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Gender Difference Added? Institutional Variations in the Gender Gap in First Class DegreeAwards in Mathematical SciencesAuthor(s): Vanessa SimoniteSource: British Educational Research Journal, Vol. 31, No. 6 (Dec., 2005), pp. 737-759Published by: Taylor & Francis, Ltd. on behalf of BERAStable URL: http://www.jstor.org/stable/30032598

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British Educational ResearchJournalVol. 31, No. 6, December2005, pp. 737-759 TaylorFrancisGroupRoutledge

Gender difference added? Institutionalvariations in the gender gap in firstclass degree awards in mathematicalsciencesVanessa Simonite*Oxford Brookes University, UK(Submitted 12 February 2004; resubmitted20 May 2004; conditionally accepted 5 July2004; accepted 13 August 2004)

This articleshows how multilevelmodellingcan be used to study institutionalvariationsin thegender differencesin achievement. The results presented are from analyses of the degreeclassificationsof 22,433 individualswho graduatedin mathematicalsciences,fromuniversitiesinthe UK, between 1994/95 and 1999/2000. The analyses were designed to measure genderdifferencesin the achievementof firstclass honoursin mathematicalscience degreesas a wholeand withinindividualinstitutions.Afterallowingfor students'entryqualifications,age, type ofcourse and institution attended, no systematic gender difference was detected in the achievementof firstclasshonoursin mathematicalsciencesat anylevelof entryqualifications.However,therewere statistically significant variations between universities in 'gender difference added'. Thisvariation between institutions in gender difference added was explained by the significant genderdifferences in the first class degree awards made by Oxford and Cambridge universities, with nosignificant evidence of gender differences in the first class degree awards made by otherinstitutions.

IntroductionIn the UK, degree awards are subdivided according to a graduate's level ofachievement: an honours degree is distinguishedfrom the lesser qualificationof an'ordinary' degree and within honours degrees, awards are classified as first class,upper or lower second class or third class. In spite of calls for the abolition of thesubdivided honours degree (Winter, 1993; MacFarlane, 1998) or for its simplifica-tion to a system of awards and awards with distinction (National Committee of

* Department of Mathematical Sciences, Oxford Brookes University, Wheatley Campus, OxfordOX33 1HX,[email protected] 0141-1926 (print)/ISSN 1469-3518 (online)/05/060737-23 2005 BritishEducationalResearchAssociationDOI: 10.2307/30000008


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738 V. SimoniteInquiryinto HigherEducation [NCIHE], 1997), UK degreeclassificationscontinueto be awardedand throughthe attentiongiven to them, acknowledgedas important.Wright (2001) described higher education qualifications as affecting financialrewards,working conditions and future career prospects, and the Dearing report(NCIHE, 1997, p. 404) described students as viewing degree classifications ascontributing to life chances on graduation. Knight (2002) argued that quality inhighereducationcannotbe advanced throughanalysesof degreeclassificationssincethese providean incompletepictureof students'achievements.Clearly,one smallsetof categories, such as degree class, cannot describe in full a student's learningandachievementsoverthe courseof a degree,but as long as UK degreeawardscontinueto be made in this way andused in the public sphere,then in the interestsof fairness,an essentialelement of quality,patternsof variationin degreeawardsand the extentto which differentkinds of graduates benefit need to be studied.

The analysesreportedin this articleuse datafromthe HigherEducationStatisticsAgency (HESA), the body responsible for the collection and dissemination ofstatistics related to higher education in the UK. The analyses investigate thedifferences between the proportions of men and women graduatingfrom univer-sities in the UK who achieve first class honours in mathematical sciences. Theobjectives of the analysis were to determine whether such differences exist, afterallowingfor the effects of entryqualificationsand otherperformance-relatedfactorsthat may differ between men and women, to explore the extent to which thesedifferences vary from one institution to another and to provide an exemplar ofhow institutional variations in gender differences in achievement at degree levelcan be studied.

BackgroundStudies comparing the achievements of men and women graduating fromuniversitiesin the UK have found that gender differencesin achievementvaryfromone subject to another (Rudd, 1984; Clarke, 1988; Peers, 1994; Tomlinson &MacFarlane,1995; Hartleyetal., 1997). Wheresuch differenceshavebeen detected,within some subjects or institutions, the most consistent finding is a tendency formen to achieve proportionatelymore firsts and thirds than women (Rudd, 1984;Clarke, 1988; Cohen & Fraser, 1992; Tomlinson & MacFarlane, 1995; Chapman,1996; McCrum, 1998).

