Deck 15: GlM 4: Repeated-Measures Designs

Question 1

Departures from sphericity can be measured using:

A)Neither of these estimates
B)Both of these estimates
C)The Greenhouse-Geisser estimate
D)The Huynh-Feldt estimate

Answer 1

B

Question 2

Imagine I ran a one-way repeated-measures ANOVA with five levels on the independent variable. The results revealed a Greenhouse-Geisser estimate, = .977, and the Huynh-Feldt estimate, = .999. What do these values tells us about the assumption of sphericity?

A)The assumption of sphericity is likely to have been violated.
B)We cannot tell anything about the assumption of sphericity from these values.
C)We do not need to check the assumption of sphericity for a one-way repeated-measures ANOVA.
D)The assumption of sphericity is likely to have been met.

Answer 2

D

Question 3

Imagine we were trying to interpret the results of a 3  3 two-way repeated-measures ANOVA. The data analysis contains no information about sphericity. In this situation, which of the following rows from the output should be interpreted?

A)The Greenhouse-Geisser row, as it is better to assume sphericity has been violated.
B)The row labelled 'sphericity assumed', as it is better to assume sphericity has been met.
C)The Bonferroni row, as it is always better to assume sphericity has been violated.
D)The row labelled 'sphericity assumed', as sphericity is not an issue when there are only two independent variables.

Answer 3

A

Question 4

When an experimental manipulation is carried out on the same entities, the within-participant variance will be made up of:

A)The effect of the manipulation and individual differences in performance.
B)The effect of the manipulation only.
C)Individual differences in performance only.
D)Unsystematic variance only.

Question 5

How many effects will there be from a two-way repeated-measures ANOVA?

A)3
B)2
C)It will vary depending on how many levels of your independent variable there are.
D)4

Question 6

Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., 'Come on, you Reds!'), one at which they were instructed to sing negative songs towards the opposition (e.g., 'You're getting sacked in the morning!') and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups.

-Looking at the output below, which of the following sentences is correct? $$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\text { Descriptive Statistics }\\\begin{array} { | l | c | c | c | } \hline & \text { Mean } & \begin{array} { c } \text { Std. } \\\text { Deviation }\end{array} & \mathrm { N } \\\hline \begin{array} { l } \text { Number of goals scored } \\\text { When supporters sang } \\\text { songs of encouragement } \\\text { to their team }\end{array} & 2.90 & 1.197 & 10 \\\begin{array} { l } \text { Number of goals scored } \\\text { when supporters sang } \\\text { songs of abuse towards } \\\text { the opposition }\end{array} & .70 & .675 & 10 \\\begin{array} { l } \text { Number of goals scored } \\\text { when supporters sat } \\\text { quietly }\end{array} & 1.50 & 1.080 & 10 \\\hline\end{array}\end{array}$$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Tests of Within-Subjects Effects
Measure: MEASURE_1
$\begin{array}{|ll|r|r|r|r|r|}\hline \text { Source } & &{\begin{array}{c}\text { Type III Sum } \\\text { of Squares }\end{array}} & {\text { df }} & \text { Mean Square } & {\mathrm{F}} & {\text { Sig. }} \\\hline \text { Singing } & \text { Sphericity Assumed } & 24.800 & 2 & 12.400 & 11.235 & .001 \\& \text { Greenhouse-Ceisser } & 24.800 & 1.577 & 15.727 & 11.235 & .002 \\& \text { Huynh-Feldt } & 24.800 & 1.855 & 13.370 & 11.235 & .001 \\& \text { Lower-bound } & 24.800 & 1.000 & 24.800 & 11.235 & .008 \\\hline \text { ErroriSinging) } & \text { Sphericity Assumed } & 19.867 & 18 & 1.104 & & \\& \text { Greenhouse-Ceisser } & 19.867 & 14.192 & 1.400 & & \\& \text { Huynh-Feldt } & 19.867 & 16.695 & 1.190 & & \\& \text { Lower-bound } & 19.867 & 9.000 & 2.207 & & \\\hline\end{array}$

A)The results showed that the number of goals scored was significantly affected by the type of singing from the supporters, F(2, 18) = 11.24, p = .001.
B)The results showed that the number of goals scored was significantly affected by the type of singing from the supporters, F(1.58, 14.19) = 11.24, p = .002.
C)The results showed that the number of goals scored was significantly affected by the type of singing from the supporters, F(2, 12.4) = 11.24, p = .001.
D)The results showed that the number of goals scored was significantly higher when supporters sang positive songs towards their team, F(2, 18) = 11.24, p = .001.

