GOLDSMITHS
University of London
PSYCHOLOGY DEPARTMENT
MSc in RESEARCH METHODS IN PSYCHOLOGY 2003
You are reminded that you may not present substantially the same material in any two pieces of work submitted for assessment, regardless of the form of assessment. For instance, you may not repeat substantially the same material in a formal written examination or in a dissertation if it has already formed part of an essay submitted for assessment. This does not prevent you from referring to the same texts, examples or case studies as appropriate, provided you do not merely duplicate the same material.
PS 71020A STATISTICAL METHODS
3 HOURS
Answer THREE questions.
ONE from Section A, ONE from Section B and ONE from Section C. Each question is worth 50 marks and the marks for each part of each question are indicated where appropriate. The mark for the whole paper will be converted to a mark on a 0-100 scale.
Note that there is attached SPSS printouts for questions 1, 3, 5, 7 & 9
SECTION A
1. Most studies of schizotypal personality have identified 4 aspects of schizotypy: reality distortion (RD) schizotypy; cognitively disorganised (CD) schizotypy; anhedonic (Anh) schizotypy; and impulsive nonconformist (IN) schizotypy. Eysenck argued that measures of these facets of schizotypy were just reflections of his big three personality dimensions: Anh schizotypy being an inverse reflection of extraversion; CD schizotypy reflecting neuroticism; and with RD and IN schizotypy reflecting psychoticism. A researcher decided to test these ideas using factor analysis by taking measures of the 4 kinds of schizotypy and the 3 Eysenck dimensions from the same participants. The researcher carried out a principal components analysis (PCA) asking for 3 components to be retained in the solution.
(i) How does a PCA differ from a factor analysis? (5 marks)
The researcher requested the following options during the analysis: a varimax rotation; a scree plot; exclusion of cases listwise; KMO measure of sampling adequacy and Bartlett’s test of sphericity; and an anti-image correlation matrix.
(ii) Explain what each of these options is and what purpose they serve in PCA. (15 marks)
The results of this analysis on 211 participants are shown in the printout.
(iii) Go through the printout and comment on what is shown in each section of output with particular reference to the answers given in (ii) above (15 marks)
The researcher decided that two further trait anxiety-neuroticism scores (Anx1 and Anx2), which she had for each participant, should be added to the analysis. The results of the second analysis are also shown in the printout.
(iv) To what extent do the results from the second PCA support or reject Eysenck’s explanation of schizotypal personality structure? (10 marks)
(v) From the information given briefly consider whether the second analysis is likely to represent a “good” PCA and suggest further analyses that might be attempted. (5 marks)
2. An applied psychologist recruited a representative sample of 1000 primary and secondary schoolchildren and administered to each participant a road-crossing test using a virtual reality simulator. An important dependent variable was the “risky road use” index (1-100; 100 =maximum risk-taking). This was computer-scored during the session in the simulator. The researcher hypothesised that the personality traits of impulsiveness and anxiety, plus performance measures of psychomotor speed and distance estimation, would each make an independent contribution to the amount of risky road use observed. These hypotheses were expected to be true even after any contribution of the child’s sex, age, socio-economic status, and road use experience were accounted for. From the point where the researcher had gathered the DV and the 8 predictors from each child, explain step-by-step, in detail, how she would test her hypotheses using multiple regression. Describe the statistical outcomes which would confirm or reject her predictions.