In higher education as a whole, a number of studies have found relationshipsbetween entry qualificationsand performance in first degree programmes (Sear,1983; Bourner& Hamed, 1987;Johnes, 1992; Peers, 1994, Peers &Johnson, 1994;Chapman, 1996). Two studies, including a meta-analysis of studies examiningtherelationshipbetween entryqualificationsand degreeclass, have shown thatwhile thestrength of this relationshipvaried from one subject to another, it is stronger inmathematics than in many other subjects (Peers & Johnson, 1994; Chapman, 1996).More recently, entry qualifications were found to be such an important determinantof degree classifications in mathematical sciences that recent improvements in


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Variationsin degreeawards 739degreeawardscan be explainedin termsof upward trends in achievement at A level(Simonite, 2004). There are key differences in the prior achievementsof male andfemale undergraduates in mathematics: Kitchen (1999) reports that amongststudents entering mathematics degree courses, the proportion of male studentsincreases with the level of attainment in A level mathematics and this may beexpected to lead to differencesin the achievementsof male and female graduatesatdegree level.

Another factor that needs to be taken into account when comparing degreeclassifications between men and women is the distribution of male and femalegraduates by institution. Universities vary in both the proportions of first classhonours degrees awarded and in the proportions of male and female studentsenrolled on mathematics courses (Cohen & Fraser, 1992). As a result, thedistribution of male and female students across institutions may influence thenational percentagesof men and women who achieve firsts.

Fraser (1994) reported that 'sex differences in mathematics degree results aresmall, but show a pattern found in other studies, namely greater variation inattainmentfor men than forwomen'. As in otherdegree subjects, greaterdifferencesin the proportions of male and female graduates achieving firsts in mathematicalsciences are found at Oxford and Cambridgethan at other universitiesin the UK.Gipps and Murphy (1994) discuss a series of papers on this subject, listing thefactors that have been proposed as explanationsfor the lower percentage of firstsachievedby women. These include a predominantlymasculine culture, the lack ofwomen academics, the encouragement of 'combative' rather 'collaborative' stylesof learningand an emphasis, in assessingstudents, on high pressure,timed, formalexaminations.Differences in the achievements of men andwomen are more extremein mathematicsthan in other subjects. McCrum (1998) presents evidence to showthat in mathematics,at equal mean A level scores, men graduatingfrom Oxforddobetter than women. These studies of achievement in mathematics are based ondegree awards made some time ago: Fraser's (1994) findings are based on awardsmade in pre-1992 universities between 1985 and 1987 and McCrum's (1998) onawardsmade between 1974 and 1991. Since the periods coveredby these studies,there have been extensive changes, in the numbers of students entering highereducation, the natureof assessment within highereducation and in the distributionof degree classifications(Elton, 1998). In addition, there have been changes in thecontent of mathematics degrees (Kahn & Hoyles, 1997) with a broader rangesubjects being covered and an increase in interim assessment. Following thesechanges, it is now useful to re-examinethe differencesbetween men's and women'sachievements in mathematicalsciences using more recent data in order to updateFraser's (1994) findings. Simonite (2004) reported that while women were morelikely to achieve a good degree in mathematicalsciences than men with the sameentry qualifications, there were no statistically significant differences in theproportions of firsts. This article studies the proportions of men and womenachieving first class honours in more detail, by examining the variations betweeninstitutions.


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740 V. SimoniteThe dataThe data for this article were supplied by the Higher Education Statistics Agency(HESA). The sample consists of 22,433 individuals with UK domicile whograduated in mathematical sciences between 1994/95 and 1999/2000. The data foreach graduate consist of age, gender, degree classification, year of graduation,university attended, mode of study, type of entry qualifications and, where relevant,the associated point score based on the grades achieved in A levels or ScottishHighers. A levels are the standard qualifications for entry to universities in the UKand Highers are the equivalent qualifications for students in Scotland. The gradesachieved in these entry qualifications are converted to a point score. For the purposeof this article, each individual's entry qualifications were classified as correspondingto one of eight categories. One category identifies students whose entry qualifica-tions were unknown or missing from the data provided to HESA and a secondcategory identifies students whose entry qualifications consisted of A levels orScottish Highers, but whose grades were unknown. The proportions of students withunknown entry qualifications were highest in the first two years, when the data

40

30

20

10

0

SEX

Percent

first 2i 2iithird/passunclassified

malefemale

Degree classification

Source:HESA studentdata1994-2000.Figure 1. Degree classifications achieved by men and women graduates in mathematical sciences,

1994/05-1999/00


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Variations in degreeawards 741

30

20

10 SEXmale

0 female

Percent

15orunder16-21 22-26 27-29 30pointsAleveldkpointsOtherqualificationsUnknownEntryqualifications

Source:HESA studentdata 1994-2000.Figure 2. Entry qualifications of male and female graduates in mathematical sciences, 1994/95-1999/2000collection system was new, and fell in subsequent years. A third category identifiesstudents who had entry qualifications other than A levels or Highers. The remainingstudents, whose entry qualifications consisted of A levels or Highers with knowngrades, were divided as equally as possible into five groups, leading to the followingcategories: 15 or fewer points, 16-21 points, 22-26 points, 27-29 points or 30 ormore points.

Entry qualifications and percentages of firsts achieved by male and femalegraduatesFigure 1 shows the degree classifications of graduates in the sample by gender: thegraph shows greater variation in the achievements of male graduates, who haveslightly higher proportions of firsts and thirds than women. This is the patternidentified in other studies (Rudd, 1984; Clarke, 1988; Cohen & Fraser, 1992;Tomlinson & MacFarlane, 1995; Chapman, 1996; McCrum, 1998).

