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In a drug experiment, a reaction time measure was obtained from each participant before the administration of the drug 1 1 PS115–4–FY 1 PS115–4–FY There are 57 marks available. The marks available for each question are shown in brackets at the end of the question. Question 1 In an experiment investigating single word reading, each participant had to name a series of 100 words as quickly as possible. Table q1 below shows some reaction times in milliseconds (ms) for a single participant. The reaction times have been put in order from the shortest reaction time to the longest reaction time: only the shortest seven times and the longest seven times are shown. The median for these 100 reaction times is 576 ms. The mean for these 100 reaction times is 623 ms. The standard deviation of these 100 reaction times is 151 ms. Table q1 Trial number 121 46 13 45 32 54 50 … … 12 136 41 122 144 40 88 Reaction time (ms) 340 353 378 423 431 444 445 … … 971 973 999 1015 1105 1155 1181 FOR FULL MARKS SHOW YOUR WORKING in question Q1ai (a)The experimenter plans to use the participant’s average reaction time when the data are analysed further. However, she has been advised that first she should remove any reaction times that are more than 2.5 standard deviations above the mean. (i) How many of the values shown in Table q1 would need to be removed if the psychologist followed this advice? Show your working in the box provided. Number of values to be removed = ________ (ii) Based on Table q1, list all the values that would be removed in the box below. (b)You have been shown only some of the values for this participant. Nonetheless, from the scores and summary statistics it is possible to infer the following about the 100 reaction times for this participant. (i) The scores have… (Place an X under ONE correct answer) a positively skewed distribution. a negatively skewed distribution. an approximately normal distribution. (ii) My answer in (i) is true because (Place an X next to ALL the answers that apply) Statement Select all that apply a) high scores are more spread out than low scores b) low scores are more spread out than high scores c) the median is higher than the mean d) the mean is higher than the median e) the median and the mean are the same [4 marks] Question 2 The table below shows the frequency distribution of responses by a sample of participants to a single attitude item on a questionnaire. Response Frequency –2 2 –1 2 0 7 +1 5 +2 6 FOR FULL MARKS SHOW YOUR WORKING in questions Q2d-f (a)According to the table, how many participants provided a response? Answer (a) ________ (b)What was the modal response? Answer (b) ________ (c)What was the range? Answer (c) ________ (d)What was the median response? SHOW YOUR WORKING in the box provided. Answer (d) ________ (e)What was the mean response? SHOW YOUR WORKING in the box provided. Give your answer correct to 2 decimal places (2 d.p.) Answer (e) ________ (f)What was the interquartile range? SHOW YOUR WORKING in the box provided. Answer (f) ________ [6 marks] Question 3 A psychologist conducted a study into sex differences in spatial ability, which was assessed using a task called the visual matrices test. There were 28 participants: 14 men and 14 women. Table q3 summarises their scores. The psychologist analysed sex-differences on the visual matrices test using an independent samples t-test. Table q3. Summary of visual matrices scores. Sex Mean SD Male 58 8.1 Female 47 7.7 FOR FULL MARKS SHOW YOUR WORKING for question Q3a (a)Use the information above to calculate the t-value for the t-test that the psychologist conducted. Give your answer correct to 2 decimal places (2 d.p.). SHOW YOUR WORKING in the box provided. You should set out your calculation so that it is clear how you have obtained your answer. Answer (a), t = ________ (2 d.p.) (b) What is the number of degrees of freedom for this t-test? df = __________ (c) For this t-test, what is the critical value for t for a two-tailed test performed at the .05 level? Critical t = __________ (d) Using the table for the t distribution, and for the value you have calculated in part (a), which of the following apply? Place an X under ALL that apply. p > .50 p > .05 p < .05="" p="">< .02="" p="">< .01="" p="">< .001="" (e)="" which="" of="" these="" statements="" is="" correct?="" place="" an="" x="" next="" to="" one="" of="" the="" following="" statements="" the="" mean="" difference="" is="" statistically="" significant.="" the="" mean="" difference="" is="" not="" statistically="" significant.