The Research Skills exam:

The four horsemen of the apocalypse: pestilence, war, famine and the RS exam.

The exam format:

Open book - you can use your notes, books and an approved calculator in the exam.

Two hours and five sections -

Section 1: basic concepts.

Section 2: pick a test and use it.

Section 3: which test?

Section 4: pick a test and conclusions

Section 5: write a results section.

Preparation is everything:

Open book - make sure your notes are useable under conditions of stress!

Are they clear?

Do you know where everything is?

Write clear, step-by-step guides to calculations.

Be strategic – don’t start at page 1 and work through. Answer all the easy questions first, then tackle tricky stuff if there is time.

Section 1: Basic concepts

Ten multiple choice questions, testing knowledge of basic statistical concepts.

Revise by writing clear definitions of terms such as "mean", "standard deviation", "normal distribution", "ratio data", "one-tailed test", etc.

Read all of the alternatives carefully, before making your choice.

1 The Standard deviation is:

(a) a statistic that tells us how well our sample mean is likely to reflect the true, population, mean.

(b) a statistic that tells us how scores are distributed around the mean of the set of scores.

(c) a statistic that tells us whether scores are normally distributed.

(d) a statistic that tells us what is the most commonly-occurring value in a set of scores.

(e) none of the above.

Correct definition [ b ]

2. p < .05 means:

(a) the obtained result is not due to chance.

(b) the obtained result is a fairly important effect.

(c) the obtained result is likely to occur by chance 95% of the time.

(d) the obtained result is likely to occur by chance less than 5 times in a hundred.

(e) the obtained result is likely to occur by chance 5 times in a hundred.

Correct definition [ d ]

Section 2: Pick a test and use it:

Given a set of data, you have to

(a) decide which test is appropriate to use;

(b) perform your chosen test on the data.

Only one of the following tests will be correct:

Independent-means t-test Repeated-measures t-test

Wilcoxon Mann-Whitney

Friedman's Kruskal-Wallis

Spearman's rho Pearson's r

Chi-Square

Are there sex differences in car parking ability?

9 women and 9 men park their cars while the experimenter times how fast they do it.

subject time to park: (sec) subject time to park (sec)

male 1 30 female 1 66

male 2 45 female 2 65

male 3 48 female 3 67

male 4 55 female 4 73

male 5 34 female 5 58

male 6 28 female 6 41

male 7 44 female 7 59

male 8 37 female 8 62

male 9 52 female 9 54

(a) Pick the right test:

Two, or more than two conditions? Men vs. women.

Eliminates Kruskal-Wallis and Friedman's

Scores or frequencies? Each participant provides a score.

Eliminates Chi-square

Relationships or differences? Men versus women.

Eliminates Pearson's r and Spearman's rho

(a) Pick the right test:

Independent or repeated measures? Men vs. women.

NOT Wilcoxon M/W Independent t NOT Matched t

Ordinal, interval or ratio data? Time to park is ratio

NOT Wilcoxon NOT M/W Independent t Matched t

Data normally distributed? No reason to think not!

NOT Wilcoxon NOT M/W Independent t Matched t

Homogeneity of variance? No reason to think not!

NOT Wilcoxon NOT M/W Independent t Matched t

Correct test: Independent-means t-test.

(b) Perform this test on the data,

Report the test statistics clearly and in the proper format, and say what the results mean in words.

"An independent-means t-test was performed on these data. This revealed that women and men differed significantly in the amount of time they took to park their cars (men: mean = 41.44 sec, s.d. = 9.65 sec; women: mean = 60.56 sec, s.d. = 9.23 sec: (t(16) = 4.29, p < .001)".

Section 3: Which test?

 On the basis of a brief description of an experiment and some data, you choose the most appropriate test. For each question give the letter corresponding to the correct test.