Figure 2 shows the distribution of male and female graduates by entryqualifications. This diagram shows that, as reported by Kitchen (1999), amongst


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742 V. Simonite40

30

20

10male

0 female

Percentage

%firsts

15orunder16-2122-2627-2930pointsAleveldkpointsOtherqualificationsUnknown

Gradepoints2 4 6 8 10 12 14 16 1820 22 24 26 28 30Source: HESA studentdata 1994-2000.

Figure 3. Distribution of men and women by grade point scores, graduates in mathematicalsciences 1994/95-1999/2000

50

40

30

20 SEX10 male0 female

EntryqualificationsSource:HESA studentdata1994-2000.

Figure 4. Proportions of male and female graduates achieving first class degree awards by entryqualifications, cohorts graduating 1994/95-1999/2000


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Frequency

per% 20

10

00.0 2.5 5.0 7.5 10.012.515.017.520.022.525.027.5 30.032.535.037.540.042.545.0

Degree awards: percentage firsts

Source:HESAstudentdata1994-2000.Figure 5. First class degree awards by institution

mathematicalscience graduates,a higher proportion of men compared to womenwere found in the group with the highest attainmenton enteringhigher education.Figure 3 shows in more detail the entry qualificationsof men and women withknown grades in A level or Higher examinations.The high proportionsof men andwomen withthe highestpossible score of 30 points suggestthe existenceof a 'ceiling'in point scores, with a failure to discriminate between students with higherattainment.The ceiling effect is more markedfor male graduatesthan for women,whose attainmenton entering higher education was generallylower. Note that thisresultdoes not reflecta higherlevel of achievementby male A level candidateseitherin general, or in subjects related to mathematics, but appears to be a feature ofentrantsto degree courses in mathematical sciences.Figures 1-3 show that amongst graduates in mathematical sciences during theperiod covered by the data, men were more likely to graduate with a first classhonours degree but were also better qualifiedas entrants.Figure4 shows, for eachcategoryof entry qualifications,the percentage of male and female graduateswhoachieved first class degree awards. As one would expect, there is a positive


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744 V. Simonite

Frequency

per% 30

20

10

010 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

Percentage of male graduates

Source: HESA studentdata 1994-2000.Figure 6. Percentage of male graduates for each institution

association between the number of points achieved in entry qualifications and theprobability of achieving a first. Figure 4 also shows that amongst graduates whoseentry qualifications are known, women achieved slightly higher proportions of firstclass awards in all categories of entry qualifications other than the highest, forstudents with 30 points.

One of the categories of entrants in which men achieved a higher proportion offirsts than women is that of 'entry qualifications unknown'. This category accountsfor 15.5% of the sample overall, but more than 75% of such cases occurred in thefirst two years when the data collection system was new and a number of institutionsdid not supply data for any mathematical science graduates.

First class degree awards by institutionOverall, 19.8% of the UK graduates in mathematical sciences between 1994/95 and1999/2000 for whom HESA have records were awarded firsts. Figure 5 shows howthe percentage of firsts varied from one institution to another. It is to be expected


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12

10

8

6

4

2

0

Frequency

pergradepoint

7 11 15 19 23 279 13 17 21 25 29Mean grade point score

Source:HESA studentdata 1994-2000.Figure 7. Graduates' grade point scores: institutional means

Frequency

per% 50

40

30

20

10

00 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Percentage of graduates with 30 pointsFigure 8. Percentage of entrants with 30 points in each institution



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746 V. Simonitethat the percentagesof firstclass degree awardswill be most extremefor institutionswith smallnumbersof graduates.Some institutions, all with fewer than 20 graduatesduring the period covered by the data, did not awardany first class degrees. Twoinstitutionsawardedfirststo more than 40% of graduates:CanterburyChristchurchUniversity College, with less than 10 graduates,and Cambridge,with 45.6% firstsamongst 1089 graduates.Graduates by institution: gender and entry qualificationsIn the sample as a whole, 60.9% of graduates were male. Figure6 shows thepercentages of graduatesin mathematicalscience from each institution who weremale. With the exception of Cambridge, where 81.6% of graduates were male,institutions with the most extreme percentages (below 10% or above 80%) are alluniversitieswith small (less than 20) numbersof students graduatingbetween 1994/95 and 1999/2000.

