Portfolio of Statistical ExercisesFor this portfolio of statistical exercises you will be presented with FIVE research questions and datasets which you need to conduct the relevant statistical test(s) for and write-up the findings in an appropriate format. You should attempt each question. The mark that you receive will reflect how well you have answered
allFIVE research questions and therefore missing any questions out will adversely affect you mark.
For each exercise requiring data analysis you are required to conduct and then report the findings of an appropriate analysis of the data provided in the reporting style that we have shown you. You should screen the data prior to any analyses and routinely report appropriate estimates of effect size and other relevant statistical information where appropriate. You should also include appropriate and clearly expressed hypotheses.
You should include any calculations and all relevant SPSS outputs (e.g.., data screening checks, analyses, etc) as appendices.
For each question/exercise you should include the following sections:
- Hypothesis or hypotheses: This should be clearly written and explain what you are testing for based upon the description of the research question.
- Results: As stated above, in this section you should justify your selection of the test used and write up the results in the reporting style you have been shown.
- Discussion: There should be a brief (i.e., a paragraph) discussion of the findings of the results in light of the research question.
- Appendix: Please include any calculations and all relevant SPSS outputs for the question at the end of the answer to the question (in other words, don’t have a single appendix at the end with all of the outputs for all of the questions – it makes it more difficult for us to check them for an assessment like this).
Exercise 1An opportunity sample of 50 undergraduate students were asked to complete a series of personality questionnaires investigating the “Dark Triad” of personality (Lee & Ashton, 2005).
The average scores for each questionnaire and for each participant are recorded below. Each mean score ranges from 1 to 10, where 1 is low and 10 is high. The questionnaires record scores on “Psychopathy” (i.e., patterns of callousness, manipulation without remorse, and exploitative behaviour of others), “Machiavellianism” (i.e., manipulativeness, insincerity, callousness), and “Narcissism” (i.e., dominance, exhibitionism and exploitation of others).
The following data were obtained from the students:
Participant
Number
|
Psychopathy
|
Machiavellianism
|
Narcissism
|
---|
1 |
7.44 |
9.13 |
6.50 |
2 |
8.89 |
7.77 |
8.87 |
3 |
7.07 |
8.28 |
6.20 |
4 |
7.17 |
7.38 |
7.27 |
5 |
7.80 |
9.62 |
6.00 |
6 |
9.23 |
9.52 |
9.13 |
7 |
5.09 |
9.72 |
4.32 |
8 |
9.65 |
9.57 |
9.32 |
9 |
8.55 |
8.42 |
8.55 |
10 |
6.58 |
7.02 |
6.59 |
11 |
7.38 |
5.95 |
7.32 |
12 |
7.77 |
8.64 |
5.20 |
13 |
7.18 |
7.97 |
7.21 |
14 |
7.82 |
8.02 |
7.80 |
15 |
7.89 |
7.67 |
7.83 |
16 |
9.51 |
9.78 |
9.60 |
17 |
8.38 |
9.78 |
8.38 |
18 |
8.34 |
5.95 |
8.24 |
19 |
9.41 |
8.74 |
9.36 |
20 |
7.23 |
9.34 |
7.23 |
21 |
8.99 |
7.08 |
8.76 |
22 |
7.84 |
9.53 |
7.65 |
23 |
4.48 |
6.70 |
3.56 |
24 |
9.03 |
8.40 |
7.89 |
25 |
7.40 |
7.44 |
6.93 |
26 |
3.93 |
8.83 |
3.85 |
27 |
7.24 |
5.46 |
7.24 |
28 |
6.79 |
8.79 |
6.56 |
29 |
8.71 |
8.28 |
7.65 |
30 |
7.58 |
6.37 |
7.42 |
31 |
8.88 |
6.14 |
8.88 |
32 |
8.15 |
6.37 |
8.20 |
33 |
8.11 |
9.91 |
8.00 |
34 |
9.07 |
9.16 |
8.90 |
35 |
7.70 |
7.03 |
7.12 |
36 |
7.14 |
8.42 |
7.23 |
37 |
8.76 |
9.04 |
8.69 |
38 |
7.74 |
8.38 |
7.74 |
39 |
7.45 |
8.96 |
7.42 |
40 |
9.27 |
6.88 |
9.21 |
41 |
7.50 |
6.39 |
7.48 |
42 |
9.80 |
7.67 |
6.56 |
43 |
7.43 |
8.69 |
7.43 |
44 |
8.36 |
7.09 |
8.32 |
45 |
8.48 |
6.06 |
8.51 |
46 |
6.97 |
7.13 |
5.30 |
47 |
8.79 |
9.71 |
8.71 |
48 |
8.38 |
9.10 |
5.36 |
49 |
8.09 |
7.48 |
7.98 |
50 |
8.50 |
7.35 |
8.23 |
Do Machiavellianism and Narcissism scores predict Psychopathy?Exercise 2A social psychologist was interested in examining the effect of being observed on sports performance, and if competition can interact with this. He suspected that competition and observation would both make the cyclists faster. He measured a group of professional cyclists on how fast they rode the same distance under a series of controlled conditions. All the cyclists did all of the conditions. They rode the same distance on their own, and being observed by an audience of 20 people. They also rode the same distance at the same time as another cyclist (i.e., just the two of them with no audience), and when they were both being observed by an audience of 20 people.
