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Exam 17: Multivariate Analysis of Variance Manova

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Question 1

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A psychologist was interested in gauging the success of a mood manipulation during one of her experiments. She had three groups of participants who underwent different types of mood induction: disgust mood induction, negative mood induction and positive mood induction. After the mood induction, participants were asked to endorse nine statements relating to their mood (on a 5-point Likert scale from 1 = disagree to 5 = agree) : (1) When you're smiling the whole world smiles with you, (2) I love the pretty flowers, (3) I could never touch a dead body, (4) I would never eat catfood, (5) If someone served me monkey brain soup I would vomit, (6) I feel fed up, (7) Bodily fluids are nasty, (8) I could not drink from a glass that I'd used to catch a spider, (9) I am a worthless piece of scum. -Part of the SPSS output is below. Which of the following statements best summarizes the output?

A) The type of mood induction had a significant effect on responses to all of the nine items.
B) The type of mood induction had a significant effect on responses to at least one of the nine items.
C) The type of mood induction had a significant effect on responses to more than half at least of the nine items.
D) The type of mood induction that a person had could be significantly determined from a linear combination of responses to the nine items.

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Question 2

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Which of the following is not an assumption of MANOVA?

A) Sphericity
B) Independence
C) Multivariate normality
D) Random sampling

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Question 3

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A scientist was interested in the success of a newly developed sleep aid called 'Night Owl' on time taken to fall asleep and quality of sleep. She recruited 30 participants who were randomly allocated to receive either a dose of Night Owl or a placebo. The scientist measured the mean time taken for each participant to fall asleep (minutes) and the quality of their sleep (measured on a scale of 1 (poorest quality) to 10 (best possible quality) ) over the course of one week. -What can the scientist conclude from the output below?

The matrix is: $\left( \begin{array} { l l l l } 2 & 4 & 6 & 5 \\6 & 7 & 9 & 8\end{array} \right)$

Which of the following sentences is false?

When you have several outcome variables, what advantage does conducting a MANOVA have over conducting several ANOVAs?

Cross-products:

A psychologist was interested in gauging the success of a mood manipulation during one of her experiments. She had three groups of participants who underwent different types of mood induction: disgust mood induction, negative mood induction and positive mood induction. After the mood induction, participants were asked to endorse nine statements relating to their mood (on a 5-point Likert scale from 1 = disagree to 5 = agree) : (1) When you're smiling the whole world smiles with you, (2) I love the pretty flowers, (3) I could never touch a dead body, (4) I would never eat catfood, (5) If someone served me monkey brain soup I would vomit, (6) I feel fed up, (7) Bodily fluids are nasty, (8) I could not drink from a glass that I'd used to catch a spider, (9) I am a worthless piece of scum. - What analysis should be done to see if the mood inductions had an effect on responses to these nine items?

A scientist was interested in the success of a newly developed sleep aid called 'Night Owl' on time taken to fall asleep and quality of sleep. She recruited 30 participants who were randomly allocated to receive either a dose of Night Owl or a placebo. The scientist measured the mean time taken for each participant to fall asleep (minutes) and the quality of their sleep (measured on a scale of 1 (poorest quality) to 10 (best possible quality) ) over the course of one week. -How could the scientist analyse her data to investigate whether participants in the Night Owl group fell asleep faster and had a better quality of sleep than those in the placebo group?

A psychologist was interested in gauging the success of a mood manipulation during one of her experiments. She had three groups of participants who underwent different types of mood induction: disgust mood induction, negative mood induction and positive mood induction. After the mood induction, participants were asked to endorse nine statements relating to their mood (on a 5-point Likert scale from 1 = disagree to 5 = agree) . - A discriminant function analysis was performed on the data. The output is below. Which statement best sums up the results? $\begin{array}{l}\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\text { Wilks' Lambda }\\\begin{array} { | l | r | r | r | r | } \hline \text { Test of Function(s) } & \begin{array} { c } \text { Wilks' } \\\text { Lambda }\end{array} & \text { Chi-square } & \text { df } & \text { Sig. } \\\hline 1 \text { through 2 } & .615 & 30.128 & 18 & .036 \\2 & .901 & 6.452 & 8 & .597 \\\hline\end{array}\end{array}$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$ Eigenvalues $\begin{array}{|l|r|r|r|r|}\hline \text { Function } & \text { Eigenvalue } & \% \text { of Variance } & \text { Cumulative } \% & \begin{array}{c}\text { Canonical } \\\text { Correlation }\end{array} \\\hline 1 & .465^{\mathrm{a}} & 80.9 & 80.9 & .563 \\2 & .110^{\mathrm{a}} & 19.1 & 100.0 & .314 \\\hline\end{array}$ a. First 2 canonical discriminant functions were used in the analysis.

A scientist was interested in the success of a newly developed sleep aid called 'Night Owl' on time taken to fall asleep and quality of sleep. She recruited 30 participants who were randomly allocated to receive either a dose of Night Owl or a placebo. The scientist measured the mean time taken for each participant to fall asleep (minutes) and the quality of their sleep (measured on a scale of 1 (poorest quality) to 10 (best possible quality) ) over the course of one week. -What does the output below show? $\quad$$\quad$ Box's Test of Equality $\quad$$\quad$$\quad$ of Covariance $\quad$$\quad$$\quad$$\quad$ Matrices ${ } ^ { a }$ $\begin{array}{|l|r|}\hline \text { Box's M } & .229 \\\text { F } & .070 \\\text { df1 } & 3 \\\text { df2 } & 141120.000 \\\text { Sig. } & .976\\\hline\end{array}$ Tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups. a. Design: Intercept + Drug Bartlett's Test of Sphericity ${ } ^ { a }$ $\begin{array}{|l|r|}\hline \text { Likelihood Ratio } & .000 \\\text { Approx. Chi-Square } & 101.046 \\\text { df } & 2 \\\text { Sig. } & .000\\\hline\end{array}$ Tests the null hypothesis that the residual covariance matrix is proportional to an identity matrix. a. Design: Intercept + Drug

In MANOVA, it can be a good idea to:

Which of the following statements about MANOVA is false?

A psychologist was interested in gauging the success of a mood manipulation during one of her experiments. She had three groups of participants who underwent different types of mood induction: disgust mood induction, negative mood induction and positive mood induction. After the mood induction, participants were asked to endorse nine statements relating to their mood (on a 5-point Likert scale from 1 = disagree to 5 = agree) . -Which statement best sums up this part of the output?

MANOVA requires:

A psychologist was interested in gauging the success of a mood manipulation during one of her experiments. She had three groups of participants who underwent different types of mood induction: disgust mood induction, negative mood induction and positive mood induction. After the mood induction, participants were asked to endorse nine statements relating to their mood (on a 5-point Likert scale from 1 = disagree to 5 = agree) . -Which statement best sums up this part of the output?

Which of the following statements is false?

Which of the following is false with regard to Box's test?

When following up a significant MANOVA, what is the advantage of conducting discriminant function analysis over separate ANOVAs?

If we ran Box's test prior to conducting a MANOVA and obtained a value with an associated p-value less than .05, what would this tell us?