Question 1

One advantage of the repeated-measures ANOVA is that it eliminates "individual differences" as a source of variability.Explain why there are no individual differences in the numerator and in the denominator of the F-ratio.

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The answer of One advantage of the repeated-measures ANOVA is...

Question 2

Explain why MS_within is not an appropriate error term (denominator)for the repeated-measures F-ratio.

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The answer of Explain why MS_within is not an appropriate...

Question 3

The result of a repeated-measures ANOVA stated that F(3,21)= 4.57,p < .05.The study used a sample of n = 7 participants.

Accepted Answer

The degrees of freedom for the error term in a repeated-measures ANOVA should be calculated as (n-1)(k-1), where n is the number of participants and k is the number of conditions. With n = 7 and k = 4, the correct degrees of freedom for the error term should be (7-1)(4-1) = 18, not 21.

Question 4

A repeated-measures study compares three treatments with a sample of n = 12 subjects.For the analysis of variance,df_error = 33.

Accepted Answer

This is not a valid scenario for a repeated-measures ANOVA, as there is no clear indication of multiple measurements for each subject. Additionally, the given information does not provide enough context to determine the correct degrees of freedom for the F statistic.

Question 5

Because the repeated-measures ANOVA removes variance caused by individual differences,it usually is more likely to detect a treatment effect than the independent-measures ANOVA is.

Accepted Answer

The repeated-measures ANOVA is usually more powerful than the independent-measures ANOVA because it removes individual differences variability and therefore increases the likelihood of detecting a treatment effect.

Question 6

The F-ratio for a repeated-measures ANOVA has df = 2,16.The research study compared 3 treatments with a sample of n = 8 participants.

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The answer of The F-ratio for a repeated-measures ANOVA has...

Question 7

One major difference between the independent_measures ANOVA and the repeated_measures ANOVA is that SS_total is calculated differently for each type of ANOVA.

Accepted Answer

The SS_total is calculated the same way for both independent measures ANOVA and repeated measures ANOVA. The difference lies in how the SS_between and SS_within are partitioned.

Question 8

A researcher conducts a repeated-measures study comparing three treatment conditions with a sample of n = 12 participants.The results are evaluated with a repeated-measures ANOVA and an incomplete summary table follows.Provide the missing values.(Hint: Begin with values for df).​  _____________________________________________

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The answer of A researcher conducts a repeated-measures study comparing...

Question 9

The F-ratio for a repeated-measures ANOVA has df = 1,15.The research study used a total of n = 16 participants.

Accepted Answer

The degrees of freedom for the F-ratio in a repeated-measures ANOVA are always 1 for the numerator and the number of participants minus 1 for the denominator. In this case, the number of participants is 16, so the degrees of freedom for the denominator are 15.

Question 10

The following data were collected from a repeated-measures study.Perform an ANOVA and then analyze the data with a t test.Use the .05 level of significance for both.​ $$\begin{array} { c c c } 
&  { \text { Treatment } } \
& \text { A } & B \
 \mathrm { G } = 36 & 2 & 6 \
\mathrm { G } ^ { 2 } = 1296 & 2 & 6 \
\mathrm { ZX } ^ { 2 } = 192 & 4 & 4 \
& 4 & 8 \
& & \
& \mathrm { T } = 12 & \mathrm {~T} = 24 \
&\mathrm { SS } = 4 & \mathrm { SS } = 8
\end{array}$$

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The answer of The following data were collected from a...

Question 11

For a repeated-measures ANOVA,if SS_{between subjects} = 40 and SS_{within treatments} = 70,then SS_error = 30.

Accepted Answer

In a repeated-measures ANOVA, SS_error is calculated as SS_within treatments - SS_between subjects. Here, 70 - 40 = 30.

Question 12

The first stage of a repeated-measures ANOVA is identical to the analysis in an independent-measures ANOVA.

Accepted Answer

The first stage of a repeated-measures ANOVA is identical to the analysis in an independent-measures ANOVA because it involves testing for the overall effect of the independent variable on the dependent variable.

Question 13

A repeated-measures t test produces a t statistic of t = 4.00 with df = 12.If the same data were evaluated with a repeated-measures ANOVA,the F-ratio would be F = 16.

Accepted Answer

The t statistic and F-ratio values are related but not the same. In general, a higher t statistic indicates a larger difference between means and a lower probability of obtaining such a difference by chance, while a higher F-ratio indicates greater variance between groups and a lower probability of obtaining such a variance by chance. In this case, a t statistic of 4.00 with df = 12 indicates a significant difference between means, while an F-ratio of 16 would also indicate a significant difference between means and suggest more variance between groups. Therefore, it is possible for the t test and ANOVA to yield different test statistics but still reach the same conclusion about the significance of the results.

Question 14

A repeated-measures t test produces a t statistic of t = 4.00 with df = 12.If the same data were evaluated with a repeated-measures ANOVA,the F-ratio would have df = 2,12.

Accepted Answer

A repeated-measures ANOVA with an F-ratio having df = 2,12 suggests there are three levels or conditions being compared, not just two as in a t-test. A repeated-measures t-test compares only two conditions, so the equivalent ANOVA would have df = 1,12 for the F-ratio, reflecting one condition contrast and the same denominator degrees of freedom.

Question 15

The following data were collected from a repeated-measures study. a. Determine if there are any significant differences among the four treatments. Use the .05 level of significance. b. Compute the percentage of variance explained by the treatment effects (η²).Treatments

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