The mean number of points for students with known A level or Higher grades ineach institutionis shown in Figure7. This graph shows that institutionsappearto beclustered in two groups, one centred around 10-12 points and the other clusteredaround20-22 points. These two clusterscorrespondto the differentbut overlappingdistributions of entry qualifications for students graduating from new and olduniversities, with means of 11.5 (SD=2.92) and 21.4 (SD=4.29) pointsrespectively.Another measure of the entry qualifications of a university'sgraduates is thepercentageof students with known gradepoint score who have the maximum (30)points. Overall, 24.6% of graduateswith known gradesachieved30 points. Figure8shows that this measureof an institution'sintakehas a strongpositive skew, with atleast 50% of graduates in six institutionswith entryqualificationscorrespondingtothe maximum 30 points recorded by HESA. These institutions, and thecorrespondingpercentages were: Cambridge (94.3%), Oxford (85.8%), LondonSchool of Economics and Political Science (LSE) (54.8%) Durham (54.3%),Warwick(53.4%), Nottingham (52.2%)In this diagram,Oxford and Cambridgeappearat the extreme right, with LSE,Durham, Warwickand Nottingham in the next clusterof universitieswith 50-55%of entrantswith known gradeshaving30 points. In 1999/2000 these six institutionsaccounted for 21% of all reported UK graduatesin mathematicalsciences.

These preliminaryanalysesshow that while the achievementof a firstclass degreein mathematical sciences appearsto depend on a graduate'sgender, it also variesaccordingto the individual'sentry qualificationsand the institution attended. Toconstruct a fair measure of the difference between the proportions of men andwomen achieving firsts requires a statistical model that is capable of taking intoaccount a graduate's entry qualifications, institution and other performance-relatedfactors such as age and mode of study in order to separate the effects of gender fromthose of other performance-related variables which may differ between male andfemale graduates. To study the extent to which, other things being equal, gender


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Variationsin degreeawards 747differencesvaryfromone institution to another,the impact of each institution on theachievementof both male and female graduatesneeds to be explicitly incorporatedinto the model. The next section describes the statistical methods used to studygender differencesin the percentageof firsts.Statistical models and resultsThe 22,433 individuals in the sample comprise 536 cohorts graduatingfrom 98institutions.The clusteringof graduates within cohorts and universitiesgives rise tointra-universityand intra-cohort correlationsbetween the outcomes for differentstudents and this means that a multilevelmodelling approachis needed in ordertoachieveappropriateestimatesand standarderrors (Goldstein, 1995). In the analysesreported below, this was achieved by fitting models based on a three-levelhierarchicalstructurerepresenting the clustering of graduateswithin cohorts andof cohortswithininstitutions.These models allowgenderdifferencesin achievementto be defined as functions of variablesmeasured at student or universitylevel and asvaryingfrom one universityto another.The analyses presented here were designed to measure differences in theproportions of first class honours degrees in mathematical sciences achieved bymen and women, after controlling for entry qualificationsand other performance-related factors, and the extent to which these varyfrom one institution to another.A series of multilevel logistic regressionmodels was fitted, analysing the odds ofachievinga firstclass degree.The models were fitted using the multilevelmodellingsoftwarepackage, MLwiN (Rasbashetal., 2002) with parameterestimatesobtainedby penalised quasi-likelihood(PQL) estimation (Goldstein & Rasbash, 1996).The model specifications are given in Table 1. The dependent variableyijkisdefined as equal to 1 if the ith student in the jth cohort graduatingfrom the kthuniversity graduate achieves a first and 0 otherwise. This variablehas mean nijk,where 7ijkis the probabilitythat the graduateachievesa first.The characteristicof astandard Bernoulli distribution, that the variance is equal to nijk( -7ijk) is relaxedthrough the introduction of an 'extra binomial' parameter,a2 (Goldstein, 1995).When a~= 1, yijk has simple Bernoulli distribution with variance 7ijk(l-nijk) butallowinga2 to take other values means that the varianceof yjk is no longer whollydetermined by the mean.

The first model fitted, model A, represents the odds of achieving a first as afunction of gender and as varyingbetween cohorts and universities.The constantterm flo represents the mean (across institutions) log of the odds that a femalegraduatein mathematicalsciences achievesa first.The variablemaleijkis definedas 1if graduatei in cohortj from university k is male and 0 otherwise so that, for malegraduates,the log of the odds of achievinga first are 17maleunits higher than for afemale graduate in the same cohort. The random term v0kallows the proportion offirsts achieved by women to vary from one institution to another, while vFmalekrepresents the additional impact on performance of being male in institution k. Thevariation in Vmalekbetween institutions is a loa:if gender differences are the same,


