Question 1

The following table shows the results of a repeated-measures ANOVA.Based on this table, what is the value for $\eta$² for factor A?

Accepted Answer

The answer of The following table shows the results of...

Question 2

A two-factor research study is used to evaluate the effectiveness of a new blood-pressure medication.In this two-factor study, Factor A is medication versus no medication and factor B is male versus female.The medicine is expected to reduce blood pressure for both males and females, but it is expected to have a much greater effect for males.What pattern of results should be obtained if the medication works as predicted?

Accepted Answer

The medication is expected to reduce blood pressure overall (main effect for medication) and have a greater effect for males (interaction between medication and gender).

Question 3

If the mean and variance are computed for each sample in an independent-measures two-factor experiment, then which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?

Accepted Answer

Large differences between sample means and small sample variances will produce large F-ratios because the F-ratio is a ratio of variance between sample means to variance within samples.

Question 4

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no main effect for factor B?

Accepted Answer

The answer of The following data represent the means for...

Question 5

The following table shows the results of a two-factor analysis of variance with two levels of factor A, three levels of factor B, and a separate sample of n = 5 participants in each of the treatment conditions.Note that several values are missing in the table.What is the missing value for the F-ratio for the AxB interaction? $\begin{array}{ccccc}
\text { Source } & \mathrm{SS} & \mathrm{df} & \mathrm{MS} & \
\hline \text { Between } & 80 & \mathrm{xx} & & \
\text { A } & 8 & \mathrm{xx} & \mathrm{xx} & \mathrm{F}=\mathrm{xx} \
\mathrm{B} & \mathrm{xx} & \mathrm{xx} & 20 & \mathrm{~F}=\mathrm{xx} \
\mathrm{AxB} & \mathrm{xx} & \mathrm{xx} & \mathrm{xx} & \mathrm{F}=\mathrm{xx} \
\text { Within } & \mathrm{xx} & \mathrm{xx} & \mathrm{xx} & \
\text { Total } & 176 & \mathrm{xx} & &
\end{array}$

Accepted Answer

The F-ratio for the AxB interaction is calculated using the formula $ F = \frac{MS_{AxB}}{MS_{Within}} $. Given the total SS is 176 and between SS is 80, the within SS is 96. With 2 levels of A and 3 levels of B, the df for AxB is (2-1)(3-1)=2. The df for within is 30-6=24. Solving for MS and F, the missing F-ratio is 4.

Question 6

For the following data, what is the value of SS_B?

Accepted Answer

The answer of For the following data, what is the...

Question 7

The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B.Based on this information, what can you conclude about the main effects?

Accepted Answer

The significance of the main effects does not provide any information about the significance of the interaction. The interaction effect is independent of the main effects, so you cannot conclude anything about its significance based solely on the main effects.

Question 8

A two-factor ANOVA produces an F-ratio for factor A with df = 1, 36 and an F-ratio for factor B with df = 2, 36.Which of the following describes the experiment producing these F-ratios?

Accepted Answer

The degrees of freedom (df) for an F-ratio in ANOVA are determined by the number of levels of the factor minus one (for the numerator) and the total number of observations minus the number of levels of the factor (for the denominator). Given df = 1,36 for factor A, this indicates 2 levels of factor A (since 2-1=1) and given df = 2,36 for factor B, this indicates 3 levels of factor B (since 3-1=2). Therefore, the experiment must have 2 levels of factor A and 3 levels of factor B.

Question 9

For the following data, what is the value of SS_within?

Accepted Answer

The answer of For the following data, what is the...

Question 10

For the following data, what is the value of SS_bet._treatments?

Accepted Answer

The answer of For the following data, what is the...

Question 11

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction?

Accepted Answer

The answer of The following data represent the means for...

Question 12

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, what is df_{within treatments}?

Accepted Answer

The degrees of freedom within treatments (df_within) is calculated as the total number of observations minus the number of treatment conditions. There are 2 levels of factor A and 2 levels of factor B, resulting in 2 x 2 = 4 treatment conditions. With n = 10 participants per condition, there are 4 x 10 = 40 total observations. Therefore, df_within = 40 - 4 = 36.

Question 13

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the SS value for factor A (SS_A)?

Accepted Answer

The answer of For a two-factor study with 2 levels...

Question 14

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor B?

Accepted Answer

There are 2 levels of factor A and 3 levels of factor B, with 10 subjects in each treatment condition. So, there are 2 x 3 x 10 = 60 participants in total. Since there are 3 levels of factor B, there are 60 / 3 = 20 participants in each level of factor B.

Question 15

In a two-factor experiment with 2 levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others.What result(s) would be produced by this pattern of treatment means?

Accepted Answer

The answer of In a two-factor experiment with 2 levels...

Question 16

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A?