="" (f)="" which="" of="" the="" following="" would="" be="" the="" most="" appropriate="" conclusion="" to="" a="" results="" section="" for="" this="" study.="" select="" only="" one="" option="" by="" placing="" an="" x="" in="" the="" box="" provided.="" (1)="" performance="" by="" men="" and="" women="" was="" not="" significantly="" different="" on="" this="" task.="" (2)="" men="" performed="" significantly="" better="" than="" women="" on="" this="" task.="" (3)="" women="" performed="" significantly="" better="" than="" men="" on="" this="" task.="" (g)="" the="" results="" section="" for="" this="" study="" reports="" the="" means="" for="" each="" group.="" what="" is="" the="" purpose="" of="" reporting="" two="" means="" (i.e.,="" what="" will="" someone="" reading="" these="" results="" learn="" from="" the="" means?).="" two="" options="" are="" correct,="" so="" select="" exactly="" two="" options="" by="" placing="" an="" x="" next="" to="" your="" chosen="" options.="" (1)="" to="" inform="" the="" reader="" about="" any="" participants="" who="" are="" outliers.="" (2)="" to="" inform="" the="" reader="" about="" the="" direction="" of="" the="" difference="" between="" the="" means.="" (3)="" to="" inform="" the="" reader="" about="" the="" overall="" variability="" in="" the="" entire="" sample.="" (4)="" to="" inform="" the="" reader="" about="" the="" variability="" of="" the="" performance="" in="" each="" group.="" (5)="" to="" inform="" the="" reader="" about="" how="" big="" the="" difference="" between="" the="" two="" groups="" is.="" (6)="" to="" inform="" the="" reader="" about="" how="" big="" the="" variability="" between="" the="" two="" groups="" is.="" (h)="" what="" is="" the="" purpose="" of="" conducting="" a="" test="" of="" significance="" on="" the="" mean="" difference?="" two="" options="" are="" correct,="" so="" select="" exactly="" two="" options="" by="" placing="" an="" x="" next="" to="" your="" chosen="" options.="" (1)="" a="" test="" of="" significance="" is="" used="" so="" that="" we="" can="" see="" whether="" the="" identified="" difference="" definitely="" exists="" in="" the="" sample.="" (2)="" a="" large="" mean="" difference="" is="" always="" statistically="" significant,="" so="" a="" significance="" test="" is="" needed="" here,="" because="" the="" mean="" difference="" is="" less="" than="" d="">< 1. (3) a test of significance is used so we can see whether the identified difference definitely exists in the population. (4) even a large mean difference might not be statistically significant due to large variability in the data. a test of significance takes variability into account. (5) a test of significance is used to quantify the probability that the alternative hypothesis is true. (6) even a large mean difference might not be statistically significant due to small sample size. a test of significance takes sample size into account. [11 marks] question 4 in a large clinical trial, participants were treated for anxiety either with a drug alphanol or a drug betaprax. the level of anxiety experienced was measured using a standardised test. this test assigns each person a single score (an “anxiety score”), where higher scores indicate greater anxiety. for participants taking betaprax, the mean anxiety score was 38.5 with a standard deviation of 5.5. among participants taking alphanol, the mean anxiety score was 32.4. both sets of scores were normally distributed. what percentage of the participants who took betaprax are expected to have an anxiety score greater than 32.4 (i.e., greater than the mean score for participants who took alphanol?) show your working in the box provided, and give the final percentage correct to 1 decimal place. answer: __________ (1 d.p.) [4 marks] question 5 a poster encouraging healthy eating was displayed in a chain of restaurants. a researcher used two different designs, one with a positive message (about the good things that happen if you eat healthily) and one with a negative message (about the risks of eating unhealthy food). the posters were changed on consecutive days and the number of people buying healthy items from the salad menu was recorded. table q5 shows the results from one restaurant. for full marks show your working in questions q5b and q5e table q5. number of customers who bought a salad. positive message negative message male customers 19 39 female customers 35 32 (a) the data in the table can be correctly described as (place an x under all that apply): nominal categorical ordinal interval (b) the investigators initially tested whether the type of message made a difference to the number of salads sold (regardless of sex). calculate the percentage of the total number of salads sold on days with each type of message. show your working in this box. percentage with positive message: % (1 d.p.) percentage with negative message: % (1 d.p.) (c) the investigators assumed that, if the poster design made no difference to eating habits, approximately the same number of salads would be sold in each case. what specific statistical test could the investigators use to test the effect of message on the number of salads sold? suitable test: 1.