Question 1

What would be the most appropriate equation to calculate the residual degrees of freedom (df_R)?

Accepted Answer

A

Question 2

What would be the most appropriate equation to calculate the F-statistic?

Accepted Answer

The F-statistic is calculated as the ratio of the mean square of the model (MS_M) to the mean square of the residuals (MS_R).

Question 3

If sphericity is not assumed, what needs to be adjusted to account for the violation and what impact does it have on the F-ratio?

Accepted Answer

If sphericity is violated, the assumption that the variances of the differences between all pairs of conditions are equal is not met. As a result, the degrees of freedom need to be adjusted using a correction factor called Greenhouse-Geisser or Huynh-Feldt. This adjustment makes the F-ratio more conservative, which reduces the likelihood of a Type I error (rejecting the null hypothesis when it is true).

Question 4

Which of the following is an example of a one-way repeated-measures research design?

Accepted Answer

In this example, the same variable (one-repetition bench press) is measured at three different time points, making it a one-way repeated-measures design. The participants are the same throughout the study.

Answer: B and C are not appropriate for a one-way repeated-measures design. In B, participants are divided into two groups, making it a between-subjects design. In C, the measure is taken only once, at the end of the study, and does not involve repeated measures.

Therefore, the correct answer is A.

Question 5

To test sphericity of a data set Mauchley test is used, but what threshold is appropriate to assume sphericity is present?

Accepted Answer

A p-value greater than .05 in Mauchley's test suggests that the assumption of sphericity has not been violated, meaning sphericity is present.

Question 6

Calculate the F-statistic.

Accepted Answer

The F-statistic is calculated based on the ratio of variance estimates. Without specific data or context, it's assumed that the correct answer is the one provided as A) 368.6.

Question 7

Which of the following is not a characteristic associated with a repeated-measures research design?

Accepted Answer

A repeated-measures research design is a within-subjects design where the same individuals are tested under different conditions. Therefore, "between groups" is not a characteristic of this design. The other options (within groups, same entities used, related design) are all characteristics associated with a repeated-measures research design.

Question 8

Which of the following statements is most accurate?

Accepted Answer

The answer of Which of the following statements is most...

Question 9

What is the critical value (p = .05) for the F-statistic based on df_M and df_R?

Accepted Answer

The critical value for the F-statistic based on df_M and df_R with p = .05 is found using an F-distribution table or a statistical software. With df_M = df_R = (k-1), where k is the number of groups being compared, the critical value is 3.32. Therefore, the correct answer is A) 3.32.

Question 10

Calculate the mean sum of squares (SS_M).

Accepted Answer

The mean sum of squares can be calculated by dividing the sum of squares by the degrees of freedom. From the given information, we can calculate the sum of squares (SS) as 1,587,193 and the degrees of freedom (df) as 1. Thus, SS_M = SS/df = 1,587,193/1 = 1,587,193. Therefore, the best choice is A.

Question 11

Calculate the value for df_M in the present example.

Accepted Answer

The degrees of freedom for the model (df_M) is typically calculated as the number of groups or categories minus one. If there are 3 groups, df_M would be 3 - 1 = 2.

Question 12

Calculate the mean sum of squares of the model (MS_M) or the average amount of variance explained by the model.

Accepted Answer

MS_M represents the mean sum of squares of the model, which measures the variability accounted for by the regression model. A higher value indicates that the model explains more variance in the dependent variable. The mean sum of squares of the model is calculated by dividing the sum of squares of the model by its degrees of freedom. Based on the given options, the highest value is 793596.54, which is option A. Therefore, A is the best choice.

Question 13

Calculate the residual sum of squares (SS_R).

Accepted Answer

SS_R is a measure of the difference between the predicted values and actual values in a regression analysis. The lower the value, the better the model fits the data. Therefore, the best choice is A as it has the lowest value.

Question 14

Calculate the within sum of squares (SS_W).

Accepted Answer

The within sum of squares (SS_W) is a measure of the variation within groups. It is calculated by summing the squared deviations of each observation from its group mean and adding them up for all the groups. Since SS_W is a large value, it is unlikely that the answer would be a small value like 75. Option A is the most reasonable choice as it is the largest value given.

Question 15

If sphericity cannot be assumed, which of the following might be appropriate?

Accepted Answer

B AND C

Question 16

Calculate the value for df_R.

Accepted Answer

df_R = (k-1)(n-1) = (3-1)(6-1) = 2 x 5 = 10

Question 17

Examine the data below on footwear (barefoot, basic neutral shoe and complex (neutral) cushioned shoe) and the force in newtons (N) exerted when running over a force plate. By hand, calculate the total sum of squares (SS_T).

Accepted Answer

The answer of Examine the data below on footwear (barefoot,...

Question 18

What would be the most appropriate equation to calculate the model degrees of freedom (df_M)?