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748 V. Simoniteother things being equal, in all institutions,then ~ale, will be zero. The cohort levelterm uojkintroduces between-cohort variationin performance. Tests based on thelog likelihood ratio (McCullagh & Nelder, 1989) show that after fitting model Athere is no overall difference between men and women in the proportions ofgraduatesin mathematicalsciences who achievefirst class degrees(X2=1.362, df= 1,p=.243) but there is statisticallysignificant evidence that gender differencesin theodds of achieving a first vary from one university to another (X2=5.741, df= 1,p=.017).Model A is a simple starting point, that does not take into account the effects ofgraduates'entryqualifications,age or mode of study on the outcome of graduation.In model B, additionalexplanatoryvariableshave been added to the model, so thatthe odds of achievinga firstarerepresented as a function of a graduate'sgender,age(mature/other), mode of study (full time/parttime/sandwich) and entry qualifica-tions. The measure of entry qualifications used is based on the eight-categoryvariabledescribedearlier,but students whose entryqualifications are unknown areidentified separatelyby year to cater for the possibility that the characteristicsofstudents in this categoryvaried from one year to another. No furtherparameterswere added to caterfor generaltrends in degreeawardsas an earlierstudy based onthe same data (Simonite, 2004) had established that the variations in degreeclassificationsover time are accounted for by changes in the entry qualifications ofstudents graduating in mathematical sciences in successive years. As Scottishuniversities have a somewhat differentsystem for awardingfirstdegrees, graduatingfrom a Scottish university has been representedas potentiallyhaving an impact onthe proportions of graduateswho achievea first.Interaction terms were included toallow for the possibilitythat the gender differentialmay vary from one gradepointcategoryto another.The randompartsof the model are defined in the same way asfor model A so the effect of being male on the chancesof obtaininga firstis definedas varyingfrom one institutionto another.In model B the constant term representsthe mean acrossinstitutionsof the log of the odds of achievinga firstin mathematicalsciences for a female,non-mature,full-timestudent, with 22-26 points in A levelsorScottish Highers,who did not graduatefroma Scottishuniversity.In additionto thefixed parameter fmale, model B includes additional parameters representing theinteractionbetween gender and the number of points correspondingto the gradesachievedin A levels or Highers before enteringhighereducation. Table 2 shows theestimates of model parametersand standarderrorsformodelsA and B with those formodels describedlater.

The results of fitting model B show that, other things being equal, maturestudents, students on sandwich courses or who enter higher education with gradescorrespondingto 27 or more points are significantlymore likely to achieve a firstclass degree in mathematicalsciences.

Comparing male and female graduates within categories defined by the gradesachieved in entry qualifications, joint 95% confidence intervals were calculated forthe gender difference in each category, with positive values signifying higherachievement by male graduates. These confidence intervals are shown in Table 3.


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Variations in degree awards 749Table 1. Model specifications

A yijk - Bernoulli (ik)Yijk(0,a2)

logVmalek)

V]kmale

B As before but with

logVmalek)where {xpijk,p= 1, ... P} are additional student level variables and{Wlijk, ... W4ijk} identify students with 30, 27-29, 16-21 and < 15 pointsrespectively

C As beforebut with

loglpropmalepropmaleik

+mxpropmalepromaleijkmalekwhere {x}pijk and {Wqi}k)now include the variables meanptsiykand propmaleik

D For Cambridge:

logmalexcambridgeimalejk

For Oxford:

logmalexoxfordmaleijk

Otherwise, as for model C

None of the intervals provides statistically significant evidence of a gender difference.With no evidence of significant gender differences in the proportions of firsts for thesector as a whole at any level of entry qualifications, we now consider the randomparameter oale. The estimated value of this parameter, shown in Table 2, is


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750 V. Simonitesignificantlygreater than zero (X= 6.356, p=.012) so the analysis confirms thatgender differences in achievement vary from one institution to another, afterallowingfor student's age, type of course and entryqualifications.

Table 2. Parameter estimates and standard errors models A-DModel A Model B Model C Model D

Fixed:ConsMaleMatureSandwichPart timeEntry qualifications:30 points27-29 points16-21 points< 15 pointsDk gradesOther qualsDkeq yrlDkeqyr2Dkeqyr3Dkeqyr4Dkeqyr5Dkeqyr6ScottishMale x 30 pointsMale x 27-29 pintsMale x 16-21pointsMale x < 15 pointsPropmaleM x propmaleMeanptsM x meanptsCambridgeM x CambridgeOxfordOxfordmaleRandom:Institution:

2vOGvOmale

2vmaleCohort au2Q2e

-1.533(0.047)-0.062(0.053) -1.7290.0250.2250.428

-1.019

(0.107)(0.086)(0.075)(0.097)(0.351)

2.026(0.113)0.796(0.107)-0.488(0.111)-0.969(0.136)-0.009(0.112)-0.462(0.129)0.354(0.224)

-0.215(0.214)-0.007(0.176)0.693(0.211)0.401(0.277)0.174 (0.358)0.223(0.182)

-0.250(0.125)-0.120(0.125)-0.183(0.136)-0.111(0.164)

0.078(0.027)0.040(0.020)0.077(0.032)0.052(0.015)0.985(0.010)

0.329(0.073)-0.113(0.045)0.100(0.040)0.066(0.018)1.000(0.010)

-1.890 (0.094)0.126 (0.085)0.196 (0.075)0.379 (0.095)-1.051 (0.0350)2.119 (0.119)0.868 (0.109)

-0.508 (0.112)-1.130 (0.139)-0.031 (0.111)-0.528 (0.130)0.363 (0.224)-0.244 (0.213)0.004 (0.175)0.678 (0.211)0.389 (0.277)0.146 (0.357)0.138 (0.153)-0.375 (0.139)-0.222 (0.130)

-0.182 (0.136)0.054 (0.171)