The following data were recorded from the cyclists (time in seconds to complete the distance):
Cycling on own
|
Cycling on own with an audience
|
Cycling in competition
|
Cycling in competition with an audience
|
412.93 |
303.06 |
290.69 |
260.91 |
391.07 |
301.38 |
318.07 |
243.60 |
391.47 |
306.03 |
328.87 |
242.74 |
406.63 |
306.74 |
305.24 |
257.32 |
384.64 |
300.91 |
332.42 |
266.78 |
413.14 |
300.30 |
242.74 |
250.07 |
405.98 |
309.73 |
294.53 |
227.26 |
402.82 |
301.31 |
315.81 |
246.67 |
374.01 |
312.85 |
263.66 |
236.79 |
397.68 |
302.35 |
306.71 |
242.75 |
388.59 |
300.07 |
294.62 |
253.57 |
416.77 |
296.77 |
291.10 |
276.61 |
384.35 |
303.30 |
323.66 |
271.55 |
397.82 |
303.60 |
311.38 |
246.61 |
425.90 |
307.20 |
284.27 |
235.72 |
419.19 |
307.41 |
286.05 |
256.43 |
416.16 |
296.62 |
312.04 |
249.86 |
403.84 |
331.47 |
273.51 |
262.71 |
405.68 |
287.41 |
301.60 |
253.55 |
405.05 |
297.05 |
305.68 |
266.64 |
Does observation and competition pressure make cycling performance improve?Exercise 3A health psychologist was interested to see if self-reported stress scores resulted in significantly different Cortisol measures.[1] She asked a sample of patients to complete a stress questionnaire and categorised them as either being “High Stress”, “Medium Stress”, or “Low Stress”, depending upon their responses on 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 measure can be assumed to be at least interval in nature).
The following data were obtained from the patients:
High Stress
|
Medium Stress
|
Low Stress
|
3.816622 |
1.047012 |
1.792735 |
3.791716 |
2.146911 |
1.422288 |
4.112685 |
2.014023 |
1.675610 |
3.877990 |
1.799969 |
1.297839 |
4.148395 |
2.402153 |
1.745501 |
4.094494 |
2.232413 |
1.461551 |
4.203315 |
1.934752 |
1.348446 |
3.969050 |
2.298638 |
1.839337 |
3.682800 |
1.416870 |
1.338415 |
3.922470 |
2.188166 |
2.003368 |
3.943557 |
2.010698 |
1.146607 |
4.095992 |
0.758262 |
1.297852 |
4.228955 |
1.704794 |
2.570737 |
3.594576 |
1.611385 |
1.226470 |
4.205555 |
1.758421 |
1.813969 |
3.720655 |
2.038071 |
1.903663 |
3.612999 |
2.219717 |
1.234318 |
4.018633 |
2.582688 |
1.402865 |
4.141084 |
3.044053 |
0.577023 |
3.816622 |
2.427801 |
1.250202 |
Are there significant differences in the Cortisol levels of these three groups?Exercise 4A social cognition experiment was conducted in order to investigate individual differences between men and women with regard to face perception. In order to investigate this, males and females were shown normal and inverted (upside down) faces of famous people and they had to press a button when they recognised the face.