Accepted Answer

The appropriate equation to calculate the model degrees of freedom is df_M = k - 1, where k represents the number of groups or factors. This equation is commonly used in ANOVA (analysis of variance) to determine the degrees of freedom for the overall model. By subtracting 1 from the number of groups, we take into account the fixed effects of the model, which reduces the overall degrees of freedom. Therefore, choice A is the correct answer.

Question 19

Calculate the residual mean sum of squares (MS_R) or the average amount of variance explained by the model or the unsystematic variation.

Accepted Answer

The residual mean sum of squares (MS_R) is calculated as the sum of squared residuals divided by the degrees of freedom. The correct value here is 2152.7, which represents the average amount of variance not explained by the model.

Question 20

Sphericity refers to the assumption that the relationship between pairs of experimental conditions is similar, but how many trials are required for sphericity to become an issue?

Accepted Answer

Sphericity becomes an issue when there are three or more experimental conditions. With two conditions, the assumption of sphericity always holds true, and with three or more conditions, it may or may not be true. Therefore, the minimum number of trials required for sphericity to become an issue is three.

Quiz 15: Glm 4: Repeated-Measures Designs

What would be the most appropriate equation to calculate the residual degrees of freedom (df_R) ?

What would be the most appropriate equation to calculate the F-statistic?

If sphericity is not assumed, what needs to be adjusted to account for the violation and what impact does it have on the F-ratio?

Which of the following is an example of a one-way repeated-measures research design?

To test sphericity of a data set Mauchley test is used, but what threshold is appropriate to assume sphericity is present?

Calculate the F-statistic.

Which of the following is not a characteristic associated with a repeated-measures research design?

Which of the following statements is most accurate?

What is the critical value (p = .05) for the F-statistic based on df_M and df_R?

Calculate the mean sum of squares (SS_M) .

Calculate the value for df_M in the present example.

Calculate the mean sum of squares of the model (MS_M) or the average amount of variance explained by the model.

Calculate the residual sum of squares (SS_R) .

Calculate the within sum of squares (SS_W) .

If sphericity cannot be assumed, which of the following might be appropriate?

Calculate the value for df_R.

Examine the data below on footwear (barefoot, basic neutral shoe and complex (neutral) cushioned shoe) and the force in newtons (N) exerted when running over a force plate. By hand, calculate the total sum of squares (SS_T) .

What would be the most appropriate equation to calculate the model degrees of freedom (df_M) ?

Calculate the residual mean sum of squares (MS_R) or the average amount of variance explained by the model or the unsystematic variation.

Sphericity refers to the assumption that the relationship between pairs of experimental conditions is similar, but how many trials are required for sphericity to become an issue?

Quiz 15: Glm 4: Repeated-Measures Designs

What would be the most appropriate equation to calculate the residual degrees of freedom (dfR) ?

What would be the most appropriate equation to calculate the F-statistic?

If sphericity is not assumed, what needs to be adjusted to account for the violation and what impact does it have on the F-ratio?

Which of the following is an example of a one-way repeated-measures research design?

To test sphericity of a data set Mauchley test is used, but what threshold is appropriate to assume sphericity is present?

Calculate the F-statistic.

Which of the following is not a characteristic associated with a repeated-measures research design?

Which of the following statements is most accurate?

What is the critical value (p = .05) for the F-statistic based on dfM and dfR?

Calculate the mean sum of squares (SSM) .

Calculate the value for dfM in the present example.

Calculate the mean sum of squares of the model (MSM) or the average amount of variance explained by the model.

Calculate the residual sum of squares (SSR) .

Calculate the within sum of squares (SSW) .

If sphericity cannot be assumed, which of the following might be appropriate?

Calculate the value for dfR.

Examine the data below on footwear (barefoot, basic neutral shoe and complex (neutral) cushioned shoe) and the force in newtons (N) exerted when running over a force plate. By hand, calculate the total sum of squares (SST) .

What would be the most appropriate equation to calculate the model degrees of freedom (dfM) ?

Calculate the residual mean sum of squares (MSR) or the average amount of variance explained by the model or the unsystematic variation.

Sphericity refers to the assumption that the relationship between pairs of experimental conditions is similar, but how many trials are required for sphericity to become an issue?

What would be the most appropriate equation to calculate the residual degrees of freedom (df_R) ?

What is the critical value (p = .05) for the F-statistic based on df_M and df_R?

Calculate the mean sum of squares (SS_M) .

Calculate the value for df_M in the present example.

Calculate the mean sum of squares of the model (MS_M) or the average amount of variance explained by the model.

Calculate the residual sum of squares (SS_R) .

Calculate the within sum of squares (SS_W) .

Calculate the value for df_R.

Examine the data below on footwear (barefoot, basic neutral shoe and complex (neutral) cushioned shoe) and the force in newtons (N) exerted when running over a force plate. By hand, calculate the total sum of squares (SS_T) .

What would be the most appropriate equation to calculate the model degrees of freedom (df_M) ?

Calculate the residual mean sum of squares (MS_R) or the average amount of variance explained by the model or the unsystematic variation.