

Accepted Answer

The F statistic notation F(3,28) indicates that there were four groups compared, not three, because the first number (3) represents the degrees of freedom between groups, which is the number of groups minus one.

Question 17

$S S _ { \text {between } }$ measures the size of the mean differences from one treatment to another.

Accepted Answer

This statement is true. SS (sum of squares) between treatments measures how much the means of each treatment differ from the overall mean, indicating the size of the treatment effects.

Question 18

Posttests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.

Accepted Answer

Posttests such as Scheffé are typically used for analyses of variance with more than two treatment conditions to determine which treatment conditions differ significantly from each other. When comparing only two treatment conditions, it is sufficient to examine the main effects of the ANOVA and the confidence interval of the difference between the means.

Question 19

If an analysis of variance produces $S S _ { \text {between } }$ = 20 and $\text { SSwithin }$ = 40,then ² = 0.50.

Accepted Answer

The answer of If an analysis of variance produces \(S...

Question 20

For an ANOVA,if $S S _ { \text {between } }$ = 40 and $\text { SSwithin }$ = 60,then ² = 40/100.

Accepted Answer

η² (eta-squared) is calculated by dividing the sum of squares between groups by the total sum of squares. Therefore, η² = SSbetween / (SSbetween + SSwithin). Given SSbetween = 40 and SSwithin = 60, η² = 40 / (40 + 60) = 0.4 = 40%.

Quiz 12: Introduction to Analysis of Variance

Posttests are only needed if H₀ is rejected in an ANOVA comparing more than two treatments.

The distribution of F-ratios is negatively skewed.

In analysis of variance,large sample variances reduce the likelihood of rejecting the null hypothesis.

An ANOVA is used to determine whether any significant difference exists between treatment means,and posttests are used to determine exactly which treatment means are significantly different.

If an analysis of variance produces a value of F = 0,then all the samples have the same mean.

If an analysis of variance produces a value of F = 1.00,then all the samples have the same mean.

$\text { SSwithin }$ measures the size of the sample variances.

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments.If the t statistic has df = 12,then an ANOVA evaluating the same data would produce an F-ratio with df = 1,11.

A research report presents the results of an independent-measures ANOVA as follows: F(3,28)= 5.36,p < .01.The research study used a total of 31 participants.

Effect size for analysis of variance is measured by $Effect size for analysis of variance is measured by ²,which equals S S _ { \text {between } } divided by \text { SSwithin } .$ ²,which equals $S S _ { \text {between } }$ divided by $\text { SSwithin }$ .

A research report presents the results of an independent-measures ANOVA as follows: F(3,28)= 5.36,p < .01.If all the samples were the same size,then each sample had n = 7 participants.

A researcher conducts an ANOVA to evaluate the mean difference between two treatments using the data from an independent-measures study and obtains F = 4.00.If the researcher had used an independent-measures t test,then t would be t = 2.00.

An ANOVA comparing two treatment conditions produces $\text { SSwithin }$ = 80 and $S S _ { \text {between } }$ = 50.For these data, $An ANOVA comparing two treatment conditions produces \text { SSwithin } = 80 and S S _ { \text {between } } = 50.For these data, ²= 25/80.$ ²= 25/80.

The larger the differences among the sample means,the larger the numerator of the F-ratio will be.

A research report presents the results of an independent-measures ANOVA as follows: F(3,28)= 5.36,p < .01.The research study compared three treatments.

$S S _ { \text {between } }$ measures the size of the mean differences from one treatment to another.

Posttests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.

If an analysis of variance produces $S S _ { \text {between } }$ = 20 and $\text { SSwithin }$ = 40,then $If an analysis of variance produces S S _ { \text {between } } = 20 and \text { SSwithin } = 40,then ² = 0.50.$ ² = 0.50.

For an ANOVA,if $S S _ { \text {between } }$ = 40 and $\text { SSwithin }$ = 60,then $For an ANOVA,if S S _ { \text {between } } = 40 and \text { SSwithin } = 60,then ² = 40/100.$ ² = 40/100.

