 ## Intermediate Questions

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The owner of the large chain of coffee shops called ‘MoonBucks’ decided to calculate how much revenue was gained from lattes each month in a nationwide sample of 2445 cafés. To measure the variance of revenue gained from lattes, he computes SS = 351,936 for this sample.

• What are the degrees of freedom for variance?
• Compute the variance.
• Compute the standard deviation.

1. 144
2. 12
3. 2444

If we calculated an effect size and found it was r = .42 which expression would best describe the size of effect?

1. Small
2. Small to medium
3. Medium to large
4. Large

If we use the mean as a model, what does the variance represent?

1. The average error between the model and the observed data.
2. The total error between the model and the observed data.
3. The squared total error between the model and the observed data.
4. The square-rooted average error between the model and the observed data.

#### Answer: The average error between the model and the observed data

Which of the following best describes the variable ‘Gender’?

1. A between-group variable.
2. A coding variable.
3. All of the possible answers are correct.
4. A grouping variable.

Which of the numbers below might IBM SPSS report as 10.574 E−05?

1. 0.00010574
2. 10.569
3. 1057400.0
4. 0000.10574

Which of the numbers below might IBM SPSS report as 8.96 E+03?

1. 89.60
2. 8960.0
3. 0.008960
4. 8.960

Which of the following does a box–whisker plot not display?

1. The mean
2. The median
3. Outliers
4. The lower quartile

What type of graph can we use to compare frequency distributions of several groups simultaneously?

1. A histogram
2. A bar chart
3. A population pyramid
4. A boxplot.

Out of the following options, which type of bar chart would we produce to look at the mean ratings of two new varieties of Sauvignon Blanc (wine)?

1. Clustered bar chart
2. Stacked bar chart
3. Simple 3-D bar chart
4. Simple bar chart

Out of the following options, which type of bar chart would we produce to look at the mean ratings of ‘taste’ and ‘value for money’ for two new varieties of Sauvignon Blanc wine?

1. Clustered bar chart
2. All of the options are possible.
3. Stacked bar chart
4. 3-D bar chart

#### Answer: All of the options are possible

Out of the following options, which type of graph could we use to compare frequency distributions of several groups simultaneously?

1. Population pyramid
2. Simple histogram
3. Frequency polygon
4. Simple 3-D bar chart

Which of the following are assumptions underlying the use of parametric tests (based on the normal distribution)?

1. All of the options are true.
2. Some feature of the data should be normally distributed.
3. The samples being tested should have approximately equal variances.
4. The data should be at least interval level.

#### Answer: All of the options are true

Approximately what percentage of people would have scores lower than an individual with a z-score of 1.65 in a normally distributed sample?

1. 95%
2. 98%
3. It is not possible to calculate this unless the mean and standard deviation are given.
4. 1%

Assuming the assumptions of parametric tests are met, non-parametric tests, compared to their parametric counterparts:

1. Are all of these.
2. Are more conservative.
3. Are less likely to accept the alternative hypothesis.
4. Have less statistical powe

#### Answer: Are all of these

How much variance has been explained by a correlation of .9?

1. 18%
2. 9%
3. 81%
4. None of these

A correlation of .7 was found between time spent studying and percentage on an exam. What is the proportion of variance in exam scores that can be explained by time spent studying?

1. .70
2. .49
3. .30
4. .7

Which of the following statistical tests allows causal inferences to be made?

1. Analysis of variance
2. Regression
3. None of these, it’s the design of the research that determines whether causal inferences can be made.
4. t-test

#### Answer: None of these, it’s the design of the research that determines whether causal inferences can be made

Which of the following statements about outliers is not true?

1. Outliers are values very different from the rest of the data.
2. Influential cases will always show up as outliers.
3. Outliers have an effect on the mean.
4. Outliers have an effect on regression parameters.

#### Answer: Influential cases will always show up as outliers

For which regression assumption does the Durbin–Watson statistic test?

1. Linearity
2. Homoscedasticity
3. Multicollinearity
4. Independence of errors

A researcher was interested in stress levels of lecturers during lectures. She took the same group of 8 lecturers and measured their anxiety (out of 15) during a normal lecture and again in a lecture in which she had paid students to be disruptive and misbehave. What test is best used to compare the mean level of anxiety in the two lectures?

1. Independent samples t-test
2. Paired-samples t-test
3. One-way independent ANOVA
4. Mann–Whitney test

What does the error bar on an error bar chart represent?

1. The confidence interval around the mean.
2. The standard error of the mean.
3. The standard deviation of the mean.
4. It can represent any of these.

