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

Question 1

A health psychologist was interested in the effects of smoking on the suppression of the immune system. Three groups of adults were exposed (in a highly ethical way) to either a cold virus, a flu virus or were left freezing wet in the outside in the middle of winter to catch pneumonia (no more than smokers deserve!). The severity of the disease was then measured as a percentage (0% = not contracted, 100% = contracted to a very severe degree). The psychologist also measured the number of cigarettes that each person smoked per day. The psychologist was interested in the differences in the severity of the three illnesses and the impact of cigarette usage. What technique should be used to analyse these data?

A) Two-way repeated-measures ANOVA.
B) Two-way independent ANOVA.
C) Two-way mixed ANOVA.
D) One-way analysis of covariance.

Answer 1

One-way analysis of covariance.

Question 2

Which of the following is not considered to be an assumption of ANCOVA?

A) Homogeneity of variance
B) Homogeneity of regression
C) Heterogeneity of variance
D) Linearity

Answer 2

Heterogeneity of variance

Question 3

Consider the graph below. This is the graph of the results of an experimental learning condition as the independent variable and 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 learning condition has altered IQ.
C) IQ has altered the learning condition.
D) Not enough information.

Answer 3

Although the independent variable has had an effect on the dependent variable, the covariate is the more likely explanation of effect.

Question 4

A scatterplot and a summary table for the ANCOVA on the data relating to it are given below. What does the interaction term suggest?

A) The effect is significant (p < .05) and the assumption of homogeneity of regression slopes has been violated.
B) The effect is significant (p < .05) and the assumption of homogeneity of regression slopes has been maintained.
C) The effect is not significant (p > .05) and the assumption of homogeneity of regression slopes has been violated.
D) The effect is not significant (p > .05) and the assumption of homogeneity of regression slopes has been maintained.

Question 5

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

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 6

Under what circumstances would you not consider using analysis of covariance?

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

Question 7

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

A) The slopes are equal.
B) The intercepts for each line are equal.
C) The group means are equal
D) The slopes are all equal to 1.

Question 8

Using the SPSS output below, which of the following statements best reflects the effect of 'Grade'?

A) The grade of exam had a significant relationship with the level of anxiety experienced.
B) The grade of exam did not have a significant relationship with the level of anxiety experienced.
C) The type of instrument played had a significant relationship with the grade of exam being taken.
D) The type of instrument played did not have a significant relationship with the grade of exam being taken.

Question 9

Adjusted group means are

A) Means across all groups when the covariate has been accounted for.
B) Means across the covariate.
C) Means across the groups that are significantly different.
D) All the means added together.

Question 10

What does ANCOVA allow the researcher to do with data?

A) Manipulate the predictor variables in the data
B) Remove from a dependent variable irrelevant or error variance that cannot be predicted from the independent variable
C) Reduce the power in the experiment
D) None of the above

Question 11

A music teacher had noticed that some students went to pieces during exams. He wanted to test whether this performance anxiety was different for people playing different instruments. He took groups of guitarists, drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. He also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8). He wanted to see whether the type of instrument played affected performance anxiety when controlling for the grade of the exam. The first part of the SPSS output is below. What does this part of the output tell us?

A) The type of instrument played did not have a significant effect on anxiety.
B) The grade of exam taken did not have a significant effect on anxiety.
C) The variances of anxiety scores were roughly the same in the different groups of musicians.
D) The variances of anxiety scores were different in the different groups of musicians.

Question 12

A music teacher had noticed that some students went to pieces during exams. He wanted to test whether this performance anxiety was different for people playing different instruments. He took groups of guitarists, drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. He also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8). He wanted to see whether the type of instrument played affected performance anxiety when controlling for the grade of the exam. What analysis should he use?

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

Question 13

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 14

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 15

What makes ANCOVA different from ANOVA?

A) ANCOVA can include dummy variables.
B) ANCOVA can include one or more continuous variables that predict the outcome.
C) ANCOVA can include continuous variables that are not part of the main experimental manipulation but influence the dependent variable.
D) ANCOVA can include continuous variables that are not part of the main experimental manipulation but influence the independent variable.

Question 16

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 17

In an experiment to study the effectiveness of three different teaching programmes on children's achievement in mathematics, what might not be an appropriate covariate?

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

Question 18

What does the relationship of the data in the following scatterplot indicate?

A) A positive relationship where height increases with age for both sexes
B) A larger relationship for males
C) A negative relationship for both sexes
D) None of the above

Question 19

A music teacher had noticed that some students went to pieces during exams. He wanted to test whether this performance anxiety was different for people playing different instruments. He took groups of guitarists, drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. He also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8). He wanted to see whether the type of instrument played affected performance anxiety when controlling for the grade of the exam. The second part of the SPSS output is below. Which of the following statements best reflects the effect of 'Instru'?