The following data were obtained from an opportunity sample of students (time of recognition in milliseconds):
Males recognising normal faces
|
Males recognising inverted faces
|
Females recognising normal faces
|
Females recognising inverted faces
|
373 |
467 |
317 |
400 |
356 |
479 |
321 |
435 |
337 |
436 |
322 |
413 |
328 |
459 |
297 |
424 |
327 |
401 |
297 |
371 |
351 |
447 |
277 |
424 |
339 |
502 |
324 |
388 |
333 |
509 |
317 |
415 |
350 |
484 |
295 |
382 |
355 |
483 |
298 |
443 |
332 |
460 |
291 |
422 |
369 |
466 |
274 |
428 |
317 |
470 |
281 |
396 |
335 |
485 |
293 |
393 |
374 |
468 |
334 |
378 |
328 |
501 |
320 |
404 |
334 |
454 |
286 |
414 |
345 |
496 |
291 |
413 |
339 |
510 |
298 |
394 |
382 |
453 |
281 |
395 |
345 |
451 |
328 |
407 |
343 |
434 |
289 |
423 |
372 |
420 |
279 |
363 |
327 |
448 |
279 |
425 |
341 |
457 |
312 |
428 |
372 |
470 |
309 |
343 |
334 |
517 |
286 |
396 |
304 |
491 |
292 |
395 |
362 |
495 |
312 |
409 |
337 |
482 |
307 |
383 |
312 |
454 |
243 |
391 |
367 |
452 |
340 |
365 |
352 |
507 |
285 |
384 |
362 |
437 |
339 |
387 |
354 |
436 |
313 |
398 |
375 |
446 |
281 |
388 |
352 |
470 |
304 |
404 |
365 |
492 |
317 |
392 |
374 |
446 |
293 |
415 |
386 |
463 |
313 |
400 |
Are there gender differences in the speed of recognising famous normal and inverted faces?Exercise 5Data was collected from 150 participants using a new short (seven item) questionnaire examining non-clinical paranoia (i.e., paranoia that is not to the level of representing a mental illness). The questions were measured on a five-point Likert scale and ranged from: 1 = “Not at all applicable to me” to 5 = “Extremely applicable to me”. The seven items were as follows:
- Someone has it in for me.
- I sometimes feel as if I’m being followed.
- I believe that I have often been punished without cause.
- Some people have tried to steal my ideas and take credit for them.
- My parents and family find more fault with me than they should.
- Someone has been trying to influence my mind.
- I am bothered by people outside, in cars, in stores, etc, watching me.
The data collected were as follows:
Q1
|
Q2
|
Q3
|
Q4
|
Q5
|
Q6
|
Q7
|
1 |
1 |
2 |
2 |
2 |
2 |
1 |
4 |
4 |
5 |
5 |
4 |
3 |
5 |
3 |
3 |
5 |
5 |
4 |
2 |
2 |
3 |
3 |
3 |
3 |
3 |
1 |
1 |
3 |
3 |
5 |
4 |
3 |
3 |
