Question 1

When conducting an ANCOVA, which would be the most appropriate order?
A) Explore the data, correct outliers, check independence of treatment variable and covariate, run ANCOVA.
B) Explore the data, check independence of treatment variable and covariate, run ANCOVA, correct outliers.
C) Check independence of treatment variable and covariate, explore the data, correct outliers, run ANCOVA.
D) Correct outliers, check independence of treatment variable and covariate, explore the data, run ANCOVA.

Accepted Answer

First, explore the data to understand its structure and identify any potential issues. Then, correct outliers to ensure they don't skew results. Next, check the independence of the treatment variable and covariate to meet ANCOVA assumptions. Finally, run the ANCOVA.

Question 2

Which contrast would be most appropriate if you wished to compare each learning style against a control group (i.e. kinaesthetic)?
A) Simple
B) Repeated
C) Deviation
D) Difference

Accepted Answer

A

Question 3

Because the research design is slightly more complicated, partial eta squared can be used. What is the correction expression for the calculation? A) SS_M / (SS_M + SS_R) B) SS_M × (SS_M + SS_T) C) SS_M × (SS_M / SS_T) D) SS_M / (SS_M / SS_T)

Accepted Answer

Partial eta squared is calculated as the ratio of the sum of squares due to the main effect (SS_M) to the sum of squares due to the main effect plus the sum of squares due to the residual (SS_R).

Question 4

Why might you wish to include covariates in an ANOVA? (You may select more than one option.)
A) To reduce within-group error variance.
B) To eliminate confounds in the results.
C) To reduce between-group error variance.
D) When the assumption of homogeneity of variance is violated.

Accepted Answer

Including covariates in an ANOVA can help reduce within-group error variance by accounting for variability related to the covariate, and it can help eliminate confounds by controlling for variables that might influence the dependent variable.

Question 5

What graphical illustration might you use to visually inspect the homogeneity of regression slopes (i.e. different variables)?
A) Scatterplot
B) Histogram
C) Box-whisker plot
D) Bar chart

Accepted Answer

A scatterplot would be the best choice to visually inspect the homogeneity of regression slopes. It allows for a visual comparison of the relationships between different variables and can show any differences in slopes.

Question 6

Analyse the following illustration. Which scenario is referable when trying to explain the impact a covariate has on an outcome variable? 
A) A
B) B
C) C
D) None of the scenarios are appropriate.

Accepted Answer

In scenario B, the covariate is being held constant in order to isolate its impact on the outcome variable. This is commonly done in regression analysis and other statistical modeling techniques to determine the specific effect of a particular variable on an outcome, while controlling for other factors that may also influence the outcome. In scenarios A and C, the covariate is not being held constant, making it difficult to determine its separate impact on the outcome.

Question 7

What is the purpose of using an ANCOVA?
A) Examining the effect a treatment or experimental variable has on an outcome variable, whilst isolating the effects of a different variable which may also have an effect on the outcome variable.
B) Examining the effect an outcome variable has on an experimental or treatment variable, whilst isolating the effects of a different variable which may also have an effect on the outcome variable.
C) Examining the effect an independent variable has on a treatment or experimental variable, whilst isolating the effects of the outcome variable.
D) Examining the effect an independent variable has on an outcome variable, whilst isolating the effects of the experimental or treatment variable.

Accepted Answer

ANCOVA (Analysis of Covariance) is used to examine the effect of a treatment or experimental variable on an outcome variable while controlling for the effects of a different variable that may also affect the outcome variable. ANCOVA is used to improve the accuracy of statistical analysis by adjusting for the effects of a covariate. Hence, option A is the correct answer.

Question 8

Having run a simple contrast with the univariate test, interpret the following table and decide which of the following statements is most appropriate. 
A) There was a statistically significant result for visual learning when compared with kinaesthetic learning.
B) There was a statistically significant result for auditory learning when compared with kinaesthetic learning.
C) There were no statistically significant results identified.
D) Both the visual and auditory learning styles were statistically significant when compared with kinaesthetic approach.

Accepted Answer

The answer of Having run a simple contrast with the...

Question 9

How is eta squared calculated? A) SS_M / SS_T B) SS_R / SS_M C) SS_M × SS_R D) SS_T × SS_R

Accepted Answer

Eta squared is calculated as the ratio of the model sum of squares (SS_M) to the total sum of squares (SS_T).

Question 10

Analyse the following data. What is the proportion of variance accounted for by the learning style alone? 
A) 4%
B) 5%
C) 40%
D) 50%

Accepted Answer

The answer of Analyse the following data. What is the...

Question 11

If you were to analyse the effect of caffeine dose (no caffeine, high and low doses) on reaction time, which of the following might be considered the most reasonable covariate?
A) Motivation
B) Team cohesion
C) Intelligence
D) Aerobic capacity

Accepted Answer

Motivation can influence reaction time independently of caffeine dose, making it a reasonable covariate to control for in the analysis.

Question 12

Eta squared is a measure of effect size, but how is it also expressed? A) r² B) SD² C) y² D) x²

Accepted Answer

Eta squared is often expressed as r² because both represent the proportion of variance explained by a variable in the context of ANOVA or regression analysis.

Question 13

Analyse the following graph. The data shows the results of three groups of 15 athletes who were instructed to complete a basketball shooting exercise (success rate from 20 free throw shots) having received one of three methods of instruction, auditory (shooting technique being verbally described by a coach), visual (shooting technique being verbally described by a coach) or kinaesthetic (no coaching, just asked to perform the shooting exercise). Motivation acted as the covariate of interest. How would you describe the regression slopes? 
A) Positive and homogeneous
B) Positive and heterogeneous
C) Negative and homogeneous
D) Negative and heterogeneous

Accepted Answer

The answer of Analyse the following graph. The data shows...