Question 7

Exercise Two-way repeated-measures ANOVA compares:

A)Two means when there are more than two independent variables, and the same entities have been used in all conditions.
B)Several means when there are two independent variables, and the same entities have been used in some of the conditions.
C)Several means when there are more than two independent variables, and some have been manipulated using the same entities and others have used different entities.
D)Several means when there are two independent variables, and the same entities have been used in all conditions.

Question 8

When conducting a repeated-measures ANOVA which of the following assumptions is not relevant?

A)Independent residuals
B)They are all relevant
C)Homogeneity of variance
D)Sphericity

Question 9

What is Repeated-measures factorial design?

A)An experiment, which compares the means of two or more categorical predictors, each of which is measured using different entities in all conditions.
B)An experiment, which compares the means of two or more categorical predictors, each of which is measured using the same entities in all conditions.
C)An experiment, which compares the means of one categorical predictor, which is measured using the same entities in all conditions.
D)An experiment, which compares the means of one categorical predictor, which is measured using different entities in all conditions.

Question 10

The results of a one-way repeated-measures ANOVA with four levels on the independent variable revealed a significance value for Mauchly's test of p = 0.048. What does this mean?

A)That Tukey's test should be used.
B)The assumption of sphericity has been violated.
C)The assumption of sphericity has been met.
D)This value can be ignored because sphericity is not an issue in a one-way repeated-measures ANOVA design.

Question 11

When entering data for a repeated-measures design in SPSS:

A)Each row of the data editor should represent data from one entity, while each column represents a coding variable.
B)It doesn't matter how you enter repeated-measures data into SPSS.
C)Each row of the data editor should represent data from one entity, while each column represents a level of a variable.
D)Each row of the data editor should represent a level of a variable, while each column represents data from one entity.

Question 12

Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., 'Come on, you Reds!'), one at which they were instructed to sing negative songs towards the opposition (e.g., 'You're getting sacked in the morning!') and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups.

-An ANOVA with a simple contrasts using the last category as a reference was conducted. Looking at the output tables below, which of the following sentences regarding the contrasts is correct? $$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Descriptive Statistics }\\\begin{array} { | l | c | c | c | } \hline & \text { Mean } & \begin{array} { c } \text { Std. } \\\text { Deviation }\end{array} & \mathrm { N } \\\hline \begin{array} { l } \text { Number of goals scored } \\\text { when supporters sang } \\\text { songs of encouragement } \\\text { to their team }\end{array} & 2.90 & 1.197 & 10 \\\begin{array} { l } \text { Number of goals scored } \\\text { when supporters sang } \\\text { songs of abuse towards } \\\text { the opposition }\end{array} & .70 & .675 & 10 \\\begin{array} { l } \text { Number of goals scored } \\\text { when supporters sat } \\\text { quietly }\end{array} & 1.50 & 1.080 & 10 \\\hline\end{array}\end{array}$$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Tests of Within-Subjects Contrasts
Measure: MEASURE_1
$\begin{array}{ll|r|r|r|r|r}\text { Source } & \text { Singing } & \begin{array}{c}\text { Type III Sum } \\\text { of Squares }\end{array} & {\text { df }} & \text { Mean Square } & {\text { F }} & {\text { Sig. }} \\\hline \text { Singing } & \text { Level 1 vs. Level 3 } & 19.600 & 1 & 19.600 & 7.230 & .025 \\& \text { Level 2 vs. Level 3 } & 6.400 & 1 & 6.400 & 6.000 & .037 \\\hline \text { Error(Singing) } & \text { Level 1 vs. Level 3 } & 24.400 & 9 & 2.711 & & \\& \text { Level 2 vs. Level 3 } & 9.600 & 9 & 1.067 & &\end{array}$

