Question 1

If the null hypothesis is true for a one-factor within-subjects analysis of variance, then Fobs should be approximately and the null hypothesis should.

Accepted Answer

If the null hypothesis is true, the Fobs should be close to 1.00. Therefore, if the Fobs is close to 1.00, the null hypothesis should not be rejected.

Question 2

Suppose 11 participants were tested under four treatment conditions in a one-factor within-subjects design. The numerator of the F statistic for the analysis of variance would have degrees of freedom.

Accepted Answer

The degrees of freedom for the numerator of the F statistic in a one-factor within-subjects design is equal to the number of treatment conditions minus one. With four treatment conditions, the calculation is 4 - 1 = 3.

Question 3

If Fobs does not fall into the rejection region in a one-factor within-subjects analysis of variance, then the.

Accepted Answer

When Fobs does not fall into the rejection region in a one-factor within-subjects analysis of variance, it indicates that the observed differences among the treatment means are not statistically significant enough to reject the null hypothesis, suggesting that any observed differences could be due to chance.

Question 4

The situation that presumably exists if the independent variable has an effect is represented by in a one-factor within-subjects analysis of variance.

Accepted Answer

H1 represents the alternative hypothesis, which states that there is an effect of the independent variable.

Question 5

If you fail to reject H0 in a one-factor within-subjects analysis of variance, then you conclude that the.

Accepted Answer

If you fail to reject the null hypothesis in a one-factor within-subjects ANOVA, then you conclude that there is not enough evidence to support the claim that the treatment means differ by more than sampling error alone. This means that any differences observed in the treatment means can be attributed to chance or random error, and not to the effects of the treatment itself. However, it does not necessarily mean that the variances of each treatment condition are equal or not equal - this is a separate issue that is examined through tests of homogeneity of variance.

Question 6

If the independent variable does have an effect in a one-factor within-subjects analysis of variance, then MSA will be MSA × S, and the resulting F statistic will be.

Accepted Answer

When the independent variable has an effect in a one-factor within-subjects ANOVA, MSA will increase, causing the resulting F statistic to be larger than 1.00. Therefore, option C is the correct choice.

Question 7

Suppose 11 participants were tested under four treatment conditions in a one-factor within-subjects design. The denominator of the F statistic for the analysis of variance would have degrees of freedom.

Accepted Answer

In a one-factor within-subjects design, the degrees of freedom for the denominator (error term) is calculated as (n-1)(k-1), where n is the number of participants and k is the number of conditions. Here, n=11 and k=4, so (11-1)(4-1) = 30.

Question 8

If the alternative hypothesis is accepted in a one-factor within-subjects analysis of variance on three levels of the independent variable, then.

Accepted Answer

Accepting the alternative hypothesis in a one-factor within-subjects analysis of variance (ANOVA) suggests that there is a statistically significant difference among the treatment means. However, it does not specify which means differ from each other. Therefore, multiple comparison tests are needed to identify the specific pairs of treatment means that are significantly different.

Question 9

A one-factor within-subjects experiment uses three treatments and a total of nine subjects; thus the df associated with the mean square in the denominator of the F statistic for the analysis of variance equals.

Accepted Answer

The answer of A one-factor within-subjects experiment uses three treatments...

Question 10

If SSA = 27.00, SSA × S = 99.00, SSS = 44.00, dfA = 3, dfA × S = 33, and dfS = 11, then MSA equals in a one-factor within-subjects analysis of variance.

Accepted Answer

To find MSA, we need to use the formula:

MSA = SSA / dfA

We are given that SSA = 27.00 and dfA = 3, so:

MSA = 27.00 / 3 = 9.00

Therefore, the answer is B) 9.00.

Question 11

If SSA = 27.00, SSA × S = 99.00, SSS = 44.00, dfA = 3, dfA × S = 33, and dfS = 11, then Fobs equals in a one-factor within-subjects analysis of variance.

Accepted Answer

Fobs is calculated using the formula F = (SSA/dfA) / (SSA×S/dfA×S). Substituting the given values, F = (27.00/3) / (99.00/33) = 9.00 / 3.00 = 3.00.

Question 12

If the alternative hypothesis is accepted in a one-factor within-subjects analysis of variance on three levels of the independent variable, then it may be concluded that the .

Accepted Answer

If the alternative hypothesis is accepted in a one-factor within-subjects ANOVA, it means that there is a significant difference between at least two treatment means. Thus, we can conclude that the means differ by more than just sampling error, which is the null hypothesis assumption.

Question 13

If the null hypothesis is true for a one-factor within-subjects analysis of variance, then Fobs should be.

Accepted Answer

The F-ratio in an analysis of variance (ANOVA) is calculated as the ratio of the variance between groups to the variance within groups. If the null hypothesis is true (meaning there are no real differences among the group means), the expected value of the F-ratio is approximately 1.00. This is because both the numerator and the denominator are estimating the same quantity (the variance of the population), leading to a ratio close to 1.

Question 14

If Fobs does not fall into the rejection region in a one-factor within-subjects analysis of variance, then the.

