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Are exam results gender related?

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Introduction

Exam Results Aim Are exam results gender related? Introduction This coursework aims to determine if exam results are independent of gender. There may be many reasons as to why one sex may perform better in exams than the other. However why one sex may perform better than another is not an aim of this coursework, only to determine which sex, if any. Should one sex be found achieve better grades in exams, various possible reasons will be discussed. However, the question "Why?" is only a secondary aim of this coursework; as simply put, this is Maths, not Sociology. Hypothesis There have been many articles in the media that girls do better in exams than boys and my own experience agrees with this statement. I think girls are generally better at all subjects, and excel at subjects such as art, languages and English, but perform slightly less well in subjects such as science, maths and IT. Also, I generally feel that girls do better at essay writing subjects than boys. Having made a hypothesis, I must remain working through this investigation. I must not try to make the data fit the hypothesis, but make calculations using the data. Once calculations have been made, then I may think about to what extent the data matches the hypothesis, if at all. Also I must keep in mind not to try to disprove the hypothesis, as I am a boy and I "would like" to find that boys do better than girls. What Data Will Be Analysed In order to answer the question, "Are exam results gender related?" data concerning exam results must be analysed. This data are the results from Beauchamp College students taking exams in June 1999. This data was chosen because it was easily available. It must be noted, that as this is data from one school, the conclusions drawn in this coursework does not necessarily apply to students in other schools, in other parts of the country. ...read more.

Middle

Contingency table for total GCSE passes/fails: Pass Fail Male 1194 932 Female 1775 582 Calculating the expected frequencies, assuming that pass/fail are independent of gender: Pass Fail Male p(male) x p(pass) x no. students p(male) x p(fail) x no. students Female p(female) x p(pass) x no. students p(female) x p(fail) x no. students Pass Fail Male 1408.007 717.993 Female 1560.993 796.007 Calculating X2 value. The critical value for 1 degree of freedom at 5% significance level is 3.84. 183.19 is greater than the critical value, therefore the difference is significant. The critical value at 1% is 6.63. 183.19 is greater than this value, so the difference is very significant. The critical value at 0.01% is 10.83, which is lot less than the X2 value 183.19. This means that the difference is extremely significant. This means that if the model were correct, such a high X2 value would only happen in less than 0.01% of the cases. This means that it is highly improbable that the model is true, and so should be rejected. The evidence suggests that exam results, overall, are not independent of gender. To determine which sex does better, a simple percentage calculation can be carried out. About 75% of girls pass, which the boy pass rate is about 56%. This, along with the chi-squared test shows that overall for GCSE, girls do better at exams than boys. Possible reasons for this will follow later in this coursework. Other Calculations In addition to performing a chi-squared test for independence for all GCSE subjects together, they were done separately also, for both A Level and GCSE. The results of these tests are outlined in the following table. The X2 statistic is the value comparing the observed frequencies of pass and fail, against expected frequencies if exam results are independent of gender. The actual frequencies used in these calculations can be found in Appendix A. ...read more.

Conclusion

Possible Improvements A system to take into account the actual grades achieved by both genders could improve the viability of any conclusions drawn from the results. I carried out some research, and discovered that for 2x2 contingency tables with 1 degree of freedom, a correction for the X2 formula should have been carried out. This is called the Yates Correction. Here is an excerpt from a page from the Internet concerning this: Yates Correction. The approximation of the Chi-square statistic in small 2 x 2 tables can be improved by reducing the absolute value of differences between expected and observed frequencies by 0.5 before squaring (Yates' correction). This correction, which makes the estimation more conservative, is usually applied when the table contains only small observed frequencies, so that some expected frequencies become less than 10 (for further discussion of this correction, see Conover, 1974; Everitt, 1977; Hays, 1988; Kendall & Stuart, 1979; and Mantel, 1974). * http://tiger.ees.kyushu-u.ac.jp/~hu/Reference/Online/textbook/stbasic.html This means that the formula for X2 should be: This should especially be used in cases where the X2 value is close to the critical value. This could be used for, Maths GCSE, as its value was close to the critical value. Possible Extensions Data could be analysed, using the above refinements, for other schools, whole regions or whole countries to find if exam results are gender related. If data was available, analysing how students progress from GCSE to A Level, according to gender could be done. This could help find whether boys do mature at A Level, or some other reason is behind the fact that at A Level there is no distinction between the results of boys and the results of girls. Appendix A Actual frequencies used in X2 statistic calculations: Subject Boy Pass Boy Fail Girl Pass Girl Fail All GCSE 1194 932 1775 582 Science 264 164 352 124 French 86 70 165 40 Maths 136 136 164 109 English 145 104 205 46 IT 40 22 36 12 All A Level 311 150 302 165 ?? ?? ?? ?? 2 MATHEMATICKS COURSEWORK. OCTOBER 14, 2000 1 ...read more.

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