Mann Whitney U test as applied to the change in the mathematics exam method in Sudan" Case study of south Darfur state"

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1 Ma Whitey U test as applied to the chage i the mathematics exam method i Suda" Case study of south Darfur state" Author: dr. Abdalla Ahmed AlkhalifaAbdalla Tabuk Uiversity KSA)-Faculty of Sciece dr.a.alkhalifa@gmail.com Abstract I 005 Suda miistry of educatio chaged the system of mathematics examiatio for secodary certificate from two exam papers "two sessios" to oe exam paper "oe sessio". This chage may affect studet's academic attaimet positively or egatively. Therefore, it is very importat to test this effect, which is the mai objective of this paper. The study covers south Darfur state i Suda, as oe of states far from the capital Khartoum. Data source is miistry of educatio i south Darfur state "Neyala office" for three years precedig ew system ad three years with ew system. The statistical test will be use is Ma-Whitey U test. The most result obtaied from the study is that there is o sigificat differece betwee attaimet after ad before applyig the ew system. Key words: Ma-Whitey; attaimet commoly usedfor comparisobetweetwo idepedet samplesto determieif the samplesbelogto oepopulatiosorot.itis the firsttestto deal withcases ofuequalsamples. Itroductio: I 005 Suda miistry of educatio chaged the system of mathematics examiatio for secodary certificate from two exam papers "two sessios" to oe exam paper "oe sessio". This chage may affect studet's academic attaimet positively or egatively. Therefore, it is very importat to test this effect, which is the mai objective of this paper. The study covers south Darfur state i Suda, as oe of states far from the capital Khartoum. Data source is miistry of educatio i south Darfur state "Neyala office" for three years precedig ew system ad three years with ew system. The statistical test will be use is Ma-Whitey U test. Ma-WhiteyTest isoe of the mostoparametric tests used, 1555

2 samplesadarrage them i ascedig or descedig orderadthe value ofuaccoutequal to the sumof values of larger sample -ifsamples havedifferetsizes- which aresmaller thaall values ofthe smallersample. If thesample dataxissmallerady is larger, the Meas values of Y less tha all values of X, ad y X y) Meas values of X less tha all values of Y. Ad U takes the form: U= mi [ Y x), x X y) ] y The use 1 ad ad U to fid critical value for give sigificat value α from Ma- Whitey table for small samples, this value associate with oe side test, i case of two side test this value is multiplied. Aother way is to fid out lower critical value U-) from Ma- Whitey table for small samples usig, adsigificat value α ad Assumptio to use Ma-Whitey U Test: 1. Samples should be idepedet ad take radomly ad variable uder study is cotiuous ad ordial.. should have idepedece of observatios 3. Ma-Whitey Y < x) U test ca be x used whe two variables are ot ormally distributed Test hypotheses: Null hypotheses H0: both samples comes from same populatio Alterative hypotheses HA: both samples comes from differet populatio, also it ca be oe side test to the right or to the left idicatig that oe is better or worse tha the other. Test procedure: There are three directiosdepedig othe size ofthe testsamples. If thesize ofthe firstsample data1ad the size ofthe secodsample data so that their sumis equal to), the three directiosof the testare: Fist, Icase ofverysmallsamples1, <8)thataytwo samples1, is Less tha or equal to 8, Themergethe two 1556

3 I this case, U ormally distributed with: E Ad U) ) 1) 1 1 Va U) 1 Ad hece, U E U ) Z Va U) U ) 1 1 ).. 1) The, compare Z to tabulated Z at a give α However, i case that there are some values or raks foud i the tow samples, this will effect o the test, so that correctio factor "CF" used where: CF ) ) 1) 1 Where,τ the umber of equal cases for each rak. Ad modified Z is: Z [ U 1 1 ) 1) CF hece the upper value U+) ca obtaied as U+= 1 U-. Secod i case 9 0: I this case, Ma- Whitey test calculated as follows: 1. Merge both samples ad fid raks for all values by givig each value its rak i the merged group ad the average of raks to those which are equal, the fid sum of raks for the first sample R1 ad fro the secod sample R.. R 1 + R = 3. The statistic U is: U 1 = 1 ) + U = ) ) ) +1) R 1 R 4. Fid the critical value U from Ma- Whitey table associated with 1 ad ad compare it to the smaller U1 ad U, if the smaller U is less tha tabulated U the reject H0 ad if its greater the, reject HA Third, I case of > 0: 1557

4 Data descriptio: Table 1: data descriptio Boys school Girls school year school Karari boys) Techical school boys) Neyala boys) Almustafa boys) Alkhair boys) Maximum Miimum Mea Stadard deviatio Alwehda girls) Alegaz girls) Neyala girls) Umelmomii girls) Albirraghibgirls) Maximum Miimum Mea Stadard deviatio It ca observed from table 1 that the attaimet of girls is higher tha boys, the dispersio of data before the ew system is higher tha after applyig the system idicatig that there wasmore homogeeity i the attaimet after applyig ew system. Modifyig data: Averages foud for the years before ew system ad for the years after, to compare betwee them, the data take the followig shape; 1558

5 Table : Data before ad after the ew system averages of attaimet for the years Before ew system averages of attaimet for the years after ew system Figure 1: compariso betwee attaimet before ad after the ew system Before After Hypothesis: H0: No sigificat differece betwee attaimet after ad before applyig the ew system. HA: Attaimet after applyig ew system is better tha before Model applicatio: 1559

6 Data fulfilled the requiremets of Ma Whitey test sice its cotiuous ad samples are idepedet ad all variables i each sample are also idepedet. Figure 1 shows that the two samples are ot idetical, so compariso betwee meas is better tha betwee medias. SPSS output of Ma-Whitey U test: Table 3: Raks VAR00001 N Mea Rak Sum of Raks VAR0000 before after Total 0 Table 4: Test Statistics b VAR0000 Ma-Whitey U Wilcoxo W Z Asymp. Sig. -tailed).496 Exact Sig. [*1-tailed Sig.)].59 a a. Not corrected for ties. b. Groupig Variable: VAR The attaimet of girls is higher tha boys i south Darfur state.. The attaimet after applyig the ew system has less dispersio tha before applyig the ew system. 3. There is o sigificat differece betwee attaimet after ad before applyig the ew system, the the oly Although, table 3 shows higher mea rak for "after", Ma-Whitey U test As P>0.05, coclude that the data does ot provide statistically sigificat Evidece of a differece betwee after ad before applyig the ew system. Results: 1560

7 . Eldirdeer, AbdelmoemMohemed - Parametric ad o-parametric statistics - Alamalkutob publisher Jea Dickiso Gibbos Noparametric Statistics:a itroductio-sage publicatios Myles Hollader et.al oparametric statistical method Published by Jog willy ad sos Peter Spret ad Nigel C. Smeeto Applied oparametric statistics published by Taylor ad fracisgroup,llc -007 beefit gaied from applyig the ew system is the reductio from two sessios to oe sessio for the mathematics examiatio ad hece reductio i time of correctig aswer books. Recommedatio: Accordig to the above results, the study recommeded that it's better to cotiue i applyig the ew system. Refereces: 1. Abu hatab, Fuad ad Sadig, Amal Research methodology ad methods of statistical aakysis Egyptia Aglo library