3. Chickens have a high mortality rate between hatching and point of sale. A chicken farmer suspected that some chicken feeds and some breeds may affect chick survival quite dramatically. The farmer consulted his neighbour, a psychologist, and they carried out 2 studies of chicken survival. Both studies used two feeds: Food 1 and Food 2. In the first study 100 chicks from each of 3 breeds (Breeds 1 to 3) were quasi-randomly allocated at hatching to receive one of the two feeds (ensuring that each feed was given to 50 chicks of each breed). The farmer recorded how many chicks survived to the point of sale (18 weeks) in each cell of the design. The result is shown in the cross-tabulation printout. The variable survived has a value of 1 if the chick survived and 0 otherwise. The psychologist used multinomial logistic regression (and some chi-squared statistics) to analyse the data, producing the printout shown below. In the second study, 100 chicks from each of 3 further breeds (Breeds 4 to 6) were quasi-randomly allocated as before to receive one or other of the same two feeds. The results of study 2 are also shown below. Comment in detail about what the various parts of the printout show, what models the psychologist fitted to the data in each study, and end up with the recommendations that the psychologist would make to the farmer about the breeds, and about what foods he should use with which breeds.
SECTION B
4. Two researchers, A and B, consulted a statistician about the use of analysis of covariance (ANCOVA) to analyse their findings. Researcher A was carrying out a word memory study using a between-groups design with participants randomised to one of the two groups involved. Each group received a different type of study instructions and the researcher wanted to know if word study instructions affected subsequent memory performance. He had also taken a quick measure of IQ from all participants. He found that the groups differed significantly in mean level of IQ and that IQ was significantly correlated with memory performance across all participants combined. Researcher B was looking at the performance on a particular test of attention in a group of chronic schizophrenic patients and age-matched controls. She had also taken a quick measure of IQ from all the participants and found a significantly lower mean IQ in the chronic schizophrenic patients. IQ was also significantly correlated with attention performance across all participants combined. Both researchers wanted to control for the IQ difference in analysing the possible between-groups difference in memory, or attention, performance.
(i) What advice should the statistician have given to researchers A and B about whether ANCOVA was a suitable technique for achieving their desired aim, and what reasons should the statistician have given? Give some other (hypothetical) research example(s) that the statistician might have used to clarify his explanations further. (25 marks)
(ii) In fact the statistician was also able to advise correctly about another use that ANCOVA might have been put to in their studies. What is the logic behind this application of ANCOVA? How did he advise researchers A and B on whether to use ANCOVA for this second purpose? (10 marks)
(iii) Apart from general checks that need to be made before carrying out an analysis of variance, what additional specific test would the statistician have advised the researchers to employ before carrying out any ANCOVA he might have recommended? What diagram did he draw to illustrate the need for this test? (10 marks)
(iv) Briefly describe one other use to which ANCOVA can be put. (5 marks)
5. A researcher tested 3 groups of participants: non-smokers (NS); ex-smokers who have successfully quit and remained abstinent for over a year (Quit-1yr); and smokers who have quit smoking during the last week (Quit-1wk). The participants were coded with the SPSS variable subjtype (1=NS; 2=Quit1yr; and 3 =Quit1wk). Within each group participants were randomly assigned to receive nicotine or placebo tablets in a double-blind design. The drug group of a participant was coded after the experiment was completed using the SPSS variable druggrp (1=placebo; 2=nicotine). The dependent variable was performance on a reaction time (RT) task used to measure concentration. The mean RTs in each cell of the design and the results of a two-way between-subjects ANOVA are shown in the printout below.
The researcher believed in a withdrawal model of the effects of nicotine on cognitive performance. This model predicts a particular pattern of mean RTs across the cells of the design. Specifically, RT task performance is predicted to be slower for the Quit-1wk participants receiving placebo relative to the other groups receiving placebo (and the other two groups should not differ from one another under placebo); the RT under nicotine should be faster than the RT under placebo for the Quit-1wk group but the same comparison for the other 2 groups should not be significant.
(i) Do the pattern of means and the overall ANOVA lend any support to this model? (5 marks)
The researcher decided to test the model using planned between-subjects t-tests each based on pairs of cell from the overall experiment (data from the other 4 cells were not used). The researcher correctly deemed that 9 such tests were needed and the results are shown in the table below.
