# Discovering Statistics Using IBM SPSS Statistics

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## In at the Deep End Questions

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

__Answer choices__

- SS = s2/(n – 1).
- s2 = SS(n – 1).
- n = (s2/SS) – 1.
- 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?**

__Answer choices__

- 0.0228
- 0.2524
- 0.1826

#### Answer: 0.2524

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

__Answer choices__

- Log transformation
- Square root transformation
- Reciprocal transformation
- Tangent transformation

#### Answer: 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?**

__Answer choices__

- The population distribution of the mean
- The sampling distribution of the mean
- The bootstrap distribution of the mean
- 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? **

__Answer choices__

- Paired samples t-test
- Mann–Whitney test
- Wilcoxon rank-sum test
- Wilcoxon signed-rank test

#### Answer: 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? **

__Answer choices__

- Independent t-test
- Wilcoxon signed-rank test
- Dependent (related) t-test
- Mann–Whitney test

#### Answer: 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, and a documentary about wildlife. The resulting data were skewed. What test should be used to analyse the data? **

__Answer choices__

- Independent analysis of variance
- Repeated-measures analysis of variance
- Friedman’s ANOVA
- Kruskal–Wallis test

#### Answer: Friedman’s ANOVA

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

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

__Answer choices__

- 4.5
- 4
- 3
- 6

#### Answer: 4.5

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

__Answer choices__

- 20%
- 2%
- 8%
- 36%

#### Answer: 36%

**What is b0 in regression analysis? **

__Answer choices__

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

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

**The t-test tests for:**

__Answer choices__

- Differences between means
- Whether a correlation is significant
- Whether a regression coefficient is equal to zero
- All of these

#### Answer: All of these

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

__Answer choices__

- It makes the data normally distributed.
- It aids the interpretation of the indirect effect.
- Because it reduces multicollinearity between main effects and the interaction effect.
- 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?**

__Answer choices__

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

#### Answer: Use Friedman’s ANOVA

**Which of these statements describes a Bonferroni correction?**

__Answer choices__

- You apply a criterion for significance based on the usual criterion for significance (.05) divided by the number of tests performed.
- You divide the F-ratio by the number of tests performed.
- The degrees of freedom are corrected to make the F-ratio less significant.
- 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?**

__Answer choices__

- Games–Howell
- Bonferroni
- Cramér
- REGWQ

#### Answer: Cramér

**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?**

__Answer choices__

- Independent analysis of variance
- Repeated measures analysis of variance
- Analysis of covariance
- Mixed analysis of variance

#### Answer: Analysis of covariance

**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?**

__Answer choices__

- Two-way repeated-measures ANOVA
- Two-way independent ANOVA
- One-way analysis of covariance
- 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? **

__Answer choices__

- 22.7
- 33.8
- 1
- 0

#### Answer: 0

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

__Answer choices__

- 3
- 7
- 8
- 4

#### Answer: 8

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

__Answer choices__

- Correct the model degrees of freedom and correct the error degrees of freedom.
- Correct the model degrees of freedom.
- Correct the error degrees of freedom.
- 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?**

__Answer choices__

- It is the assumption that the variances for levels of a repeated-measures variable are equal.
- It is tested using Mauchly’s test in SPSS.
- It is automatically met when a variable has only two levels.
- 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?

__Answer choices__

- One-way independent ANOVA
- One-way repeated-measures ANOVA
- Two-way mixed ANOVA
- Two-way independent ANOVA

#### Answer: Two-way mixed 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?**

__Answer choices__

- A mixed design
- A repeated-measures design
- A matched design
- A between-subjects design

#### Answer: A mixed design

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

__Answer choices__

- Homogeneity of regression slopes
- Sphericity only
- Homogeneity of variance and sphericity
- Multicollinearity

#### Answer: Homogeneity of variance and sphericity

**Which of these is a form of oblique rotation?**

__Answer choices__

- Equamax
- Quartimax
- Varimax
- Promax