Accepted Answer

The answer of For a two-factor experiment with 2 levels...

Question 17

In a line graph showing the results from a two-factor experiment, the levels of factor B are presented on the X-axis and separate lines are used to display the means for A1 and A2.If the points on the line for A1 are consistently 5 points higher than the corresponding point on the line for A2, what pattern of results is indicated?

Accepted Answer

An A-effect is indicated because the lines for A1 and A2 are parallel, indicating that the difference between A1 and A2 is the same at all levels of B. No interaction is indicated because the lines are parallel, indicating that the effect of A does not depend on the level of B.

Question 18

If the results of a two-factor experiment are presented in a line graph, then what pattern appears in the graph if there is an interaction?

Accepted Answer

An interaction in a two-factor experiment is indicated by lines that move toward each other or cross, showing that the effect of one factor depends on the level of the other factor.

Question 19

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the value of SS_{between treatments}?

Accepted Answer

The between-treatments sum of squares is calculated as the sum of the squared differences between the treatment means and the overall mean, multiplied by the number of participants in each treatment condition. In this case, the overall mean is (4 + 1 + 3 + 2) / 4 = 2.5. The squared differences between the treatment means and the overall mean are (4 - 2.5)^2 = 2.25, (1 - 2.5)^2 = 2.25, (3 - 2.5)^2 = 0.25, and (2 - 2.5)^2 = 0.25. The between-treatments sum of squares is therefore (2.25 + 2.25 + 0.25 + 0.25) * 10 = 50.

Question 20

If a two-factor analysis of variance produces a statistically significant interaction, then what can you conclude about the interaction?

Accepted Answer

The significance of the interaction effect is independent of the significance of the main effects. A significant interaction indicates that the effect of one factor depends on the level of the other factor, regardless of whether the main effects are significant.

Quiz 14: Two-Factor Analysis of Variance

If the mean and variance are computed for each sample in an independent-measures two-factor experiment, then which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no main effect for factor B?

For the following data, what is the value of SS_B?

The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B.Based on this information, what can you conclude about the main effects?

A two-factor ANOVA produces an F-ratio for factor A with df = 1, 36 and an F-ratio for factor B with df = 2, 36.Which of the following describes the experiment producing these F-ratios?

For the following data, what is the value of SS_within?

For the following data, what is the value of SS_bet._treatments?

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, what is df_{within treatments}?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the SS value for factor A (SS_A) ?

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor B?

In a two-factor experiment with 2 levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others.What result(s) would be produced by this pattern of treatment means?

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A?

If the results of a two-factor experiment are presented in a line graph, then what pattern appears in the graph if there is an interaction?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the value of SS_{between treatments}?

If a two-factor analysis of variance produces a statistically significant interaction, then what can you conclude about the interaction?

Quiz 14: Two-Factor Analysis of Variance

The following table shows the results of a repeated-measures ANOVA.Based on this table, what is the value for η\etaη 2 for factor A?

If the mean and variance are computed for each sample in an independent-measures two-factor experiment, then which of the following types of sample data will tend to produce large F-ratios for the two-factor ANOVA?

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no main effect for factor B?

For the following data, what is the value of SSB?

The results from a two-factor analysis of variance show a significant main effect for factor A and a significant main effect for factor B.Based on this information, what can you conclude about the main effects?

A two-factor ANOVA produces an F-ratio for factor A with df = 1, 36 and an F-ratio for factor B with df = 2, 36.Which of the following describes the experiment producing these F-ratios?

For the following data, what is the value of SSwithin?

For the following data, what is the value of SSbet.treatments?

The following data represent the means for each treatment condition in a two factor experiment.Note that one mean is not given.What value for the missing mean would result in no AxB interaction?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, what is dfwithin treatments?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the SS value for factor A (SSA) ?

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor B?

In a two-factor experiment with 2 levels of factor A and 2 levels of factor B, three of the treatment means are essentially identical and one is substantially different from the others.What result(s) would be produced by this pattern of treatment means?

For a two-factor experiment with 2 levels of factor A and 3 levels of factor B and n = 10 subjects in each treatment condition, how many participants are in each level of factor A?

If the results of a two-factor experiment are presented in a line graph, then what pattern appears in the graph if there is an interaction?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the value of SSbetween treatments?

If a two-factor analysis of variance produces a statistically significant interaction, then what can you conclude about the interaction?

For the following data, what is the value of SS_B?

For the following data, what is the value of SS_within?

For the following data, what is the value of SS_bet._treatments?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, what is df_{within treatments}?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the SS value for factor A (SS_A) ?

For a two-factor study with 2 levels of factor A, 2 levels of factor B, and a separate sample of n = 10 participants in each treatment condition, the two means for level A1 are 4 and 1, and the two means for level A2 are 3 and 2.For these data, what is the value of SS_{between treatments}?