="" (3)="" a="" test="" of="" significance="" is="" used="" so="" we="" can="" see="" whether="" the="" identified="" difference="" definitely="" exists="" in="" the="" population.="" (4)="" even="" a="" large="" mean="" difference="" might="" not="" be="" statistically="" significant="" due="" to="" large="" variability="" in="" the="" data.="" a="" test="" of="" significance="" takes="" variability="" into="" account.="" (5)="" a="" test="" of="" significance="" is="" used="" to="" quantify="" the="" probability="" that="" the="" alternative="" hypothesis="" is="" true.="" (6)="" even="" a="" large="" mean="" difference="" might="" not="" be="" statistically="" significant="" due="" to="" small="" sample="" size.="" a="" test="" of="" significance="" takes="" sample="" size="" into="" account.="" [11="" marks]="" question="" 4="" in="" a="" large="" clinical="" trial,="" participants="" were="" treated="" for="" anxiety="" either="" with="" a="" drug="" alphanol="" or="" a="" drug="" betaprax.="" the="" level="" of="" anxiety="" experienced="" was="" measured="" using="" a="" standardised="" test.="" this="" test="" assigns="" each="" person="" a="" single="" score="" (an="" “anxiety="" score”),="" where="" higher="" scores="" indicate="" greater="" anxiety.="" for="" participants="" taking="" betaprax,="" the="" mean="" anxiety="" score="" was="" 38.5="" with="" a="" standard="" deviation="" of="" 5.5.="" among="" participants="" taking="" alphanol,="" the="" mean="" anxiety="" score="" was="" 32.4.="" both="" sets="" of="" scores="" were="" normally="" distributed.="" what="" percentage="" of="" the="" participants="" who="" took="" betaprax="" are="" expected="" to="" have="" an="" anxiety="" score="" greater="" than="" 32.4="" (i.e.,="" greater="" than="" the="" mean="" score="" for="" participants="" who="" took="" alphanol?)="" show="" your="" working="" in="" the="" box="" provided,="" and="" give="" the="" final="" percentage="" correct="" to="" 1="" decimal="" place.="" answer:="" __________="" (1="" d.p.)="" [4="" marks]="" question="" 5="" a="" poster="" encouraging="" healthy="" eating="" was="" displayed="" in="" a="" chain="" of="" restaurants.="" a="" researcher="" used="" two="" different="" designs,="" one="" with="" a="" positive="" message="" (about="" the="" good="" things="" that="" happen="" if="" you="" eat="" healthily)="" and="" one="" with="" a="" negative="" message="" (about="" the="" risks="" of="" eating="" unhealthy="" food).="" the="" posters="" were="" changed="" on="" consecutive="" days="" and="" the="" number="" of="" people="" buying="" healthy="" items="" from="" the="" salad="" menu="" was="" recorded.="" table="" q5="" shows="" the="" results="" from="" one="" restaurant.="" for="" full="" marks="" show="" your="" working="" in="" questions="" q5b="" and="" q5e="" table="" q5.="" number="" of="" customers="" who="" bought="" a="" salad.="" positive="" message="" negative="" message="" male="" customers="" 19="" 39="" female="" customers="" 35="" 32="" (a)="" the="" data="" in="" the="" table="" can="" be="" correctly="" described="" as="" (place="" an="" x="" under="" all="" that="" apply):="" nominal="" categorical="" ordinal="" interval="" (b)="" the="" investigators="" initially="" tested="" whether="" the="" type="" of="" message="" made="" a="" difference="" to="" the="" number="" of="" salads="" sold="" (regardless="" of="" sex).="" calculate="" the="" percentage="" of="" the="" total="" number="" of="" salads="" sold="" on="" days="" with="" each="" type="" of="" message.="" show="" your="" working="" in="" this="" box.="" percentage="" with="" positive="" message:="" %="" (1="" d.p.)="" percentage="" with="" negative="" message:="" %="" (1="" d.p.)="" (c)="" the="" investigators="" assumed="" that,="" if="" the="" poster="" design="" made="" no="" difference="" to="" eating="" habits,="" approximately="" the="" same="" number="" of="" salads="" would="" be="" sold="" in="" each="" case.="" what="" specific="" statistical="" test="" could="" the="" investigators="" use="" to="" test="" the="" effect="" of="" message="" on="" the="" number="" of="" salads="" sold?="" suitable="">