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34 | A2 PSYCHOLOGY: THE STUDENT’S TEXTBOOKAgain, some straightforward mathematics cansimplify it further to:10 (11)U B=80+ –742This is equal to:U110B=80+ –742which equals:so finallyU B=80+55–74U B=61Step 4: Select the smallest value of U and consultthe tables for a critical valueIn our case, the smallest value of U calculated wasU A: this is our observed value at 19. We now needto consult the table of critical values for the Mann-Whitney. To do this we need to know the numberof participants in each group. We had eight malesand ten females, so we read across the top of thetable until we reach 8, and we then read down tothe N=10 line.A portion of the table is reproduced for you here,but make sure you refer to the real table in theappendix of this book to be sure you know how toread it.N17891011N27 8 9 10 114 6 7 9 106 7 9 11 137 9 11 13 169 11 13 16 1810 13 16 18 21You can see that the critical value of U for N of8 and N of 10 is 11. If your value of U is equalto or less than the critical value then you can sayconfidently, with 95% certainty, that your resultsdid not happen by chance.Our value of U was 19. This is not smaller than11, so we cannot reject our null hypothesis. Eventhough the graph and the descriptive statisticssuggested that it might be the case, we cannot saywith confidence that women are indeed better atdoing more than one task at once. This is a verygood example of why we should always do thestatistics! If we had not done so, we might havemade the error of rejecting our null hypothesisby mistake, and accepting our hypothesis eventhough the difference could well have happenedby chance.Chi-square (c 2 )Chi-square test (pronounced ‘ky square’) is oftenwritten as c 2 . We use this test when we have numbersof people in different categories. Here’s anexample from earlier, to help clarify what we mean:‘Researchers are investigating whether psychologystudents and maths students revise differently andwhether this influences test scores. The two methodsused are cramming information or organisedrevision. Students can be either psychology ormaths students (not both) and they may be organisedlearners or crammers (not both).’In this case we have a group of psychology studentsand a group of maths students. The rule isthat we cannot have a student studying both. Eachof our subject groups is split into two according tothe revision style of its members: those that cramfor exams (crammers) and those that revise in anorganised way (organised).To summarise, students can be in one of four completelyseparate categories. These are as follows.1. Psychology: Crammers2. Psychology: Organised3. Maths: Crammers4. Maths: OrganisedWhat’s important here is that no one can be inmore than one group. The Chi-square test looks atwhether the number of students in each categoryis different from what we might expect just bychance. In this way the test tells us whether thenull hypothesis (that something happened bychance) can be rejected or not, thus allowing us tomake a decision about our hypothesis.Aim:We are interested in whether the type of revision(cramming or organised) works differently for differentsubjects.Hypothesis:There will be a difference in the effectivenessof different types of revision depending on thesubject.Null hypothesis:There will not be a difference in the effectivenessof different types of revision depending on thesubject.Operationalising the variables:A self-report questionnaire of psychology andmaths students asks them to identify the type ofrevising they do, cramming or organised revision.Extract from A2 Psychology: The Student’s Textbook © Nigel Holt and Rob Lewis ISBN: 9781845901004 www.crownhouse.co.uk
DATA ANALYSIS AND REPORTING INVESTIGATIONS | 35The raw data:CrammersOrganisedPsychology535MathsEach square relating to each of the four categoriesis referred to as a ‘cell’. Each ‘cell’ contains anumber which relates to the number of studentsin that category and is referred to as the observedfrequency.The graph:We have two different groups. The appropriategraph to draw here is a simple bar chart.The question is, are the numbers of students inthese categories different from what we mightexpect to see just by chance The way to find out isto carry out a Chi-square test.Frequency (number of students)604530150PsychologyCrammersRevising styles: Maths and PsychologyPsychologyOrganisedMathsCrammersDoing the chi-square testMathsOrganisedStep 1: Add up the values in the rows and thecolumns of the results table, and calculate anoverall grand totalThe easiest way to do this is to reproduce theresults table, adding the totals of the rows andcolumns and the grand total, like this:CrammersOrganisedTotalPsychology53540(5+35)Maths501060(50+10)5010Total55(5+50)45(35+10)Grand total100(5+50+35+10)to as the expected frequency. We use the followingvery basic formula:RCE=TThe expected frequency for the cell (E) equals therow total (R) times the column total (C) divided bythe grand total (T).The four sums are easy to calculate. Make sureyou work out the row total times the columntotal before dividing by the grand total though,and make sure you use the correct row totals andcolumn totals in each calculation.Observed frequency = 5Expected frequency = (5x40)/100= 200/100 = 2Observed frequency = 50Expected frequency = (55x40)/100= 2200/100 = 22Observed frequency = 35Expected frequency = (45x40)/100= 1800/100 = 18Observed frequency = 10Expected frequency = (60x45)/100= 2700/100 = 27To summarise, the expected frequencies for ourdata look like this:CrammersOrganisedPsychology218Maths2227Step 3: Use your observed and expected frequenciesto calculate chi-squareNow that we have observed and expected frequenciesfor each cell we can calculate chi-square usingthis equation:(0–E) 2x 2 =∑ETo calculate chi-square (c 2 ) we have to calculate(O–E) 2 /E for each cell, then add up (∑) the resultsof the sums.We’ve done this for you here. Each cell containsa single calculation, using the observed andexpected frequencies for that cell.Step 2: Work out what might be expected justby chanceTo work out the number in each cell that mightoccur by chance is easy, and the result is referredExtract from A2 Psychology: The Student’s Textbook © Nigel Holt and Rob Lewis ISBN: 9781845901004 www.crownhouse.co.uk
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