A. Wilcoxon G. One-way independent-measures ANOVA.

B. Friedman H. Spearman's rho

C. Mann-Whitney I. Pearson's r

D. Kruskal-Wallis J. Chi-Squared

E. Unmatched t-test K. One-way repeated measures ANOVA

F. Independent means t-test

1. The statistics exam scores of three groups of students were recorded: group A had revised for 5 hours, group B for 10 hours and group C for 20 hours. What test is required to test the hypothesis that revision time affects exam performance?

Test: [G (one-way independent-measures ANOVA]

2. The number of students passing or failing a statistics exam in each of three groups of students was recorded: group A had revised for 5 hours, group B for 10 hours and group C for 20 hours. What test is required to test the hypothesis that revision time affects exam performance?

Test: [J (Chi-square]

Section 4: Pick a test and conclusions

Here are the instructions for this section:

In the following questions you are given some details of an experiment, the results of a number of statistical tests, and a set of conclusions. Only ONE of these tests is appropriate, and only ONE in each set of conclusions is correct. Thus only TWO of the statements are correct in each of the following questions. Indicate which two are correct by writing the appropriate letters in the table at the end of this section.

Look at the data; select the most appropriate test statistics; pick the correct conclusion for those results.

A researcher is interested in whether a drug affects appetite in rats. Eight rats were tested twice, once with the drug and once without the drug, in a random order. In order to feed, the rats need to climb a slope to get a food pellet, and the number of times each animal climbed the slope in a 5-minute period was recorded.

Statistical tests:(a) Matched sample t-test: t (7) = 5.11, p = .001. (CORRECT)(b) Independent measures t- test: t (14) = 2.60, p = .02.(c) Mann Whitney U (8,8) = 11.00, p = .03.(d) Pearson’s r = .77, p = .02(e) Spearman's rho = .80, p = .02(f) Wilcoxon test: z = 2.52, p = .01.

 Conclusions:(g) The drug makes rats’ performance more variable.(h) Rats climb the slope significantly faster after taking the drug.(i) Rats climb the slope significantly more often after taking the drug.(j) Rats climb the slope significantly less often after taking the drug. (CORRECT)(k) There is a significant correlation between the number of times that rats climb the slope with and without the drug.(l) The drug makes the food pellets significantly more tasty to the rats.

Drug: No drug:

10 15

15 22

11 18

22 24

18 19

14 22

16 19

19 23

M = 15.62 M = 20.25

SD = 4.03* SD = 3.01*

*using n-1 SD formula

Section 5: Write a results sectionRead the scenario supplied; write a results section; interpret the results appropriately:

The hypothesis is that revision combined with alcohol leads to better exam performance than revision alone. This was assessed by measuring subjects' exam performance, after either 1) subjects had revised for 5 hours a week while drinking 500 ml of gin; or 2) simply revising for 5 hours each week. The results in terms of the exam scores are shown in the table below, together with the means, standard deviations, and t statistic for the unmatched t -test used to compare the scores.

Revision Revision + gin

5 9

14 7

13 6

17 15

12 5

11 6

19 12

11 13

M =12.75 M = 9.13

SD = 4.23* SD = 3.76*

(NB: maximum exam score is 20).

t = 1.81

(*NB: using the n-1 version of the SD formula)

(a) Graph the data in a form appropriate for inclusion in a lab report:

This doesn’t have to be a work of art, but should be clear and labelled correctly. Include error bars and a title! Standard error = SD divided by square root of the number of subjects. Here, SEs are 1.40 (4.23 / square root of 8) for the sober revisers and 1.24 (3.76 / square root of 8) for the boozed ones.

Fig. 1: effects of alcohol and revision on exam performance

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8

10

12

14

16

without gin with gin

revision condition

me

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(b) Describe the data in a form appropriate for inclusion in the results section of a lab report (assuming no graph in the results section).

"An independent means t-test was performed on these data. This revealed that there was no significant difference between the mean exam scores of subjects who combined revision with alcohol consumption and those who revised without it (t(14) = 1.81, p > .05. Revision only: mean = 12.75, s.d. = 4.23 sec; revision plus alcohol: mean = 9.12, s.d. = 3.76 sec). Exam performance is not significantly enhanced by combining revision with alcohol consumption."