2 |
3 |
4 |
5 |
5 |
3 |
3 |
2 |
4 |
4 |
5 |
5 |
5 |
5 |
4 |
4 |
3 |
5 |
4 |
4 |
4 |
2 |
4 |
4 |
3 |
2 |
2 |
1 |
1 |
3 |
3 |
5 |
5 |
5 |
3 |
1 |
5 |
5 |
4 |
4 |
4 |
4 |
5 |
3 |
3 |
2 |
3 |
2 |
1 |
1 |
3 |
3 |
4 |
3 |
3 |
2 |
3 |
3 |
3 |
4 |
4 |
4 |
4 |
4 |
3 |
4 |
4 |
4 |
4 |
1 |
2 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
2 |
3 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
3 |
4 |
2 |
1 |
3 |
1 |
2 |
1 |
1 |
5 |
1 |
5 |
3 |
1 |
2 |
1 |
1 |
1 |
2 |
3 |
4 |
5 |
3 |
4 |
3 |
4 |
2 |
3 |
4 |
4 |
1 |
1 |
5 |
3 |
3 |
5 |
5 |
4 |
4 |
1 |
4 |
4 |
4 |
4 |
4 |
2 |
3 |
3 |
4 |
3 |
4 |
4 |
3 |
2 |
2 |
3 |
4 |
4 |
4 |
4 |
2 |
3 |
3 |
3 |
1 |
3 |
1 |
1 |
3 |
2 |
4 |
4 |
2 |
1 |
1 |
5 |
4 |
4 |
4 |
4 |
3 |
1 |
4 |
3 |
5 |
5 |
5 |
5 |
1 |
4 |
4 |
4 |
4 |
4 |
2 |
2 |
5 |
4 |
4 |
3 |
2 |
2 |
1 |
4 |
3 |
4 |
4 |
4 |
4 |
3 |
3 |
3 |
4 |
2 |
3 |
1 |
2 |
3 |
4 |
4 |
4 |
4 |
4 |
2 |
3 |
3 |
3 |
5 |
4 |
3 |
1 |
3 |
5 |
3 |
2 |
2 |
1 |
1 |
3 |
3 |
4 |
3 |
2 |
1 |
3 |
3 |
4 |
4 |
3 |
4 |
2 |
2 |
4 |
5 |
5 |
5 |
5 |
3 |
3 |
3 |
3 |
2 |
2 |
2 |
1 |
5 |
4 |
4 |
5 |
4 |
4 |
4 |
5 |
2 |
2 |
1 |
1 |
1 |
1 |
5 |
4 |
4 |
5 |
5 |
5 |
4 |
3 |
4 |
3 |
3 |
3 |
4 |
3 |
2 |
4 |
3 |
5 |
5 |
5 |
3 |
2 |
4 |
3 |
5 |
5 |
5 |
4 |
3 |
3 |
2 |
1 |
2 |
2 |
1 |
1 |
4 |
4 |
5 |
5 |
5 |
4 |
5 |
1 |
1 |
5 |
1 |
1 |
1 |
1 |
3 |
3 |
2 |
2 |
2 |
2 |
1 |
5 |
5 |
5 |
5 |
5 |
5 |
5 |
3 |
4 |
4 |
4 |
2 |
3 |
1 |
3 |
3 |
4 |
4 |
3 |
3 |
2 |
3 |
3 |
3 |
3 |
3 |
2 |
1 |
3 |
2 |
3 |
4 |
2 |
1 |
1 |
3 |
3 |
5 |
5 |
5 |
5 |
1 |
2 |
2 |
2 |
2 |
3 |
3 |
1 |
3 |
3 |
4 |
4 |
3 |
2 |
1 |
3 |
3 |
4 |
3 |
1 |
1 |
1 |
3 |
2 |
1 |
1 |
1 |
1 |
1 |
3 |
4 |
4 |
4 |
4 |
3 |
2 |
5 |
4 |
5 |
5 |
5 |
3 |
3 |
3 |
2 |
3 |
2 |
2 |
1 |
5 |
3 |
2 |
2 |
2 |
1 |
1 |
1 |
3 |
3 |
2 |
2 |
2 |
2 |
1 |
3 |
4 |
2 |
3 |
3 |
2 |
3 |
3 |
3 |
4 |
3 |
2 |
2 |
3 |
1 |
2 |
2 |
2 |
2 |
2 |
3 |
4 |
4 |
5 |
5 |
5 |
4 |
3 |
3 |
4 |
2 |
2 |
2 |
2 |
1 |
3 |
4 |
3 |
4 |
4 |
2 |
1 |
1 |
2 |
5 |
4 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
3 |
1 |
2 |
3 |
2 |
4 |
1 |
1 |
1 |
5 |
3 |
2 |
2 |
2 |
2 |
2 |
1 |
4 |
4 |
4 |
4 |
2 |
2 |
2 |
5 |
4 |
5 |
5 |
5 |
5 |
5 |
2 |
3 |
4 |
4 |
4 |
2 |
3 |
3 |
3 |
3 |
2 |
3 |
2 |
2 |
4 |
5 |
5 |
5 |
5 |
5 |
5 |
3 |
5 |
5 |
4 |
4 |
5 |
5 |
3 |
4 |
5 |
4 |
4 |
3 |
4 |
3 |
3 |
4 |
4 |