-2.717 (0.639)1.085 (0.690)-0.053 (0.011)0.037 (0.011)

0.118 (0.036)-0.003 (0.025)0.046 (0.029)0.067 (0.018)1.004 (0.011)

1.753 (0.093)t-0.108 (0.064)t0.175 (0.067)0.441 (0.088)-0.637 (0.278)1.771 (0.105)0.657 (0.102)

-0.527 (0.106)-0.974 (0.133)-0.004 (0.098)0.356 (0.121)0.026 (.127)0.069 (0.133)-0.006 (0.170)0.716 (0.204)0.458 (0.273)0.089 (0.356)0.093 (0.148)0.087 (0.120)t0.094 (0.117)t-0.089(0.127)t0.019 (0.162)t1.463 (0.650)t0.355(0.620)t

-0.015 (0.010)t0.010(0.009)t-2.379 (0.249)0.979 (0.176)-2.677 (0.241)0.498 (0.173)

0.122 (.037)t0.002 (0.021)t0.016 (0.020)t0.160 (0.025)0.993 (0.009)

tOxford and Cambridge graduates not included.


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Variationsin degreeawards 751Table3. Joint95% confidenceintervalsforgenderdifferencein the log (oddsof achievinga first)(male-female)by entryqualifications

Estimate(+/- joint)30 points (-.573, 0.123)27-29 points (-0.450, 0.260)22-26 points (-0.263, 0.313)16-21 points (-0.555, 0.239)


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752 V. Simonite1.5

1.1

0.8

0.4

0.0

-0.4

-0.8

-1.1

GAD

1 25 49 73 97Rank

Figure9. 95%confidenceintervals(+/- 1.96se) forgenderdifferenceaddedby eachinstitution,model Bend of the scale, Oxford Brookes University has the estimated GDA that mostfavours women, though in this case, the GDA was not significantly different from thesector mean. In Figure 10 the confidence intervals have been designed for pairwisecomparisons between institutions (Goldstein & Healy, 1995). As is usually the casewith such diagrams (Goldstein & Spiegelhalter, 1996), the vast majority of intervalsoverlap so that it is not possible to distinguish between the majority of institutions.However, unusually, this analysis shows that the GDA at the University ofCambridge is significantly higher than in other institutions, with the exception of theUniversity of Oxford. Further analyses were carried out to examine potentialexplanations for the variations in GDA.

Explaining the variation in GDA in terms of outliersOne possibility is that the variation in GDA is produced by extreme genderdifferences in just a few institutions. Langford and Lewis (1998) describe a numberof procedures for studying the effects of outliers in multilevel analyses. One of theseis to exclude those higher-level units suspected of being outliers from the randompart of the model, and to examine the results. Here, a modified version of thisapproach is used, in which institutions identified as potential outliers are excludedfrom the fixed and random parameters representing the effects of gender. In thiscase, four additional fixed parameters were introduced in order to exclude Oxfordand Cambridge graduates from the random parts of the model and from fixedparameters related to gender. Values of GDA for Oxford and Cambridge are


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Variations in degreeawards 7531.2

0.9

0.6

0.3

0.0

-0.3

-0.6

-0.9

GAD

1 25 49 73 97Rank

Figure 10. 95% confidence intervals (+/- 1.4se) for pairwise comparisons of gender differenceaddedby eachinstitution,modelB

represented by Pcambridgemaleand foxfordmalewhile values of GDA for other institutionsare represented as before. The analysis showed that while at both Oxford andCambridge, men were significantly more likely, other things being equal, to beawardeda firstthan women (95%confidence intervalfor Pcambridgemaleis .634, 1.322,X =31.1, p


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754 V. Simonitegraduates.Both variablesare centredon the averagefor the whole sample (Rasbashet al., 2002) and it is assumedthat each variablemay influence a graduate'schancesof achieving a first in mathematical sciences and the gender differential inachievement.

The results of fitting model C are shown in column 3 of Table 2. Estimates ofthe parameters related to gender measured at individual and institutionallevel show that the proportion of firsts awarded tends to be lower in institu-tions with a high proportion of males, with no statisticallysignificant differencebetween the effects of this variable on male and female graduates(mxpropmale=-1.085,se= 0.690; Z =2.470, p= .116). The mean A level points achie-ved by an institution'sgraduatesare associatedwith decreasingchancesof achievingafirstforwomen (/meanpts = -0.053, se= 0.011: Z = 11.032,p


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Variations in degree awards 7551.2"

0.9

0.6

0.3

0.0

-0.3

-0.6

GAD

7 13 19 25 31Mean A-level points

Figure 11. Relationship between GDA and mean points associated with grades achieved in Alevels or Highers

this way, the findings are that the estimated values of GDA for Oxford andCambridge are significantly greater than zero. There was no statistically significantevidence of gender differences in other institutions (arale = 0.016, se=0.020) at anylevel of entry qualifications (xj = 5.608, p=0.346). With graduates from Oxford andCambridge excluded from the parameters representing contextual effects, there wasno statistically significant evidence of a link between gender differences and themean entry points achieved by an institution's graduates (fmxmeanpts=0.010,se= 0.173). In other words, the final analysis suggests that the relationship identifiedby fitting model C, between high GDA and the level of entry qualificationsassociated with an institution, is a statistical artefact produced by the influence ofdata from two discordant institutions.

