Deck 3: One Factor Fixed-Effects Ancova With Single Covariate

Question 1

A researcher wanted to examine whether people remembered information better with auditory cues or with visual cues. Ten participants were randomly assigned to each of the two groups: one group heard a list of words from headphones, and the other group saw the same list of words from a screen. The participants were then asked to write down as many words as they could remember. The dependent variable was the number of words remembered.
-For which of the following situations is it appropriate to use ANCOVA?

A) In each group, half of the participants had a time limit to write the words down. Whether a time limit was imposed was also included in the model.
B) The participants' socioeconomic status (low, middle, or high) was expected to have an effect on their performance and was also included in the model.
C) Participants took a vocabulary test before the experiment and the scores of the test were included in the model.
D) Participants took a vocabulary test after the experiment and the scores of the test were included in the model.

Answer 1

C
(The covariate should be measured on interval or ratio scale. Also, it is better that covariates are measured prior to the administration of the treatment so that the dependence of the covariate on the treatment can be minimized.)

Question 2

A researcher wanted to examine whether people remembered information better with auditory cues or with visual cues. Ten participants were randomly assigned to each of the two groups: one group heard a list of words from headphones, and the other group saw the same list of words from a screen. The participants were then asked to write down as many words as they could remember. The dependent variable was the number of words remembered.
-Suppose the researcher used IQ as the covariate. He then found that the mean IQ is slightly different across two groups, and people with higher IQ tended to remember more words than people with lower IQ. It seems likely that

A) the assumption of independence was violated.
B) the assumption of homogeneity of variance was violated.
C) the assumption of independence of covariate and treatment was violated.
D) the assumption of homogeneity of slopes was violated.
E) there is no indication of assumption violation.

Answer 2

E
(The value of covariate can be different between groups, and a correlation between the covariate and dependent variable is desirable.)

Question 3

A researcher wanted to examine whether people remembered information better with auditory cues or with visual cues. Ten participants were randomly assigned to each of the two groups: one group heard a list of words from headphones, and the other group saw the same list of words from a screen. The participants were then asked to write down as many words as they could remember. The dependent variable was the number of words remembered.
-Suppose out of budget concerns, the researcher included only five participants in each group, tested each participant twice, and used each time as separate observations. It seems likely that

A) the assumption of independence was violated.
B) the assumption of homogeneity of variance was violated.
C) the assumption of independence of covariate and treatment was violated.
D) the assumption of homogeneity of slopes was violated.
E) there is no indication of assumption violation.

Answer 3

A
(The observations collected from the same subject are not independent.)

Question 4

A researcher wanted to examine if soil type had any effects on the heights of daylilies. Ten bulbs of daylilies were planted in each of the three different types of soil. The thickness of the soil (X) was also measured for each pot. After three months, the heights of the plants (Y) were measured. Below are the group means of the study.

-If ANCOVA is used, which group will have the highest adjusted mean height?

A) Group 1 ( )
B) Group 2 ( )
C) Group 3 ( )
D) All groups would have the same adjusted mean.
E) Any of the above situations is possible (not enough information provided).

Question 5

A researcher wanted to examine if soil type had any effects on the heights of daylilies. Ten bulbs of daylilies were planted in each of the three different types of soil. The thickness of the soil (X) was also measured for each pot. After three months, the heights of the plants (Y) were measured. Below are the group means of the study.

-If there is no correlation between X and Y, the MS_with for ANCOVA as compared to that for ANOVA will be

A) less
B) the same
C) greater
D) unpredictably different

Question 6

A researcher wanted to examine if soil type had any effects on the heights of daylilies. Ten bulbs of daylilies were planted in each of the three different types of soil. The thickness of the soil (X) was also measured for each pot. After three months, the heights of the plants (Y) were measured. Below are the group means of the study.

-If there is a substantial negative correlation between X and Y, the error variation for ANCOVA as compared to that for ANOVA will be

A) less
B) the same
C) greater
D) unpredictably different

Question 7

A researcher wanted to examine if soil type had any effects on the heights of daylilies. Ten bulbs of daylilies were planted in each of the three different types of soil. The thickness of the soil (X) was also measured for each pot. After three months, the heights of the plants (Y) were measured. Below are the group means of the study.

-If the correlation between X and Y is 0.5 for soil type 1, 0.1 for soil type 2, and -0.5 for soil type 3, it seems likely that

A) the assumption of normality is violated.
B) the assumption of homogeneity of variance is violated.
C) the assumption of linearity is violated.
D) the assumption of homogeneity of slopes is violated.
E) there is no indication of assumption violation.

Question 8

In ANCOVA, suppose Y is the dependent variable, X is the covariate, and the factor has two levels. Also all assumptions of ANCOVA are met. Which of the following situations is the most desirable?

A) r_XY = 0.5; =10, =12, =11.
B) r_XY = 0.1; =10, =12, =11.
C) r_XY = -0.1; =10, =20, =15.
D) r_XY = -0.5; =10, =20, =15.

Question 9

In an one-factor ANCOVA, suppose the factor has two levels (groups). Scatterplots of the dependent variable (Y) and the covariate (X) are generated (where group 1 is indicated by "•" and group 2 by "o"). Which of the following graphs shows the most desirable situation?

A)
B)
C)
D)