Deck 13: Analysis of Covariance

Question 1

Which of these statements is not true regarding the reporting of ANCOVA?

A) It is exactly the same as reporting ANOVA.
B) The effect of the covariate must be reported.
C) Details of the F-ratio for the experimental effect and covariate should be given.
D) Degrees of freedom from which the F-ratio is calculated should be detailed.

Answer 1

It is exactly the same as reporting ANOVA.

Question 2

An HR manager had noticed that some people 'went to pieces' during job interviews. She wanted to test whether this performance anxiety was different for people applying for jobs in different areas of the company. She took accountants, sales people and IT technicians (variable = 'job') and measured their anxiety (variable = 'anxiety') during the interview process. She also noted the seniority of the job they were applying for, ranging from level 1 (trainee) to level 8 (top management). She wanted to see whether the field of job applied for affected anxiety when controlling for position seniority. What test should she use?

A) Analysis of covariance
B) Independent Analysis of Variance
C) Repeated-measures analysis of variance
D) Mixed analysis of variance

Answer 2

Analysis of covariance

Question 3

The first part of the SPSS output for the example in Q2 is below. What does this part of the output suggest?

A) The field of job did not have a significant effect on anxiety
B) The seniority of the job did not have a significant effect on anxiety
C) The variances of anxiety scores were roughly the same for the groups tested.
D) The variances of anxiety scores were different in the groups tested

Answer 3

The variances of anxiety scores were roughly the same for the groups tested.

Question 4

In an ANCOVA with one covariate and one independent variable, what null hypothesis is not tested?

A) Equal slopes
B) Equal intercepts for each line
C) Equal group means
D) Slopes are equal to 1

Question 5

Using the SPSS output in Q4, which of the following statements best reflects what the effect of 'level' in the table tells us?

A) The seniority of the position had a significant relationship with the level of anxiety experienced.
B) The seniority of the position did not have a significant relationship with the level of anxiety experienced.
C) The field of job applied for had a significant relationship with the seniority of the job.
D) The field of job applied for did not have a significant relationship with the seniority of the job.

Question 6

In an experiment to study the effectiveness of three different chartered accountancy courses (ACA, CIMA, ACCA) on professional accountants' career achievement, what would not be an appropriate covariate?

A) IQ
B) Mathematical aptitude
C) Age
D) Height

Question 7

To 'partial out' means to?

A) Examine the model without covariates.
B) Control for the effect of a covariate.
C) Partition the covariate effects.
D) Partition the variance.

Question 8

Adjusted group means for a sample of John Lewis customers represent.

A) The means across all customer groups when the covariate has been accounted for
B) The means across the covariate
C) The means across each customer group that are significantly different from each other
D) All the means added together

Question 9

What is not true of the ANCOVA procedure in SPSS?

A) It is part of the ANOVA procedure
B) It is invoked when interval-level independents (covariates) are listed in the covariates subcommand.
C) It can be accessed either through the Univariate or Multivariate options.
D) The maximum number of covariates SPSS will process is 30.

Question 10

What assumption does ANCOVA have that ANOVA does not?

A) Homogeneity of variance
B) Homogeneity of regression slopes
C) Homoscedasticity
D) Homogeneity of sample size

Question 11

Consider the graph below. This shows the results of an experiment training condition as the independent variable and employee IQ as the covariate.

What does the graph indicate?

A) Although the independent variable has had an effect on the dependent variable, the covariate is the more likely explanation of effect.
B) The training condition has altered IQ.
C) IQ has altered learning condition.
D) Not enough information.

Question 12

The second part of SPSS output for the example in Q2 is below. Which of the following statements best reflects the effect of 'job' in the analysis?

A) The field of job applied for had a significant effect on the level of anxiety experienced.
B) The field of job applied for did not have a significant effect on the level of anxiety experienced.
C) The field of job applied for had a significant effect on the level of anxiety experienced even after the effect of the seniority of the job had been accounted for.
D) The field of job applied for did not have a significant effect on the level of anxiety experienced even after the effect of the seniority of the job had been accounted for

Question 13

What is an alternative way to model the design of an ANCOVA test?

A) Linear multiple regression with the independent variables reduced to dummy variables
B) Linear multiple regression with all the dependent variables and the covariate standardized
C) Logistic regression with the independent variables reduced to binary variables
D) Logistic regression with all the dependent variables and the covariate reduced to binary variables

Question 14

What type of analysis might you choose to implement if the assumption of homogeneity of regression slopes is violated when employing ANCOVA?

A) Multilevel linear modelling
B) Any non-parametric test
C) Logistic regression
D) None of the above

Question 15

The SPSS output below shows the final table of analysis (as used in Q2-Q5). Which of the following statements is most reflective of the output?

A) Accountants were significantly less anxious than IT technicians, but were about as anxious as sales people, and IT technicians were about as anxious as sales people.
B) Accountants were significantly less anxious than sales people and IT technicians, and IT technicians were significantly less anxious than sales people.
C) Accountants, IT technicians and sales people were all about equally anxious.
D) Accountants were significantly less anxious than sales people and IT technicians, and IT technicians were significantly more anxious than sales people

Question 16

Under which circumstance(s) should you avoid using analysis of covariance?

A) If you need to control for all extraneous variables on which the groups may differ.
B) If you have identified variables that have not been controlled for.
C) If you have controlled for all possible variables.
D) If you need to reduce unexplained variance.