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?

Accepted Answer

D

Question 2

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

Accepted Answer

Heterogeneity of variance is not an assumption of ANCOVA. The three main assumptions of ANCOVA are homogeneity of variance, homogeneity of regression, and linearity.

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?

Accepted Answer

The graph shows a correlation between the experimental learning condition and the dependent variable, but it is not clear if this correlation is causal or if it is simply due to the covariate (in this case, IQ). Therefore, the most likely explanation for the effect seen in the graph is the IQ covariate rather than the learning condition itself.

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?

Accepted Answer

The interaction term suggests that the relationship between the two variables (y and x) differs for different levels of the third variable (z). The effect is significant (p < .05), which means that the interaction term is important for explaining the variation in y. However, the assumption of homogeneity of regression slopes has been violated, which means that the relationship between y and x is not the same for all levels of z. This violates one of the assumptions of ANCOVA and could affect the validity of the results.

Question 5

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

Accepted Answer

ANCOVA can be modeled as a linear multiple regression with the independent variables reduced to dummy variables. This approach allows for the inclusion of both categorical and continuous independent variables, as well as a covariate, in the analysis. Standardizing the dependent variables and covariate (as suggested in option B) is not necessary for ANCOVA, and logistic regression (options C and D) is not appropriate for analyzing continuous dependent variables.

Question 6

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

Accepted Answer

Analysis of covariance (ANCOVA) is used to control for the effects of extraneous variables. If you have already controlled for all possible variables, ANCOVA may not be necessary.

Question 7

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

Accepted Answer

ANCOVA does not test whether the slopes are all equal to 1; it tests for equality of slopes and intercepts across groups and the effect of the independent variable on the dependent variable after controlling for the covariate.

Question 8

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

Accepted Answer

The answer of Using the SPSS output below, which of...

Question 9

Adjusted group means are

Accepted Answer

Adjusted group means are means that have been adjusted for a covariate, taking into account its effect on the outcome variable. This allows for a fair comparison of the means across different groups with different levels of the covariate.

Question 10

What does ANCOVA allow the researcher to do with data?

Accepted Answer

ANCOVA allows the researcher to control for or remove from the dependent variable any irrelevant or error variance that cannot be predicted from the independent variable. It does not allow the manipulation of predictor variables or reduce power in the experiment.

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?

Accepted Answer

The output shows the Levene's test for equality of variances. The significance value for the variable 'Instru' is greater than 0.05, indicating that there is no significant difference in the variances of anxiety scores between the groups of guitarists, drummers, and pianists. This suggests that the assumption of equal variances is met, which is important for some statistical tests. The output does not provide information on the effects of the type of instrument or grade of exam on anxiety.

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?

Accepted Answer

The music teacher should use analysis of covariance (ANCOVA) to control for the grade of the exam and determine whether the type of instrument played affects performance anxiety. ANCOVA allows for the comparison of means across groups while controlling for the effects of a covariate, in this case, the grade of the exam. This analysis would enable the music teacher to determine whether differences in anxiety scores between groups are due to the type of instrument played or differences in the grade of the exam.

Question 13

To 'partial out' means to

Accepted Answer

To 'partial out' refers to controlling for (or adjusting for) the effect of a covariate. This is often done in statistical analysis to assess the independent effect of a predictor variable of interest while controlling for the potential confounding effect of other variables (i.e. covariates).

Question 14

What assumption does ANCOVA have that ANOVA does not?

Accepted Answer

ANCOVA assumes homogeneity of regression slopes, which means that the relationship between the independent variable and the dependent variable is consistent across all levels of the covariate. This is not a requirement for ANOVA, which only assumes homogeneity of variance and homoscedasticity.

Question 15

What makes ANCOVA different from ANOVA?

Accepted Answer

ANCOVA can include continuous variables that are not part of the main experimental manipulation but influence the dependent variable.

Question 16

What is not true of the ANCOVA procedure in SPSS?

Accepted Answer

The statement "the maximum number of covariates SPSS will process is 30" is not true. There is no maximum limit on the number of covariates that can be processed in SPSS ANCOVA.

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?

Accepted Answer

Height is not relevant or related to children's achievement in mathematics, therefore it would not be an appropriate covariate. IQ, mathematical aptitude, and age are all factors that could potentially impact a child's achievement in mathematics and would be appropriate covariates.

Question 18

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

Accepted Answer

The scatterplot shows a positive relationship where height increases with age for both sexes.

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'?

Accepted Answer

The significant F value for 'Instru' in the ANCOVA table indicates that the type of instrument played had a significant effect on anxiety levels even after controlling for the grade of the exam. Therefore, option C is the correct statement. Option A is incorrect as it does not consider the control variable. Option B is incorrect as it does not consider the ANCOVA table results. Option D is incorrect as it contradicts the ANCOVA table.

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?

Accepted Answer

The answer of A music teacher had noticed that some...

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