#### Answer: It can represent any of these

Differences between group means can be characterized as a regression (linear) model if:

1. The experimental groups are represented by a binary variable (i.e. coded 0 and 1).
2. The outcome variable is categorical.
3. The groups have equal sample sizes.
4. Differences between group means cannot be characterized as a linear model, they must be analysed with an independent t-test.

#### Answer: The experimental groups are represented by a binary variable (i.e. coded 0 and 1)

A researcher measured people’s physiological reactions to horror films. He split the data into two groups: males and females. The resulting data were normally distributed and men and women had equal variances. What test should be used to analyse the data?

1. Dependent
2. Independent t-test
3. Mann–Whitney test
4. Wilcoxon signed-rank test

The combined effect of two variables on another is known conceptually as _______, and in statistical terms as _________

1. Mediation, an interaction effect
2. Moderation, a direct effect
3. Moderation, an interaction effect
4. Mediation, a direct effect

#### Answer: Moderation, an interaction effect

Imagine we wanted to look at the relationship between the number of hours spent practising the guitar per week and skill level. If we had reason to believe that the strength or direction of the relationship between these variables will be affected by level of enjoyment, what type of analysis should we conduct on these data?

1. Moderation analysis
2. Mediation analysis
3. Two-way repeated-measures ANOVA
4. ANCOVA

Grand mean centring for a given variable is achieved by:

1. Taking the mean of all scores (ignoring from which variable they come) and subtracting each score from it.
2. Taking each score and subtracting from it the mean of all scores (for that variable).
3. Taking each score and dividing it by the mean of all scores (for that variable).
4. Taking each score, subtracting the mean and then dividing by the standard deviation.

#### Answer: Taking each score and subtracting from it the mean of all scores (for that variable)

Imagine we wanted to look at whether enjoyment of guitar playing influences the relationship between time spent practising and skill level. How would we know if we had a significant moderation effect?

1. If the interaction of time spent practising and skill level was a significant predictor of enjoyment.
2. If the relationship between time spent practising and skill level does not change when enjoyment is entered into the model.
3. If the relationship between time spent practising and skill level disappears when enjoyment is entered into the model.
4. If the interaction of time spent practising and enjoyment was a significant predictor of skill level.

Answer: If the interaction of time spent practising and enjoyment was a significant predictor of skill level.

A researcher measured people’s physiological reactions while watching a horror film and compared them to when watching a comedy film, and a documentary about wildlife. Different people viewed each type of film. The resulting data were normally distributed and the variances across groups were similar. What test should be used to analyse the data?

1. Repeated-measures analysis of variance
2. Kruskal–Wallis test
3. Friedman’s ANOVA
4. Independent analysis of variance

#### Answer: Independent analysis of variance

Levene's test tests whether:

1. Data are normally distributed.
2. The variances in different groups are equal.
3. The assumption of sphericity has been met.
4. Group means differ.

#### Answer: The variances in different groups are equal

What assumption does ANCOVA have that ANOVA does not?

1. Homogeneity of variance
2. Homoscedasticity
3. Homogeneity of sample size
4. Homogeneity of regression slopes

#### Answer: Homogeneity of regression slopes

Which of the following are affected by including a covariate in an analysis of variance?

1. All of these.
2. The error mean square
3. The between-subjects mean square
4. The F-ratio.

What would the levels of the independent variables be for a two-way ANOVA investigating the effect of four different treatments for depression and gender?

1. 4 and 1
2. 2
3. 4 and 2
4. 6

How many independent variables were used and how were they measured in a three-way independent ANOVA?

1. Three independent variables all measured using the same entities
2. Three independent variables all measured using different entities
3. One independent variable (with three levels) measured using the same entities
4. One independent variable (with three levels) measured using different entities

#### Answer: Three independent variables all measured using different entities

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. How should these data be analysed?

1. One-way independent ANOVA
2. One-way repeated-measures ANOVA
3. Three-way repeated-measures ANOVA
4. Three-way independent ANOVA

In repeated-measures ANOVA, the assumption of independence is:

1. Always met
2. Unimportant
3. Tested using the Levene’s test
4. Always violated

A researcher tested 40 children aged 6 years. Each child engaged in a task where they had to use two dolls (one representing themselves and one representing a teacher) and they had to enact a time when their teacher had been angry with them. All children were videotaped and 20 children were told that their teacher would see the tape and 20 were not. What experimental design has been used?

1. A repeated-measures design
2. A matched design
3. A mixed design
4. A between-subjects design

A researcher tested 40 adults. Each adult had to rate their mood after listening to a tape of people being sick, and then again after a tape of people laughing. What experimental design has been used?

