## In at the Deep End Questions

Click on the question to reveal the answer.

What is the relationship between the sum of squared errors (SS), the sample size (n) and the variance (s2)?

1. SS = s2/(n – 1).
2. s2 = SS(n – 1).
3. n = (s2/SS) – 1.
4. s2 = SS/(n – 1).

#### Answer: s2 = SS/(n – 1)

Given a test is normally distributed with a mean of 30 and a standard deviation of 6:

• What is the probability that a single score drawn at random will be greater than 34?
• What is the probability that a sample of 9 scores will have a mean greater than 34?
• What is the probability that the mean of a sample of 16 scores will be either less than 28 or greater than 32?

1. 0.0228
2. 0.2524
3. 0.1826

Which of the following is not a transformation that can be used to correct skewed data?

1. Log transformation
2. Square root transformation
3. Reciprocal transformation
4. Tangent transformation

If we were to pull all possible samples from a population, calculate the mean for every sample, and construct a graph of the shape of the distribution based on all of the means, what would we have?

1. The population distribution of the mean
2. The sampling distribution of the mean
3. The bootstrap distribution of the mean
4. The standard error of the mean

#### Answer: The sampling distribution of the mean

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. The data were not normally distributed. Which test should she use to compare her experimental conditions?

1. Paired samples t-test
2. Mann–Whitney test
3. Wilcoxon rank-sum test
4. Wilcoxon signed-rank test

A researcher measured the same group of people’s physiological reactions while watching horror films and compared them to when watching erotic films. The resulting data were skewed. What test should be used to analyse the data?

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

A researcher measured the same group of people’s physiological reactions while watching horror films and compared them to when watching erotic films, and a documentary about wildlife. The resulting data were skewed. What test should be used to analyse the data?

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

Rank the score of 5 in the following set of scores:

9, 3, 5, 10, 8, 5, 9, 7, 3, 4

1. 4.5
2. 4
3. 3
4. 6

If Pearson’s correlation coefficient between stress level and workload is .8, how much variance in stress level is not accounted for by workload?

1. 20%
2. 2%
3. 8%
4. 36%

What is b0 in regression analysis?

1. The value of the outcome when all of the predictors are 0.
2. The relationship between a predictor and the outcome variable.
3. The value of the predictor variable when the outcome is zero.
4. The gradient of the regression line.

#### Answer: The value of the outcome when all of the predictors are 0

The t-test tests for:

1. Differences between means
2. Whether a correlation is significant
3. Whether a regression coefficient is equal to zero
4. All of these

Why is it a good idea to centre your variables when conducting a moderation analysis?

1. It makes the data normally distributed.
2. It aids the interpretation of the indirect effect.
3. Because it reduces multicollinearity between main effects and the interaction effect.
4. It ensures the relationship between the predictor and outcome is linear.

#### Answer: Because it reduces multicollinearity between main effects and the interaction effect

When variances across independent groups are unequal, which of the following is not an appropriate course of action?

1. Use Games–Howell post hoc tests.
2. Use Kruskal–Wallis test.
3. Use Welch’s F-ratio.
4. Use Friedman’s ANOVA.

Which of these statements describes a Bonferroni correction?

1. You apply a criterion for significance based on the usual criterion for significance (.05) divided by the number of tests performed.
2. You divide the F-ratio by the number of tests performed.
3. The degrees of freedom are corrected to make the F-ratio less significant.
4. The error in the model is adjusted for the number of tests performed.

#### Answer: You apply a criterion for significance based on the usual criterion for significance (.05) divided by the number of tests performed

Which of the following is not a type of post hoc test?

1. Games–Howell
2. Bonferroni
3. Cramér
4. REGWQ

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 while accounting for the grade of the exam. What analysis should he use?

1. Independent analysis of variance
2. Repeated measures analysis of variance
3. Analysis of covariance
4. Mixed analysis of variance

A health psychologist was interested in the effects of vitamin supplements on the immune system. Three groups of adults were exposed (in a highly ethical way) to the cold virus; one group took no supplements for a week before exposure, another had vitamin C supplements, and a third had multivitamins (excluding C). The severity of the cold was measured as a percentage (0% = not contracted, 100% = very severe symptoms). The psychologist also measured the number of cigarettes that each person smoked per day, as smoking suppresses the immune system. The psychologist was interested in the differences in the severity of the illnesses across different vitamin groups accounting for cigarette usage. What technique should be used to analyse these data?

1. Two-way repeated-measures ANOVA
2. Two-way independent ANOVA
3. One-way analysis of covariance
4. Two-way mixed ANOVA

#### Answer: One-way analysis of covariance

Imagine we conducted a study that found that pedestrians were more likely to give money to a street beggar if the beggar had a cute and hungry-looking dog with them, and this effect was identical for both male and female pedestrians. If we calculated the difference between men and women in the no dog condition and plotted this value against the difference between men and women in the dog condition, which of the following values is most likely to represent the gradient of our graph?

1. 22.7
2. 33.8
3. 1
4. 0

Imagine we conducted a three-way independent ANOVA. How many sources of variance would we have?

1. 3
2. 7
3. 8
4. 4

When the assumption of sphericity is violated, what action is needed?

1. Correct the model degrees of freedom and correct the error degrees of freedom.
2. Correct the model degrees of freedom.
3. Correct the error degrees of freedom.
4. Correct the F-ratio.

#### Answer: Correct the model degrees of freedom and correct the error degrees of freedom

Which of the following statements about the assumption of sphericity is not true?

1. It is the assumption that the variances for levels of a repeated-measures variable are equal.
2. It is tested using Mauchly’s test in SPSS.
3. It is automatically met when a variable has only two levels.
4. It is not assumed by multivariate tests.

#### Answer: It is the assumption that the variances for levels of a repeated-measures variable are equal.

Field and Lawson (2003) reported the effects of giving children aged 7–9 years positive, negative or no information about novel animals (Australian marsupials). This variable was called ‘Infotype’. Each child received all three types of information about different animals. The gender of the child was also examined. The outcome was the time taken for the children to put their hand in a box in which they believed either the positive, negative, or no information animal was housed. Which of the following is the most appropriate method to analyse their data?

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

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. Half of the participants were asked to visualize the people that they could hear on the tape, whereas the other half just listened. What experimental design has been used?

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

Which of the following assumptions are relevant in mixed ANOVA designs?

1. Homogeneity of regression slopes
2. Sphericity only
3. Homogeneity of variance and sphericity
4. Multicollinearity

#### Answer: Homogeneity of variance and sphericity

Which of these is a form of oblique rotation?