PS113 Assessment 1

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PS113 Assessment 1

July 13, 2023

please note that the maximum number o∫ marks you can obtain ∫or each question part is written next to the question. The number reΛects the importance o∫ the question, and not necessarily the length o∫ the answer you need to give. For this assessment you will receive a score out o∫ 80, plus:

. Up to 5 additional marks are available and awarded based on presentation, completeness o∫ answers, and clarity/presentation o∫ worked solutions.

. Up to 15 additional marks are available ∫or answers which go beyond the lecture materi- als, presenting relevant additional analyses and discussion, which demonstrate an enhanced understanding, and application, o∫ statistical methods.

Question 1

You are testing the hypothesis of whether brain training apps really do increase people,s working memory. You recruit 5 participants and each person,s working memory is assessed in an auditory digit span task: participants are read a series of digits and the length of the longest list that they recall is their digit span. Digit span is assessed both before and after a month of brain training. use a Type I error rate of 0.05 for all tests.

person Before Training person After Training

1                    11                    1                     15

2                    11                     2                    13

3                    15                     3                   11

4                     10                    4                   15

5                    19                     5                    10

(a)  (2 marks) calculate the mean and standard deviation of the Before condition.

(b)  (6 marks) Is this a within- or between-participants experiment?  What is an advantage and a disadvantage of using this type of design relative to the alternative? Describe an advantage and a disadvantage speciic to this experiment, rather than writing generally.

(c)  (2 marks) should you use a z-test or a t-test? Why?

(d)  (4 marks) Is this a one-tailed or two-tailed test? If it is one-tailed, is it the positive or negative tail? Justify your choices.

(e)  (6 marks) Draw picture of the null hypothesis distribution with the Type  1 error probability coloured in and labelled and also labelling with numbers the critical value(s).

(f)  (10 marks) calculate the correct statistic, subtracting the After condition from the Before con- dition. Also mark the test statistic on the plot that you created for 1e.

(g)  (4 marks) In your own words, describe what you can conclude about the null and research hypotheses from this statistical test.

(h)  (6 marks) Give one example of a threat to the internal validity and one example of a threat to the external validity of this experiment. pick examples speciic to this experiment rather than general examples.

Question 2

You are interested in the whether there is a link between playing violent video games and number of aggressive behaviours exhibited by children. For each child, you measure the number of hours a week each that he or she plays violent video games (VVG) and also the number of aggressive behaviours reported by their teachers (AB). You use a Type I error rate of .05.

person    VVG    AB        person    VVG    AB

1           21       21             5            13        13

2             8          8              6             9         11

3           15       15             7           12       12

4           13       13             8             8          7

(a)  (4 marks) Do you have a causal or non-causal hypothesis?  Why or why not?  Is this a true experiment? Why or why not?

(b)  (4 marks) Is this a one-tailed or two-tailed test? If it is one-tailed, is it the positive or negative tail? Justify your choice(s).

(c)  (4 marks) Make a scatterplot of the data, with VVG on the horizontal axis and AB on the vertical axis.

(d)  (12 marks) calculate the pearson correlation coemcient.  Is it signiicant?  (A correlation sig- niicance table is in the Howell book and on the Moodle page.)

(e)  (4 marks) In your own words, describe what you can conclude about both the null and research hypotheses from the statistical test in 2d.

(f)  (6 marks) What can you conclude about the causal relationship between playing violent video games and aggressive behaviours based on this test? Is it plausible that playing violent video games causes aggressive behaviours?  Is it plausible that performing aggressive behaviours causes people to play violent video games?  Is it plausible that a third variable causes both? Justify each of your answers, using an example speciic to this experiment for each case in which you say the causal relationship is plausible.

(g)  (6 marks) Divide the test results using a median split, where results below the median of each variable are coded as “low” and results equal to or above the median of each variable are coded as “high”. What is the conditional probability of a person having low AB given their VVG is high?

2023-07-27