A)The first contrast revealed that soccer teams scored significantly fewer goals when their supporters did not sing compared to when they sang negative songs.The second contrast revealed that soccer teams scored a similar amount of goals when their supporters sang positive songs compared to when they did not sing.
B)The first contrast revealed that soccer teams scored significantly more goals when their supporters sang positive songs compared to when they did not sing.The second contrast revealed that soccer teams scored significantly fewer goals when their supporters sang negative songs compared to when they did not sing.
C)The first contrast revealed that soccer teams scored significantly more goals when their supporters sang positive songs compared to when they did not sing.The second contrast revealed that soccer teams scored significantly fewer goals when their supporters sang negative songs compared to when they sang positive songs.
D)The first contrast revealed that soccer teams scored significantly more goals when their supporters sang positive songs compared to when they did not sing.The second contrast revealed that soccer teams did not significantly differ in the number of goals scored when their supporters sang negative songs compared to when they did not sing.

Question 13

A nutritionist conducted an experiment on memory for dreams. She wanted to test whether it really was true that eating cheese before going to bed made you have bad dreams. Over three nights, the nutritionist fed people different foods before bed. On one night they had nothing to eat, a second night they had a big plate of cheese, and the third night they had another dairy product, milk, before bed. All people were given all foods at some point over the three nights. The nutritionist measured heart rate during dreams as an index of distress. Which statement is the correct way to report these results?

A)There was no significant effect of food on the distress caused by memories, F(2, 76) = 2.27, p = .11.
B)There was a significant effect of food on the distress caused by memories, F(2, 76) = 2.27, p < .05.
C)There was a significant effect of food on the distress caused by memories, F(1.97, 74.90) = 2.27.
D)There was no significant effect of food on the distress caused by memories, F(1.97, 74.90) = 2.27.

Question 14

Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., 'Come on, you Reds!'), one at which they were instructed to sing negative songs towards the opposition (e.g., 'You're getting sacked in the morning!') and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups.

-Which of the following sentences regarding the output from Mauchly's test of sphericity below is correct?

A)Mauchly's test indicated that the assumption of sphericity had been violated, ?2 (2) = .73, p = .29.
B)Mauchly's test indicated that the assumption of sphericity had been met, ?2 (2) = 2.50, p < .05.
C)Mauchly's test indicated that the assumption of sphericity had not been met, ?2 (2) = 2.50, p > .05.
D)Mauchly's test indicated that the assumption of sphericity had been met, ?2 (2) = 2.50, p = .29.

Question 15

Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., 'Come on, you reds!'), one at which they were instructed to sing negative songs towards the opposition (e.g., 'You're getting sacked in the morning!') and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups.

- A one-way repeated-measures ANOVA was conducted and post hoc tests were selected. Looking at the output below, which of the following sentences regarding the pairwise comparisons is correct? $$\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\text { Descriptive Statistics }\\\begin{array} { | l | c | c | c | } \hline & \text { Mean } & \begin{array} { c } \text { Std. } \\\text { Deviation }\end{array} & \mathrm { N } \\\hline \begin{array} { l } \text { Number of goals scored } \\\text { when supporters sang } \\\text { songs of encouragement } \\\text { to their team }\end{array} & 2.90 & 1.197 & 10 \\\begin{array} { l } \text { Number of goals scored } \\\text { when supporters sang } \\\text { songs of abuse towards } \\\text { the opposition }\end{array} & .70 & .675 & 10 \\\begin{array} { l } \text { Number of goals scored } \\\text { when supporters sat } \\\text { quietly }\end{array} & 1.50 & 1.080 & 10 \\\hline\end{array}\end{array}$$