Accepted Answer

If Fobs does not fall into the rejection region, it means that the null hypothesis is not rejected and there is not enough evidence to support the alternative hypothesis. Therefore, we accept the null hypothesis.

Question 15

If MSA = 72.00, MSA × S = 12.00, and MSS = 24.00, then Fobs equals in a one-factor within-subjects analysis of variance.

Accepted Answer

The answer of If MSA = 72.00, MSA × S...

Question 16

If Fobs falls into the rejection region in a one-factor within-subjects analysis of variance, then the.

Accepted Answer

When Fobs falls into the rejection region in a one-factor within-subjects analysis of variance, it indicates that there is a statistically significant difference among the group means being compared, leading to the rejection of the null hypothesis and acceptance of the alternative hypothesis.

Question 17

If you reject H0 in a one-factor within-subjects analysis of variance, then you conclude that the.

Accepted Answer

If you reject H0 in a one-factor within-subjects ANOVA, it means that there is a significant difference between at least two treatment conditions. This difference cannot be explained by chance or random variability. Therefore, the correct answer is that the treatment means differ by more than chance alone (option D). Options A and B are incorrect because the equal variances assumption applies to between-subjects ANOVA, not within-subjects ANOVA. Option C is incorrect because it implies that the differences between treatment means could be due to chance or sampling error, which is not the case if H0 is rejected.

Question 18

The situation that presumably exists if the independent variable has no effect is represented by in a one-factor within-subjects analysis of variance.

Accepted Answer

H0 represents the null hypothesis, which states that there is no significant difference between the groups being compared. Therefore, if the independent variable has no effect, it would be represented by the null hypothesis in a one-factor within-subjects ANOVA.

Question 19

If the independent variable has no effect in a one-factor within-subjects analysis of variance, then MSA will be MSA × S, and the resulting F statistic will be.

Accepted Answer

If the independent variable has no effect, then the within-subjects variance (MSA) will be the same as the error variance (MSE), resulting in an F statistic of approximately 1.00. Therefore, the F statistic will be nearly equal to 1.00, as described in choice B.

Question 20

A one-factor within-subjects experiment uses three treatments and a total of nine subjects; thus the df for the mean square in the numerator of the F statistic for the analysis of variance equals .

Accepted Answer

The degrees of freedom (df) for the mean square in the numerator of the F statistic in a one-factor within-subjects experiment is equal to the number of treatments minus one. With three treatments, df = 3 - 1 = 2.

Quiz 12: One-Factor Within-Subjects Analysis of Variance

If the null hypothesis is true for a one-factor within-subjects analysis of variance, then Fobs should be approximately and the null hypothesis should.

Suppose 11 participants were tested under four treatment conditions in a one-factor within-subjects design. The numerator of the F statistic for the analysis of variance would have degrees of freedom.

If Fobs does not fall into the rejection region in a one-factor within-subjects analysis of variance, then the.

The situation that presumably exists if the independent variable has an effect is represented by in a one-factor within-subjects analysis of variance.

If you fail to reject H0 in a one-factor within-subjects analysis of variance, then you conclude that the.

If the independent variable does have an effect in a one-factor within-subjects analysis of variance, then MSA will be MSA × S, and the resulting F statistic will be.

Suppose 11 participants were tested under four treatment conditions in a one-factor within-subjects design. The denominator of the F statistic for the analysis of variance would have degrees of freedom.

If the alternative hypothesis is accepted in a one-factor within-subjects analysis of variance on three levels of the independent variable, then.

A one-factor within-subjects experiment uses three treatments and a total of nine subjects; thus the df associated with the mean square in the denominator of the F statistic for the analysis of variance equals.

If SSA = 27.00, SSA × S = 99.00, SSS = 44.00, dfA = 3, dfA × S = 33, and dfS = 11, then MSA equals in a one-factor within-subjects analysis of variance.

If SSA = 27.00, SSA × S = 99.00, SSS = 44.00, dfA = 3, dfA × S = 33, and dfS = 11, then Fobs equals in a one-factor within-subjects analysis of variance.

If the alternative hypothesis is accepted in a one-factor within-subjects analysis of variance on three levels of the independent variable, then it may be concluded that the .

If the null hypothesis is true for a one-factor within-subjects analysis of variance, then Fobs should be.

If Fobs does not fall into the rejection region in a one-factor within-subjects analysis of variance, then the.

If MSA = 72.00, MSA × S = 12.00, and MSS = 24.00, then Fobs equals in a one-factor within-subjects analysis of variance.

If Fobs falls into the rejection region in a one-factor within-subjects analysis of variance, then the.

If you reject H0 in a one-factor within-subjects analysis of variance, then you conclude that the.

The situation that presumably exists if the independent variable has no effect is represented by in a one-factor within-subjects analysis of variance.

If the independent variable has no effect in a one-factor within-subjects analysis of variance, then MSA will be MSA × S, and the resulting F statistic will be.

A one-factor within-subjects experiment uses three treatments and a total of nine subjects; thus the df for the mean square in the numerator of the F statistic for the analysis of variance equals .