Question 14

Which of the following statements best describes a covariate?
A) A variable that influences an outcome variable but is not part of the experimental design
B) An independent variable that has no influence over a specific outcome variable
C) An independent variable that is used to influence a given outcome variable
D) A variable that forms part of the experimental design and which has a direct influence over a specific outcome variable

Accepted Answer

A covariate is a variable that influences an outcome variable but is not part of the experimental design. It is measured and taken into account in statistical analysis to remove its effect and isolate the effect of the independent variable on the dependent variable. Options B, C, and D do not accurately describe a covariate.

Question 15

Calculate the mean and standard deviation of the kinaesthetic group from the data below. 
A) 13(5)
B) 12(4)
C) 11(5)
D) 10(4)

Accepted Answer

The answer of Calculate the mean and standard deviation of...

Question 16

Run an ANCOVA on the data. What effect do the independent variable (i.e. learning style) and covariate (i.e. motivation) have on the dependent variable (i.e. performance)?
A) Participant motivation and learning style were both statistically significantly predictors of performance.
B) Participant motivation and learning style were not statistically significantly predictors of performance.
C) Participant motivation was statistically significant at predicting performance, but learning style was not.
D) Learning style was statistically significant at predicting performance, but participant motivation was not.

Accepted Answer

The ANCOVA examines the effect of the independent variable (learning style) and covariate (motivation) on the dependent variable (performance). The answer indicates that both motivation and learning style were statistically significant predictors of performance.

Question 17

Run a one-way ANOVA on the covariate data to see if the means are roughly the same across the three groups. Which of the following is correct? A) F_{(2, 42)} = 1.6, p = .223 B) F_{(2, 44)} = 19.9, p = 1.6 C) F_{(2, 42)} = 268.4, p = 288.3 D) F_{(2, 44)} = 0.223, p = 19.9

Accepted Answer

The correct format for reporting a one-way ANOVA result is F(df1, df2) = F-value, p-value. In this case, the correct ANOVA result is F_{(2, 42)} = 1.6, p = .223. Therefore, the best choice is A.

Question 18

Analyse the following table. How might you express the data as a multiple regression model when dummy variables are incorporated? 
A) Performance = 4.0+(1.5×Motivation)+(-1.9×visual)+(-0.003×auditory)
B) Performance = 4.0×(1.5×Motivation)×(-1.9×visual)×(-0.003×auditory)
C) Performance = 4.0×(1.5+Motivation)×(-1.9+visual)×(-0.003+auditory)
D) Performance = 4.0-(1.5/Motivation)-(-1.9/visual)-(-0.003/auditory)

Accepted Answer

The multiple regression model with dummy variables incorporated would express the relationship between the performance variable and the motivation, visual, and auditory factors as coefficients. The coefficients for visual and auditory are negative, indicating a negative relationship, while the coefficient for motivation is positive, indicating a positive relationship. The intercept of 4.0 represents the performance level when all factors are at their reference level (i.e. motivation = 0, visual = 0, auditory = 0). Therefore, the most appropriate option is A, which represents this information in the correct equation format.

Question 19

What are the main assumptions of an ANCOVA? (You may select more than one option.)
A) Independence of the covariate and treatment effect
B) Homogeneity of the regression slopes
C) Interdependence of the covariate and the treatment effect
D) Variance explained jointly by the covariate and the experimental effect

Accepted Answer

ANCOVA assumes that the covariate and treatment effect are independent and that the regression slopes are homogenous across the groups being compared. It does not assume interdependence of the covariate and treatment effect, and the variance explained jointly by the covariate and experimental effect is not an assumption, but rather a result of the analysis.

Question 20

Based on the result in Q11, which of the statements best reflects the outcome of the one-way ANOVA?
A) The means of the three groups were not significantly different.
B) The means of the three groups were significantly different.
C) The mean of the kinaesthetic group was significantly different from the visual and auditory groups.
D) The result was clear.

Accepted Answer

The answer of Based on the result in Q11, which...

Quiz 13: Glm 2: Comparing Means Adjusted for Other Predictors Analysis of Covariance

When conducting an ANCOVA, which would be the most appropriate order?

Which contrast would be most appropriate if you wished to compare each learning style against a control group (i.e. kinaesthetic) ?

Because the research design is slightly more complicated, partial eta squared can be used. What is the correction expression for the calculation?

Why might you wish to include covariates in an ANOVA? (You may select more than one option.)

What graphical illustration might you use to visually inspect the homogeneity of regression slopes (i.e. different variables) ?

Analyse the following illustration. Which scenario is referable when trying to explain the impact a covariate has on an outcome variable?

What is the purpose of using an ANCOVA?

Having run a simple contrast with the univariate test, interpret the following table and decide which of the following statements is most appropriate.

How is eta squared calculated?

Analyse the following data. What is the proportion of variance accounted for by the learning style alone?

If you were to analyse the effect of caffeine dose (no caffeine, high and low doses) on reaction time, which of the following might be considered the most reasonable covariate?

Eta squared is a measure of effect size, but how is it also expressed?

Which of the following statements best describes a covariate?

Calculate the mean and standard deviation of the kinaesthetic group from the data below.

Run an ANCOVA on the data. What effect do the independent variable (i.e. learning style) and covariate (i.e. motivation) have on the dependent variable (i.e. performance) ?

Run a one-way ANOVA on the covariate data to see if the means are roughly the same across the three groups. Which of the following is correct?

Analyse the following table. How might you express the data as a multiple regression model when dummy variables are incorporated?

What are the main assumptions of an ANCOVA? (You may select more than one option.)

Based on the result in Q11, which of the statements best reflects the outcome of the one-way ANOVA?