DiscussionThis study used a multilevel modelling approach to cater for the clustering ofgraduates within cohorts and institutions. In research concerned with primary andsecondary education, the development of multilevel modelling techniques,combined with the availability of individual data, has been associated with thecreation of a large body of research into school effectiveness and 'value added'(Schagen & Hutchison, 2003). Data collected by HESA describing students'achievements and other characteristics at sector, institution and individual level isavailable to researchers and has widened opportunities for quantitative research inhigher education (see, for example, Yorke, 2003). The use of multilevel techniques


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756 V. Simoniteis still relativelynew in studies of higher education, so that there is enormouspotentialfornew findingsto be generatedby applyingthese techniqueseitherto datafor the whole of the highereducation sector, as in this article, or within institutions,to longitudinalanalysesof students' records (Simonite & Browne, 2003).

In analysing degree outcomes for many institutions, a numberof features specificto higher education need to be considered. The interpretationof 'value added' iscomplicated by the fact that in higher education, assessments are set withininstitutions and the examination system is designed to assure comparabilityofstandards 'between similarinstitutions' (Silver et al., 1995) ratherthan across theboard, as is the case in publicexaminations.In this article, the focus is on differencesin the achievementsof men and women within the same institutionratherthan onvalue added per se. Althoughit maybe legitimatefor mathematicalscience studentsgraduatingfrom differentinstitutionsto achieve,otherthingsbeing equal, awardsindifferentclasses, if men and women reach the same standardsof achievementthenthe gender difference added within each institutionwill be zero.

Some of the findings reportedhere are concernedwith the results for individualinstitutions. These findings have a face validity supported by previous research(Gipps & Murphy, 1994; McCrum, 1998). However, in studies of institutionalperformance it is possible for the relative positions of individual institutions tochange accordingto the underlying model fitted (Goldstein, 2001). This possibilitywas explored, within the limitations of the available data, by using a differentmeasure of institutional-levelentry qualificationsand by excluding data from thefirst two years, when the information supplied to HESA was less complete andpotentiallyless accurate.Neither of these alterationsled to conclusions differenttothose reportedabove.Preliminaryanalysesof entryqualificationsshowed that it is possible that amongstthe most highly qualifiedentrantsto mathematicalscience degrees,men might havehigher attainment than women on entering higher education, but none of theanalyses provided evidence to suggest any general tendency for men with entryqualificationscorresponding to 30 points to do better than women with the samequalifications at institutions. If it were true that amongst entrants to Oxford andCambridgemen had the higherattainmentin mathematics at the startof the coursethan women with similarentry qualifications, there is still the question of whetherthis justifies the size of the differencein their chances of achievinga first.

The significantdifferences, other things being equal, in the proportionsof firstsawardedto men and women at Oxford and Cambridgeareparticularlydisappoint-ing as these differences have such a long history. McCrum (1998) showed thatdifferenceshave existed between men's and women's performancesat Oxford inmathematicsfinals, at equal A level scores, for over a quarterof a century.In a study of researchmathematicians,Burton (1999) found a high proportionhad spent some time either working or studying at Oxford or Cambridge: negativeexperiences of 'the Oxbridge system' were reported by some of the womeninterviewed but none of the men. As there were no differences between men andwomen in their speciality within mathematics or in their ideas or practice of


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Variationsin degreeawards 757mathematics, this raises the question of the extent to which the culture at Oxbridgeinfluences the world of career mathematics within which female academics areconcentrated within the lower levels of the hierarchy, with greater teachingresponsibilities and more temporarycontracts than men (Bebbington, 2002). It isimportant that Oxford and Cambridge universities, as centres of mathematicalexcellence with a substantial share of the most able entrants to mathematicalscience degrees and with such an influence on the profession as a whole, shouldtake steps to ensure a learningenvironmentthat supports all students. However, anumber of things point to some complacency about this issue. A fact sheet(University of Cambridge, 2001) discussing women's academic achievement inall subjectsprovidesa weakdefence of the generallyhigher proportionsof male firstsat Cambridge, arguingthat although Cambridge women achieve fewer firsts thanmen, they achieve twice the percentage of firsts recorded for women graduatesaswhole. Unfortunately,this argumenttakes no account of the selective natureof theintake: women at Cambridgeare amongst the most academicallyable and wouldthereforebe expected to achieve a higher proportionof firststhan female graduatesin general. Nor does it acknowledge the lack of such differences elsewhere. TheQuality Assurance Agency reports for these departments do not refer to genderdifferencesin achievementin those sections reporting on student progression andachievement (QAA, 2000a, b) althoughin each case there must have been markeddifferencesin the percentageof firstsachievedby men and women at the time of thevisits.This article has concentrated on the distribution of first class degree awards inmathematicalsciences. There is more to be learnt about the progress of men andwomen in mathematicsdegrees from studies consideringthe whole rangeof degreeawardsor carriedout within institutions, and the importanceof the subject calls forregularreviewsof how awards aredistributed.Universitieswith largeintakes, settingadditionalpapersfor applicantsor diagnostictests for new entrantsare particularlywell placed to study the progressof differentgroups of students, while the methodsused here can be used to study patterns of achievement in higher education as awhole, in other subjectsor comparingdifferent types of students. Such studies needto consider carefully the particular features of degree-level assessment but willprovideworthwhileinformationabout how differentgroups of students farewithinhigher education.AcknowledgementsI would like to thank the School of Technology, Oxford Brookes University forsupportingthis work and staffat HESA for supplyingthe data. The conclusionsandviews expressedin this articleare the author's.ReferencesBebbington,D. (2002) Women in sciences, engineeringand technology:a review of the issues,HigherEducationQuarterly,56(4), 360-375.