A)Soccer teams scored significantly more goals when their supporters sang positive songs towards them compared to when they sang negative songs towards the opposition and compared to when they did not sing at all.Soccer teams did not significantly differ in the number of goals scored when their supporters sang negative songs compared to when they did not sing at all.
B)Soccer teams scored significantly more goals when their supporters sang positive songs towards them compared to when they sang negative songs towards the opposition, but not compared to when they did not sing at all.Soccer teams scored significantly fewer goals when their supporters sang negative songs compared to when they did not sing at all.
C)Soccer teams scored significantly more goals when their supporters sang positive songs towards them compared to when they sang negative songs towards the opposition, but not compared to when they did not sing at all.Soccer teams did not significantly differ in the number of goals scored when their supporters sang negative songs compared to when they did not sing at all.
D)Soccer teams scored significantly more goals when their supporters sang positive songs towards them compared to when they sang negative songs towards the opposition and when they did not sing at all.Soccer teams scored significantly more goals when their supporters sang negative songs compared to when they did not sing at all.

Question 16

Which of the following regarding the assumption of sphericity is false?

A)When sphericity is violated, we need to adjust the degrees of freedom for any F-ratios affected by the violation.
B)The effect of violating sphericity is a loss of power (i.e., an increased probability of a Type II error).
C)Sphericity does not affect post hoc tests.
D)When sphericity is violated, the Bonferroni post hoc test can be used.

Question 17

Which of the following statements is false?
When you have data that violate the assumption of sphericity:

A)The means are adjusted for any groups that are affected by the violation using estimates of sphericity.
B)You can use multivariate test statistics (MANOVA) instead.
C)The degrees of freedom are adjusted for any F-ratios affected by the violation using estimates of sphericity.
D)The Greenhouse-Geisser or Huynh-Feldt correction should be applied.

Question 18

Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., 'Come on, you Reds!'), one at which they were instructed to sing negative songs towards the opposition (e.g., 'You're getting sacked in the morning!') and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups.

- Which of the following could be used to analyse these data?

A)One-way between-groups ANOVA
B)Three-way repeated-measures ANOVA
C)Loglinear analysis
D)One-way repeated-measures ANOVA

Question 19

Which of the following is a source of variance in a three-way repeated-measures ANOVA?

A)The three-way interaction
B)The two-way interactions
C)All of these
D)The independent variables

Question 20

Imagine we were interested in the effect of supporters singing on the number of goals scored by soccer teams. We took 10 groups of supporters of 10 different soccer teams and asked them to attend three home games, one at which they were instructed to sing in support of their team (e.g., ‘Come on, you Reds!’), one at which they were instructed to sing negative songs towards the opposition (e.g., ‘You’re getting sacked in the morning!’) and one at which they were instructed to sit quietly. The order of chanting was counterbalanced across groups.

- An ANOVA with a simple contrasts using the last category as a reference was conducted. Looking at the output tables below, what does the first contrast (Level 1 vs. Level 3) compare? $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Tests of Within-Subjects Contrasts
Measure: MEASURE_1
$\begin{array}{|ll|r|r|r|r|r|}\hline\text { Source } & \text { Sinqing } & \begin{array}{r}\text { Type IIl Sum } \\\text { of Squares }\end{array} &{\text { df }} & \text { Mean Square } & {\text { F }} & {\text { Sig. }} \\\hline \text { Singing } & \text { Level 1 vs. Level 3 } & 19.600 & 1 & 19.600 & 7.230 & .025 \\& \text { Level 2 vs. Level 3 } & 6.400 & 1 & 6.400 & 6.000 & .037 \\\hline \text { Error(Singing) } & \text { Level 1 vs. Level 3 } & 24.400 & 9 & 2.711 & & \\& \text { Level 2 vs. Level 3 } & 9.600 & 9 & 1.067 & &\\\hline \end{array}$

A)Positive singing vs.no singing
B)No singing vs.negative singing
C)Negative singing vs.positive singing
D)We cannot tell which groups the levels represent from this output.