Comparison / Restricted to participants in the following groups/conditions / T-value / df / p-valueNicotine (N) vs placebo (P) / Quit-1wk / 3.50 / 20 / 0.002
N vs P / Quit-1yr / 0.28 / 23 / 0.78
N vs P / NS / 0.29 / 21 / 0.78
Quit-1yr vs NS / Nicotine / 0.77 / 21 / 0.45
Quit-1yr vs NS / Placebo / 0.70 / 23 / 0.49
Quit-1wk vs NS / Nicotine / 0.22 / 21 / 0.83
Quit-1wk vs NS / Placebo / 3.04 / 20 / 0.006
Quit-1yr vs
Quit-1wk / Nicotine / 0.62 / 20 / 0.54
Quit-1yr vs
Quit-1wk / Placebo / 2.74 / 23 / 0.01
(ii) Based on the table above, do the various comparisons between mean RTs show the pattern of significant and nonsignificant effects predicted by the withdrawal model. Explain your reasoning carefully. (10 marks)
A statistician was consulted and she suggested that the use of t-tests was probably not the most powerful way to check if the pattern of mean RTs was as predicted. She advised the researcher to use specific planned contrasts within the overall ANOVA and prepared appropriate syntax commands using SPSS (the GLM procedure and the LMATRIX option). The results of these contrasts are shown in the table below.
(iii) What is name for the effects being studied in the first 3 rows of the table below? (5 marks)
(iv) Do the results of the contrast analyses reveal the pattern of significant and nonsignificant differences predicted by the withdrawal model? Explain your reasoning carefully. (10 marks)
(v) What are the features of the contrast analyses which render them more powerful than the t-test approach originally used by the researcher? Are there any particular assumptions upon which the use of these contrasts critically depends? (10 marks)
Contrast / Restricted to participants in the following groups/conditions / T-value / df / p-valueNicotine (N) vs. placebo (P) / Quit-1wk / 3.51 / 64 / <0.001
N vs. P / Quit-1yr / 0.26 / 64 / 0.80
N vs. P / NS / 0.31 / 64 / 0.76
Quit-1wk vs. rest / Nicotine / 0.19 / 64 / 0.85
Quit-1wk vs. rest / Placebo / 3.61 / 64 / <0.001
Quit-1yr vs. NS / Nicotine / 0.74 / 64 / 0.46
Quit-1yr vs. NS / Placebo / 0.71 / 64 / 0.48
The syntax commands which the statistician provided are shown in the printout below.
(vi) Explain the choice and ordering of the numbers (coefficients) which appear in the LMATRIX lines of the syntax. (10 marks)
6. Two clinical psychologists (Janet and John) were recruited by a university to conduct a preliminary trial of anxiety-management counselling for high trait anxious students prior to their exams. The psychologists were first invited to carry out a brief intervention study to see if such counselling was likely to be beneficial. Two weeks before the first exam the anxious students were randomly allocated either to receive a series of general talks on revision skills (control group) or the 1-week anxiety-management training sessions. The following week, each student in the trial completed state anxiety checklists while thinking about their forthcoming exams. Two different well-known and reliable checklists (A and B) were used and each student completed both checklists on 3 occasions: 7 days before the exam, 4 days before the exam, and the day before the exam. For each participant, the psychologist also calculated two mean state anxiety scores (by averaging the 3 scores obtained with A and B checklists respectively).
Several different research questions were potentially of interest to the psychologists. The first research question was whether the treatment had a beneficial effect on state anxiety in the 1-week period prior to an exam. This question was analysed using the 2 averaged state anxiety measures from each subject.
(i) The psychologist called John was not interested in the differences in the results from the two anxiety measures (A and B). Obviously John could average the two state anxiety measures into a single measure and carry out an appropriate analysis of variance. Other than doing this, there are two other simple ways John could use analysis of variance to address the first research question. Explain in detail the pros and cons of these two analytic approaches, including any differences in their underlying assumptions? What advantages and disadvantages might each have over the simple averaging method? (20 marks)