Quiz 12: Introduction to Analysis of Variance

Posttests are only needed if H₀ is rejected in an ANOVA comparing more than two treatments.

The distribution of F-ratios is negatively skewed.

In analysis of variance,large sample variances reduce the likelihood of rejecting the null hypothesis.

After an ANOVA,a researcher computes ² to evaluate effect size and obtains11eedb96_7b94_556d_a0ba_3d9dc406b78d_TB2285_11² = 0.50.If the ANOVA had SStotal = 100,then SSwithin \text { SSwithin } SSwithin = SSbetween S S _ { \text {between } }SSbetween ​ = 50.

An ANOVA is used to determine whether any significant difference exists between treatment means,and posttests are used to determine exactly which treatment means are significantly different.

If an analysis of variance produces a value of F = 0,then all the samples have the same mean.

If an analysis of variance produces a value of F = 1.00,then all the samples have the same mean.

SSwithin \text { SSwithin } SSwithin measures the size of the sample variances.

A researcher uses an independent-measures t test to evaluate the mean difference between two treatments.If the t statistic has df = 12,then an ANOVA evaluating the same data would produce an F-ratio with df = 1,11.

A research report presents the results of an independent-measures ANOVA as follows: F(3,28)= 5.36,p < .01.The research study used a total of 31 participants.

Effect size for analysis of variance is measured by ²,which equals SSbetween S S _ { \text {between } }SSbetween ​ divided by SSwithin \text { SSwithin } SSwithin .

A research report presents the results of an independent-measures ANOVA as follows: F(3,28)= 5.36,p < .01.If all the samples were the same size,then each sample had n = 7 participants.

A researcher conducts an ANOVA to evaluate the mean difference between two treatments using the data from an independent-measures study and obtains F = 4.00.If the researcher had used an independent-measures t test,then t would be t = 2.00.

An ANOVA comparing two treatment conditions produces SSwithin \text { SSwithin } SSwithin = 80 and SSbetween S S _ { \text {between } }SSbetween ​ = 50.For these data,²= 25/80.

The larger the differences among the sample means,the larger the numerator of the F-ratio will be.

A research report presents the results of an independent-measures ANOVA as follows: F(3,28)= 5.36,p < .01.The research study compared three treatments.

SSbetween S S _ { \text {between } }SSbetween ​ measures the size of the mean differences from one treatment to another.

Posttests such as Scheffé are not necessary for an analysis of variance comparing only two treatment conditions.

If an analysis of variance produces SSbetween S S _ { \text {between } }SSbetween ​ = 20 and SSwithin \text { SSwithin } SSwithin = 40,then ² = 0.50.

For an ANOVA,if SSbetween S S _ { \text {between } }SSbetween ​ = 40 and SSwithin \text { SSwithin } SSwithin = 60,then ² = 40/100.

$\text { SSwithin }$ measures the size of the sample variances.

Effect size for analysis of variance is measured by $Effect size for analysis of variance is measured by ²,which equals S S _ { \text {between } } divided by \text { SSwithin } .$ ²,which equals $S S _ { \text {between } }$ divided by $\text { SSwithin }$ .

An ANOVA comparing two treatment conditions produces $\text { SSwithin }$ = 80 and $S S _ { \text {between } }$ = 50.For these data, $An ANOVA comparing two treatment conditions produces \text { SSwithin } = 80 and S S _ { \text {between } } = 50.For these data, ²= 25/80.$ ²= 25/80.

$S S _ { \text {between } }$ measures the size of the mean differences from one treatment to another.

If an analysis of variance produces $S S _ { \text {between } }$ = 20 and $\text { SSwithin }$ = 40,then $If an analysis of variance produces S S _ { \text {between } } = 20 and \text { SSwithin } = 40,then ² = 0.50.$ ² = 0.50.

For an ANOVA,if $S S _ { \text {between } }$ = 40 and $\text { SSwithin }$ = 60,then $For an ANOVA,if S S _ { \text {between } } = 40 and \text { SSwithin } = 60,then ² = 40/100.$ ² = 40/100.