4 |
4 |
2 |
3 |
3 |
5 |
5 |
5 |
5 |
3 |
3 |
3 |
3 |
3 |
3 |
2 |
2 |
3 |
2 |
5 |
5 |
5 |
3 |
3 |
3 |
2 |
5 |
4 |
5 |
5 |
4 |
3 |
3 |
3 |
3 |
1 |
1 |
1 |
5 |
2 |
5 |
5 |
5 |
5 |
1 |
3 |
2 |
4 |
2 |
1 |
2 |
2 |
4 |
3 |
3 |
4 |
4 |
2 |
1 |
2 |
3 |
3 |
4 |
3 |
1 |
2 |
4 |
3 |
5 |
4 |
5 |
3 |
5 |
2 |
2 |
1 |
1 |
1 |
1 |
5 |
3 |
2 |
3 |
4 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
3 |
4 |
3 |
4 |
4 |
4 |
2 |
5 |
1 |
1 |
1 |
1 |
5 |
5 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
2 |
2 |
2 |
1 |
1 |
1 |
4 |
5 |
5 |
5 |
4 |
5 |
5 |
3 |
3 |
3 |
3 |
2 |
1 |
1 |
4 |
3 |
5 |
5 |
5 |
5 |
4 |
3 |
3 |
4 |
4 |
4 |
2 |
2 |
3 |
1 |
5 |
5 |
3 |
3 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
3 |
1 |
4 |
4 |
2 |
2 |
5 |
3 |
4 |
3 |
3 |
3 |
3 |
1 |
2 |
4 |
4 |
4 |
4 |
3 |
1 |
4 |
4 |
3 |
2 |
2 |
2 |
4 |
3 |
3 |
5 |
5 |
3 |
2 |
2 |
2 |
2 |
2 |
2 |
1 |
1 |
1 |
4 |
3 |
5 |
3 |
3 |
1 |
2 |
5 |
3 |
5 |
4 |
2 |
1 |
1 |
2 |
3 |
2 |
2 |
2 |
1 |
1 |
4 |
4 |
2 |
2 |
2 |
2 |
1 |
3 |
3 |
2 |
4 |
4 |
1 |
1 |
4 |
3 |
5 |
5 |
5 |
3 |
3 |
3 |
5 |
5 |
5 |
5 |
5 |
3 |
4 |
4 |
4 |
4 |
4 |
1 |
2 |
3 |
2 |
4 |
4 |
4 |
2 |
1 |
4 |
4 |
5 |
5 |
5 |
3 |
3 |
3 |
3 |
2 |
2 |
1 |
1 |
1 |
2 |
1 |
4 |
4 |
2 |
1 |
5 |
3 |
3 |
4 |
4 |
4 |
3 |
5 |
5 |
5 |
5 |
4 |
3 |
3 |
5 |
4 |
5 |
5 |
5 |
5 |
5 |
2 |
3 |
3 |
3 |
2 |
2 |
1 |
2 |
3 |
4 |
4 |
4 |
3 |
2 |
1 |
3 |
3 |
3 |
2 |
2 |
2 |
1 |
1 |
1 |
2 |
2 |
1 |
2 |
1 |
2 |
3 |
3 |
3 |
2 |
1 |
2 |
1 |
2 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
2 |
1 |
1 |
1 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
2 |
2 |
4 |
4 |
3 |
2 |
1 |
4 |
2 |
4 |
1 |
1 |
1 |
1 |
3 |
2 |
2 |
2 |
1 |
1 |
2 |
3 |
3 |
3 |
3 |
3 |
1 |
1 |
2 |
2 |
2 |
2 |
1 |
1 |
1 |
1 |
1 |
3 |
2 |
2 |
1 |
1 |
3 |
4 |
4 |
4 |
4 |
4 |
1 |
3 |
2 |
4 |
3 |
3 |
2 |
2 |
3 |
3 |
5 |
5 |
5 |
2 |
4 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
5 |
3 |
5 |
5 |
5 |
5 |
5 |
3 |
4 |
4 |
3 |
2 |
1 |
5 |
3 |
3 |
4 |
4 |
3 |
2 |
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Validate this scale by conducting and then reporting the findings of a questionnaire reliability analysis upon this data, optimising the scale and removing any items if required.[1] Cortisol is a naturally occurring hormone which is released by the body in response to stress.