1. What is the correlation between pre-test scores and post-test scores? Assuming the obvious directional hypothesis (i.e., that those who score highly at pre-test tend to score highly at post-test), is the correlation statistically significant? Report your results in standard (APA-like) format.

2. The researcher was interested in whether or not the different maths training affected performance equally. Perform an analysis of co-variance with pre-test scores as a covariate of post-test scores to test the hypothesis that the different training regimes have different effects. Report the results in standard format.

3. The researcher realised that the data were also amenable to linear regression. Perform a linear regression with pre-test scores and condition as the predictor variables and post-test scores as the predicted / outcome variable. Report the results in standard format.

4. The researcher further realised that the data were also amenable to a mixed ANOVA. Perform the appropriate ANOVA and report the results in standard form.

5. Compare the results from questions 2, 3, and 4. Which analysis do you favour and why?

You have been hired as a data analyst for a forensic psychologist who is investigating factors that predict the odds for drug use in inner-city youths. She obtained the following data from a community sample of 953 youths who took part in a school-based survey at ages 12 and 13:

• Gender: coded as zero for male, one for female

• Free Meals at School: a measure of family poverty

• Friends' antisocial behaviours: the number of antisocial behaviours friends engaged in (range = 0 to 34, with higher values indicating higher levels of friends' antisocial behaviour).

• Friends' drug use: the number of drugs - within the last year at age 12 - the respondents reported that their friends had taken (range = 0 to 6, with higher values indicating higher levels of friends' drug use).

• Neighbourhood informal social control: degree to which adults in the neighbourhood will call the police if teens are loitering, if adults are causing problems, if individuals are drinking or taking drugs on the street (0 = low neighbourhood informal social control; 1 = medium neighbourhood informal social control; 2 = high neighbourhood informal social control).

• Drugs at 13: zero if no drugs used in the previous year, one otherwise.

The data are contained in the file "dataset_3_2.sav", which is available via Moodle. Answer the following questions by conducting logistic regression analyses with Drugs at age 13 as the outcome variable.

6. For the dichotomous variables (i.e., gender and free meals), indicate which value is more likely to co-occur with drug use at age 13. Quote statistics to support your answer.

7. Which of the five predictor variables are significant predictors of drug use at age 13? Quote relevant statistics.

8. Produce classification tables showing the prediction accuracy of a) the basic model (with no predictors), b) the full model (with all five predictors) and c) the preferred model (with only significant predictors). (You should produce a total of three classification tables.) How does the inclusion of additional predictors (from the basic model to the full model via the preferred model) alter the classification accuracy?

9. Consider a female who is eligible for free school meals, has friends' antisocial behaviour score of 25 (i.e., high level), a friends' drug use score of zero, and low neighbourhood informal social control. For each of the three models produced in question 8 (basic, full-factor and preferred), calculate the probability that this female will use drugs at age 13. Show all relevant working.

10. In answering question 9 you should have produced three probabilities: the probability that the female will use drugs at age 13 assuming the basic model, the full-factor model, and the preferred model. Which of these probabilities is more reliable and why? What interventions, if
any, might be attempted to lower the likelihood of this female using drugs at age 13?

Part -21. A researcher is interested in whether there is meaningful latent structure underlying common fears. She therefore asked 230 participants to use a 1-10 scale to rate how afraid they are of 11 things which people commonly report being afraid of.

The 11 ratings were of:
1) Snakes
2) Enclosed Spaces
3) Public Speaking
4) Death
5) Deep Water
6) Spiders
7) Restriction
8) Crowded Places
9) Heights
10) Loneliness
11)Needles

The data are contained in the file "Worksheet4_1.sav", which is available on Moodle. Perform a principal component analysis (PCA) on this data, using appropriate rotation, to investigate the latent structure of the data.

(a) Comment on the appropriateness of this dataset for PCA, in terms of sample size and sampling adequacy. Would you exclude any items on the basis of singularity, multicollinearity, or independence? Provide relevant statistics to justify your answers.

(b) How many principal components should be retained? What method of rotation have you used any why? Explain your answers quoting any relevant statistics.

(c) Which items load on which principal components? How might the researcher interpret these results in terms of the latent structure underlying fear?

2. A social psychologist is planning an experiment on the effects of implied social presence on decision making. He wants to ensure power for the experiment of at least 0.80. From previous studies he has conducted using the same decision making task, he knows that the mean score is 58.0 points, with a standard deviation of 6.4 points. From looking at the literature on implied social presence, he anticipates that his experimental manipulation will result in a mean decrease of 4 points.

(a) Calculate and report the anticipated effect size (expressed as Cohen's d). Show all working.

(b) If the psychologist was planning to use a between-subjects experimental design, how many participants should he use in each condition to ensure that the experiment has the desired power? Show all working.

(c) Suppose he was considering using a within-subjects design instead. How many participants should he use (in total) to ensure the experiment has the desired power. Show all working.

3. An educational psychologist is conducting a meta-analysis of studies investigating the effects of a specific type of cognitive training on mathematical ability. He finds nine experiments in the literature which have investigated this question by comparing performance on a standardised maths test before and after training. Table 1 reports information about these studies, including: the number of hours of training, the mean improvement from pre-test to post-test, and standard statistics taken from (or calculated from) each paper.

(a) Calculate and interpret a composite measure of significance using Fisher's Combined Test. Show all your working. You will need to consult a table of the statistic, which can be found in the appendices of most statistics textbooks.

(b) Calculate and interpret Stouffer's z as an additional measure of composite significance. Show all your working.

(c) Calculate Cohen's d for each of the studies. Calculate the composite effect size (expressed in Cohen's d) and its 95% confidence interval.

(d) Make a scatterplot showing the relationship between the number of hours of training provided by each experiment and effect size (expressed in Cohen's d).

What conclusions might the psychologist draw from this?