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Coursework 1: Portfolio of Statistical Exercises
Referral

These questions are for students who failed the first attempt and have a referral opportunity (grade capped at 40%).

This portfolio of statistical exercises consists of four research questions and datasets, for which you need to conduct the relevant statistical test(s) and write up the findings in an appropriate format. You should attempt each exercise. The mark that you receive will reflect how well you have answered all four exercises and therefore missing any out will adversely affect your mark.

For each exercise you should include the following sections:

· Hypothesis (or Hypotheses): This/these should be clearly written and explain what you expect to find, based upon the description of the research question.


· Results: In this section you should screen the data and justify your selection of an appropriate statistical analysis. You should then conduct and report the findings of the analysis, in the reporting style that we have shown you during this module. You should report appropriate estimates of effect size and other relevant statistical information where appropriate.


· Discussion: There should be a brief (i.e., a paragraph) discussion of the results; this should clearly summarise the findings, state whether or not the hypotheses were supported, and briefly comment on any other noteworthy issues relating to the findings and their interpretation.


· Appendix: Please include any calculations and all relevant SPSS or JASP outputs (e.g., data screening checks, analyses, etc.) as appendices, along with brief annotations where appropriate to demonstrate your understanding of what these calculations and outputs show. (Please include an appendix for each exercise at the end of the answer to that exercise; in other words, please don’t have a single appendix at the end with all of the outputs for all of the exercises, since it makes it more difficult for the marker to check them).

Please note: Members of staff cannot help you with questions regarding the specific exercises in this assessment. This is because a fundamental aspect of the assessment is for you to be able to identify the statistical analyses that you need to conduct in order to address the exercise questions, conduct the analyses appropriately, and then write them up in the correct manner.


Staff will happily help to clarify questions about analyses generally, but not specific questions about this assessment (e.g., “should I do a t-test for exercise 2”, etc.).

Exercise 1

A health psychologist was interested to see if self-reported stress scores resulted in significantly different cortisol measures (cortisol is a naturally occurring hormone which is released by the body in response to stress). She asked a sample of 60 patients to complete a stress questionnaire and categorised them as either being “High Stress”, “Medium Stress”, or “Low Stress”, depending upon their responses to the questionnaire. She then measured their salivary cortisol levels, which could range from 0 to 6 (the higher the number, the higher the cortisol level). The data obtained from the patients are shown in the table below.


Are there significant differences in the cortisol levels of these three groups?

Table 1. Cortisol levels of the high, medium and low stress groups.


High

Stress

Medium Stress

Low

Stress

3.425

1.047

1.793

3.792

2.147

1.422

4.142

2.370

1.245

3.878

1.800

1.298

3.192

2.241

1.745

4.094

2.232

1.872

4.203

2.199

1.348

3.969

2.299

1.839

3.683

1.417

1.338

4.423

2.188

2.003

3.943

2.011

1.198

4.096

1.352

1.298

4.229

1.705

2.571

3.872

1.611

1.452

4.311

1.758

1.814

3.721

2.038

1.904

3.613

2.152

1.234

4.019

2.583

1.763

4.141

3.044

0.872

3.299

2.428

1.250


Exercise 2

A researcher wants to see if she can reduce levels of maths anxiety in a class of 25 secondary school children, using a four-week course of anxiety-reduction therapy. She measures the children’s maths anxiety using a maths anxiety scale at three time points: before the course (pre-therapy), at the end of the course (post-therapy), and four weeks after the course has ended (follow-up). The data are shown in the table below (higher scores on the scale indicate higher levels of maths anxiety).

Does the therapy have any effect on maths anxiety?


Table 2. Maths anxiety scores at the three measurement time points.

Participant ID

Pre-Therapy

Post-Therapy

Follow-up

1

30

25

30

2

49

38

51

3

28

29

32

4

47

35

42

5

28

23

29

6

54

54

52

7

112

113

111

8

80

60

64

9

23

24

22

10

63

58

60

11

86

63

64

12

27

28

26

13

58

39

59

14

115

115

115

15

72

59

68

16

111

114

112

17

73

52

73

18

31

28

36

19

68

56

65

20

65

59

69

21

85

64

65

22

72

57

70

23

113

113

114

24

77

53

65

25

35

24

30