1. A matched design
2. A repeated-measures design
3. A mixed design
4. A between-subjects design

The power of MANOVA to detect an effect depends on:

1. A combination of the correlation between dependent variables and the effect size to be detected.
2. A combination of the correlation between independent variables and the effect size to be detected.
3. A combination of the correlation between independent and dependent variables.
4. None of these

#### Answer: A combination of the correlation between dependent variables and the effect size to be detected

What would you use Box’s test for?

1. To test for multivariate normality.
2. To test for independence of residuals
3. To test for homogeneity of variance
4. To test the assumption of homogeneity of covariance matrices.

#### Answer: To test the assumption of homogeneity of covariance matrices

If your MANOVA is statistically significant:

1. You could conduct separate Bonferroni corrected ANOVAs on each dependent variable.
2. There is no added value in performing discriminant function analysis.
3. You could conclude that all groups differ significantly.
4. None of these are correct.

#### Answer: You could conduct separate Bonferroni corrected ANOVAs on each dependent variable

A square matrix in which the diagonal elements are equal to 1 and the off-diagonal elements are equal to 0 is known as:

1. A variance–covariance matrix
2. A column vector
3. An identity matrix
4. The error sum of squares and cross-products matrix (or error SSCP)

Varimax rotation should be used when:

1. You believe that the underlying factors will be correlated.
2. You believe that the underlying factors are non-orthogonal.
3. You believe that the underlying factors are independent.
4. Kaiser’s criterion is met.

#### Answer: You believe that the underlying factors are independent

Kaiser's criterion for retaining factors is:

1. Retain any factor with an eigenvalue greater than 1.
2. Retain any factor with an eigenvalue greater than 0.3.
3. Retain factors before the point of inflexion on a scree plot.
4. Retain factors with communalities greater than 0.7.

#### Answer: Retain any factor with an eigenvalue greater than 1

What is a latent variable?

1. It is a variable that cannot be measured directly.
2. It is another name for a factor.
3. Latent variables represent clusters of variables that correlate highly with each other.
4. All of these are correct.

#### Answer: All of these are correct

On which of the following does the critical value for a chi-square statistic rely?

1. The degrees of freedom
2. The sum of the frequencies
3. The row totals
4. The number of variables

#### Answer: The degrees of freedom

Imagine you conducted a study to look at the association between whether expectant mothers in two different age groups (18–30 and 31–43 years) eat breakfast (or not) and the gender of the first-born child. Which of the following options would be the most appropriate method of analysing these data?

1. Chi-square test
2. Three-way repeated-measures ANOVA
3. Loglinear analysis
4. Two-way mixed analysis of covariance

The odds ratio is:

1. The ratio of the probability of an event not happening to the probability of the event happening.
2. The probability of an event occurring.
3. The ratio of the odds after a unit change in the predictor to the original odds.
4. The ratio of the probability of an event happening to the probability of the event not happening.

#### Answer: The ratio of the odds after a unit change in the predictor to the original odds

Larger values of the log-likelihood statistic indicate:

1. That there are a greater number of explained vs. unexplained observations.
2. That the statistical model fits the data well.
3. That as the predictor variable increases, the likelihood of the outcome occurring decreases.
4. That the statistical model is a poor fit of the data.

#### Answer: That the statistical model is a poor fit of the data

Logistic regression assumes a:

1. Linear relationship between continuous predictor variables and the outcome variable.
2. Linear relationship between continuous predictor variables and the logit of the outcome variable.
3. Linear relationship between continuous predictor variables.
4. Linear relationship between observations

#### Answer: Linear relationship between continuous predictor variables and the logit of the outcome variable

A researcher was interested in the effects of information about exercises that relieve back pain delivered in two different ways by doctors. Doctors were recruited from different hospitals and each gave several patients the information. How many levels are there in this hierarchical data structure?

1. 3
2. 1
3. 2
4. 4

A researcher was interested in the effects of information about exercises that relieve back pain delivered in two different ways. Several doctors within the same hospital delivered the information to multiple patients. How many levels are there in this hierarchical data structure?

1. 1
2. 3
3. 2
4. 4

You've done an ANCOVA but found that the assumption of homogeneity of regression slopes has been violated. Which of these is a potential solution to overcome this problem?

1. Multiple regression
2. Discriminant function analysis
3. Multilevel model
4. Factorial ANOVA

Missing data pose the least problem for:

1. Analysis of variance
2. Multiple regression
3. Principal component analysis
4. Multilevel linear models