Question 21

A researcher in a retail-marketing unit wanted to test the impact of four different advertising campaigns for a new product ('TV', 'Social Media, 'Print Media' and 'Celebrity') on a group of forty randomly selected consumers. She wanted to compare the impact of each advertising campaign on each individual consumer's likelihood of purchasing the product and across the whole group, as well as any interaction effects. What sort of test design best suits this study?

A)Independent factorial design
B)ANOVA
C)Repeated-measures factorial design
D)Multiple linear regression.

Question 22

Which of these are potential sources of bias in a Repeated measures factorial design?

A)Outliers and normality.
B)Non-normality and homoscedasticity.
C)Linearity and homoscedasticity.
D)Outliers and non-normality.

Question 23

What is the additional assumption that is applied to Repeated-measures factorial design?

A)Polynominality.
B)Synchronicity.
C)Sphericity.
D)Homoscedasticity.

Question 24

What is the consequence of violating the assumption of Sphericity?

A)It increases statistical power, effects the distribution of the F-statistic and raises the rate of Type I errors in post hocs.
B)It reduces statistical power, effects the distribution of the F-statistic and reduces the rate of Type I errors in post hocs.
C)It reduces statistical power, effects the distribution of the F-statistic and raises the rate of Type I errors in post hocs.
D)It reduces statistical power, improves the distribution of the F-statistic and raises the rate of Type I errors in post hocs.

Question 25

An educational researcher wanted to test the impact of learning environment on children's ability to concentrate on a short reading comprehension task. There were four different environmental settings: 'Noisy', 'Chill Out', 'Cold', and 'Screen on' and a group of twenty randomly selected children. He wanted to compare the impact of each setting on each child's individual concertation times and across the group, as well as any interaction effects. What sort of test design best suits this study?

A)Repeated-measures factorial design
B)Independent factorial design
C)ANOVA
D)Multiple linear regression.

Question 26

Which of the following is a test for Sphericity?

A)Fields test.
B)t-test.
C)Mauchly's test.
D)Wald's test.

Question 27

A sports dietician wanted to test the impact of four different dietary supplements ('Placebo', 'Vitamin X', 'Vitamin Z' and 'Kale') on a team of thirty randomly selected elite athletes. She wanted to compare the impact of each supplement on each athlete's individual performance scores and across the team, as well as any interaction effects. What sort of test design best suits this study?

A)Independent factorial design
B)ANOVA
C)Repeated-measures factorial design
D)Multiple linear regression.

Question 28

What is Sphericity?

A)A form of compound symmetry, which assumes that the variances of the difference between data taken from the same participant being tested are equal.
B)A form of compound symmetry, which does not assume that the variances of the difference between data taken from the same participant being tested are equal.
C)A form of parallel symmetry, which assumes that the errors of the difference between data taken from the same participant being tested are equal.
D)A form of compound symmetry, which assumes that the errors of the difference between data taken from the same participant being tested are unequal.

Question 29

Which of the following is a means to correct for Sphericity?

A)The Field Correction.
B)The Greenhouse-Geisser correction.
C)The Pearson Correction.
D)The Wilks' Lambda Correction.

Question 30

A medical researcher wanted to test the impact of four different pain-relief drugs ('Placebo', 'Drug X', 'Drug Z' and 'Drug Y') on a group of twenty randomly selected patients with a long-term chronic illness. He wanted to compare the impact of each drug on each individual patient's rating of pain and across the group of patients, as well as any interaction effects. What sort of test design best suits this study?

A)Independent factorial design
B)ANOVA
C)Repeated-measures factorial design
D)Multiple linear regression.

Question 31

Why is it important to look at the effect size?

A)Because p values are not affected by Sphericity corrections but they do alter effect sizes.
B)Because p values can be affected by Sphericity errors but they do not alter effect sizes.
C)Because p values can be affected by Sphericity corrections and alter effect sizes.
D)Because p values can be affected by Sphericity corrections but they do not alter effect sizes.