A) The type of instrument played in the exam had a significant effect on the level of anxiety experienced.
B) The type of instrument played in the exam did not have a significant effect on the level of anxiety experienced.
C) The type of instrument played in the exam had a significant effect on the level of anxiety experienced, even after the effect of the grade of the exam had been accounted for.
D) The type of instrument played in the exam did not have a significant effect on the level of anxiety experienced, even after the effect of the grade of the exam had been accounted for.

Question 20

A music teacher had noticed that some students went to pieces during exams. He wanted to test whether this performance anxiety was different for people playing different instruments. He took groups of guitarists, drummers and pianists (variable = 'Instru') and measured their anxiety (variable = 'Anxiety') during the exam. He also noted the type of exam they were performing (in the UK, musical instrument exams are known as 'grades' and range from 1 to 8). He wanted to see whether the type of instrument played affected performance anxiety when controlling for the grade of the exam. The SPSS output below shows the final tables. Which of the following statements best reflects what these tables tells us?

A) Guitarists were significantly less anxious than drummers, but were about as anxious as pianists, and drummers were about as anxious as pianists.
B) Guitarists were significantly less anxious than pianists and drummers, and drummers were significantly less anxious than pianists.
C) Guitarists, drummers and pianists were all about equally anxious.
D) Guitarists were significantly less anxious than pianists and drummers, and drummers were significantly more anxious than pianists.

Question 21

When assumptions are violated in ANCOVA, which non-parametric test can be carried out?

A) Kruskal-Wallis test
B) Chi-square test
C) Mann-Whitney test
D) None of the above

Question 22

In a study of favourable effects of berry consumption on platelet formation, blood pressure and HDL cholesterol, the following results are reported Berry consumption inhibited platelet function as measured with a platelet function analyzer (using collagen and ADP as platelet activator) [changes: 11% and -1.4% in the berry and control groups, respectively; P=0.018, ANCOVA]. Plasma biomarkers of platelet activation, coagulation and fibrinolysis did not change during the intervention. Serum HDL-cholesterol concentrations increased significantly more (P=0.006, ANCOVA) in the berry than in the control group (5.2% and 0.6%, respectively), but total cholesterol and triacylglycerol remained unchanged. Systolic BP decreased significantly (P=0.050, ANCOVA). Polyphenol and vitamin C concentrations in plasma increased, whereas other nutritional biomarkers (i.e. folate, tocopherols, sodium and potassium) were unaffected.
Source: Erlund, I., Koli, R., Marniemi, J., Puuka, P., Mustonen, P. Mattila, P. & Jula, A. (2008). Favourable effects of berry consumption on platelet function, blood pressure and HDL cholesterol. American Journal of Clinical Nutrition, 87(2). 323-331.
Which of the following would you consider a possible conclusion from this report?

A) The consumption of berries caused an increase in HDL-cholesterol, indicating a possible role in prevention of cardiovascular disease.
B) The consumption of berries did not cause any change in platelet function, thus indicating no potential role in prevention of cardiovascular disease.
C) The consumption of berries did not cause any change in the control group, thus indicating a possible role in prevention of cardiovascular disease.
D) None of the above.

Question 23

What does the effect size measure in ANCOVA?

A) The proportion of total variance in the data
B) The proportion of variance that a variable explains that is not explained by other variables in the analysis
C) The power of the experiment
D) None of the above

Question 24

The following scatterplot represents the results of a study undertaken by Chakrabarty et al. (2005) who were investigating glutamate levels in psychotropic drug-naive OCD patients and comparing them with psychiatrically normal controls. Findings were reported as follows for CSF glutamate levels in OCD patients compared to controls: F(1,29)=11.153, p = 0.002. How would these findings be interpreted? Scatterplot showing CSF glutamate levels in patients (1) and controls (2).

A) CSF glutamate levels are not significantly raised in OCD patients compared to normal controls.
B) CSF glutamate levels are significantly raised in OCD patients compared to normal controls.
C) CSF glutamate levels are unchanged in OCD patients compared to normal controls.
D) None of the above.

Question 25

The following scatterplot represents the results of a study undertaken by Chakrabarty et al. (2005) who were investigating glutamate levels in psychotropic drug-naive OCD patients and comparing them with psychiatrically normal controls. Based on this scatterplot the following ANCOVA of glutamate levels in CSF was done. Findings were reported as follows for CSF glutamate levels in OCD patients compared to controls: F(1,29)=11.153, p=0.002. What conclusion can be drawn about this result? Scatterplot showing CSF glutamate levels in patients (1) and controls (2).
ANCOVA of Glutamate Levels in CSF
Diagnosis (OCD vs Controls) and gender were included as factors, while age, number of years of illness, total Y-BOCS scores, and CGI-S scores were included as covariates in the analysis.

A) A significant main effect of gender is evident on CSF glutamate levels.
B) A significant main effect of age is evident on CSF glutamate levels.
C) A significant main effect of diagnosis is evident on CSF glutamate levels.
D) No significant effects are evident on CSF glutamate levels.