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758 V. SimoniteBourner, T. & Hamed, M. (1987) Entryqualificationsand degreeperformance(London, Council for

National Academic Awards).Burton, L. (1999) Fables: the tortoise? The hare? The mathematically underachieving male,

Genderin Education, 11(4), 413-426.Chapman, K. (1996) Entry qualifications, degree results and value-added in UK universities,OxfordReview of Education, 22, 251-264.Clarke, S. (1988) Another look at the degree results of men and women, Studies in HigherEducation, 13, 315-331.Cohen, G. & Fraser, E. J. P. (1992) Female participation in mathematical degrees at English andScottish universities, Journal of theRoyal StatisticalSociety,A, 155(2), 241-258.Elton, L. (1998) Are UK degree standards going up, down or sideways?, Studies in HigherEducation, 23(1), 35-42.Fraser, E. J. P. (1994) Problems of gender in university mathematics, BritishEducationalResearchJournal, 20(2), 147-154.Gipps, C. & Murphy, P. (1994) A fair test?Assessment,achievementand equity(Buckingham, OpenUniversity).Goldstein, H. (1995) Multilevelstatisticalmodels(2nd edn) (London, Arnold).Goldstein, H. (2001) Using pupil performance for judging schools and teachers: scope andlimitations, BritishEducationalResearchJournal, 27(4), 433-442.Goldstein, H. & Healy, M. J. R. (1995) The graphical presentation of a collection of means,Journal of the Royal StatisticalSociety,A, 159, 505-513.Goldstein, H. & Rasbash, J. (1996) Improved approximations for multilevel models with binary

responses, Journal of the Royal StatisticalSociety,A, 159, 505-514.Goldstein, H. & Spiegelhalter, D. J. (1996) League tables and their limitations: statistical issues in

comparisons of institutional performance, Journal of the Royal Statistical Society, A, 159,385-443.Hartley, J., Trueman, M. & Lapping, C. (1997) The performance of mature and younger studentsat Keele University: an analysis of archival data, Journal of AccessStudies, 12, 98-112.Johnes, J. (1992) The potential effects of wider access to higher education on degree quality,HigherEducationQuarterly,46, 88-107.Kahn, P. & Hoyles, C. (1997) The changing undergraduate experience: a case study of singlehonours mathematics in England and Wales, Studiesin HigherEducation, 22(3), 349-362.Kitchen, A. (1999) The changing profile of entrants to mathematics at A level and to mathematicalsubjects in higher education, BritishEducational ResearchJournal, 25(1), 57-74.Knight, P. W. G. (2002) The Achilles' heel of quality: the assessment of student learning, Quality

in HigherEducation,8(1), 107-115.Longford, I. H. & Lewis, T. (1998) Outliers in multilevel models (with discussion), Journalof theRoyal StatisticalSociety, Series A, 161, 121-160.MacFarlane, B. (1998) Degree classifications: time to bite the bullet, Teachingin HigherEducation,3, 401-405.McCrum, N. G. (1998) Gender and social inequality at Oxbridge: measures and remedies, OxfordReview of Education,24(3), 261-277.

McCullagh, P. & Nelder, J. (1989) Generalisedlinearmodels(London, Chapman & Hall).National Committee of Inquiry into Higher Education, (1997) Higher educationin the learningsociety Report of the National Committee (The Dearing Report) (London, HMSO).Peers, I. S. (1994) Gender and age bias in the predictor-criterion relationship of A levels and

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Tomlinson, K. & MacFarlane, B. (1995) The significance of subject choice in explaining the first-class degree divide between male and female graduates, Researchin Education,54, 95-101.University of Cambridge (2001) Fact sheet: women at Cambridge: academic performance.Available online at:http://www.admin.cam.ac.uk/news/press/factsheets/women1.html.Winter, R. (1993) Education or grading?Arguments for a non-subdivided honours degree, Studiesin HigherEducation, 18, 363-377.

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gender difference added-vanessa simonite

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