Determination of the Sampling Technique to Estimate the Performance at Grade Five Scholarship Examination

Transcription

1 Tropical Agricultural Researc Vol. 18 Determiatio of te amplig Tecique to Eimate te Performace at Grade Five colarsip Examiatio.M.R. Kumari ad. amita 1 Pograduate Iitute of Agriculture Uiversit of Peradeia Peradeia, ri Laka ABTRACT. amplig teciques ave bee give muc empasis sice te precisio of eimates greatl depeds o it. Differet metods of samplig ave to be iveigated to fid out te be samplig tecique for a give situatio. Tis ud was coducted to determie te be samplig tecique to eimate performace at te grade five-scolarsip examiatio. Te ud was doe usig results of te grade five-scolarsip examiatio eld i ears 001, 00, 003 ad 004. imple radom samplig ad ratified radom samplig wit differet allocatios were iveigated i te ud. tratificatio of te populatio was based o dirict, geder, medium ad two-wa ratificatio b geder ad dirict. Te radom samples were draw from eac ratum b tree tpes of allocatios; proportioal allocatio, equal allocatio ad ema allocatio. Te variace of sample mea was calculated for eac samplig procedure for te sample sizes 1,, 3, 4, 5 ad 10% of te populatio. Tere was -10% gai i precisio from simple radom samplig to ratified radom samplig except for equal allocatio. Two-wa ratificatio (b geder ad dirict) was more effective (o average 3% icrease i precisio) ta oe-wa ratificatio. Overall, te proportioal allocatio wit two-wa ratificatio was te mo appropriate samplig tecique to eimate te performace. ITRODUCTIO Te precisio of a eimate made from a sample depeds bot o te procedure b wic te eimate is calculated ad o te pla of samplig (Cocra, 1977). ice, tere are various samplig procedures, iveigatio of tese teciques is importat to fid out te be samplig tecique for a give situatio. Large umber of sample surves ave bee coducted i te area of educatio i ri Laka. ome of tese surves were to ud udets performace at atioal examiatios. Eimates from tose sample surves ad bee useful to implemet various ew educatioal policies ( I ri Laka, about 4 millio cildre atted govermet scools. ri Laka as ear uiversal geder equit i access to primar ad secodar educatio. Te primar educatio ccle takes udet troug grades 1-5 wile te juior secodar ad seior secodar ccles ivolve grades 6-8 ad 9-13, respectivel. Te grade five-scolarsip examiatio is oe of te atioal examiatios coducted b Departmet of Examiatios. 1 Departmet of Crop ciece, Facult of Agriculture, Uiversit of Peradeia, Peradeia, ri Laka.

2 Kumari & amita Te purpose of tis examiatio is to offer scolarsips to te be-performed udets to ud i popular scools for teir secodar educatio. tudets of govermet ad semi govermet scools are eligible to sit for tis examiatio. I eac ear tere are about 300,000 udets from all 5 diricts wo sit for tis examiatio. It cosis of two papers to evaluate udets' kowledge o Matematics ad Geeral Itelligece. At preset it as become a igl competitive examiatio i te coutr. Te role of samplig teor is tat it ca be used to develop a metod of sample selectio, wic is ecoomical ad eas to operate. Tereb it makes samplig more efficiet ad provides eimates tat are precise eoug for our purposes (Barett, 1974). Basicall tere are two approaces to samplig i.e. probabilit samplig ad o-probabilit samplig. Probabilit samplig makes coclusios tat appl to te populatio as a wole. imple radom samplig ad ratified radom samplig are some commo probabilit samplig procedures. Terefore, tese samplig procedures were give muc empasis i te preset ud. Te objective of te ud was to determie te mo appropriate samplig procedure to ud te performace at te grade-five scolarsip examiatio. ecodar data MATERIAL AD METHOD Te preset ud was carried out usig grade five scolarsip examiatio results (complete populatio data) of ears 001, 00, 003 ad 004. Te data set cosied of te variables; scool umber, serial umber, dirict umber, marks of subject-1, marks of subject-, geder ad medium. Table 1 sows te basic iformatio. Tere is virtuall a equal male to female ratio wile te iala to Tamil udets ratio is about 4:1. Te dataset was summarized ad aalzed usig MIITAB atiical software (Miitab, 1991). Table 1. Basic iformatio about te data. Year Total o. o. of males o. of females o. of iala o. of Tamil o. of absetees amplig teciques iveigated I te preset ud, samplig metods were iveigated uder two mai teciques. Te were simple radom samplig ad ratified radom samplig. Bot teciques were iveigated for te sample sizes 1,, 3, 4, 5, ad 10% of te populatio. ice tere was a sigificat positive correlatio (r0.8; p<0.05) betwee subject 1 ad subject, te total of te bot subjects was used i te aalsis.

3 amplig Tecique to Eimate te Examiatio Performace Uder simple radom samplig, samples were draw from eac of te ear 001 to 004 usig MIITAB atiical software. amplig uits were draw from populatio witout replacemet. Te precisio of eimates uder simple radom samplig was iveigated usig te measure, variace of sample mea, V (), were; ad V ( 1 f ) (1) ( ) i 1 ( i Y ) 1 () Y is populatio mea, is te sample size, is te size of te populatio ad f is samplig fractio (/). Uder ratified radom samplig, te populatio was fir divided ito rata. trata i tis ud were based o te criteria, dirict (5 rata), geder ( rata), medium ( rata) ad two-wa ratificatio b geder ad dirict (50 rata). I order to coose ratum sample size, tree tpes of allocatios were cosidered amel, proportioal allocatio, equal allocatio ad ema allocatio. Te otatios used i te computatio uder ratified radom samplig were -Total umber of uits i t ratum, - Populatio size, -umber of uits i sample i te t ratum, -ample size, i -Value obtaied from te i t samplig uit i te t ratum, f - samplig fractio for te t ratum, (3) - ratum weigt, (4) 1 i - sample mea i te t ratum, (5) Y 1 i - true mea of te t ratum, (6) i 1 ( i 1 Y ) - True variace of te t ratum. (7) Te precisio of eimates uder ratified radom samplig were iveigated usig te measure V ), were; V ( ( L ) V ( ) (8) 1

4 Kumari & amita L L 1 1 (9) L L 1 1 (10) L is te umber of rata, ) ( V is te variace of sample mea from t ratum give b; V ) ( (11) I te proportioal allocatio, te specific umber of samplig uits was draw from eac ratum proportioal to te ratum size i.e.;. Variace of sample mea uder proportioal allocatio is give b; 1 ) ( f V (1) I te case of equal allocatio, te same umber of sample uits were draw from eac ratum, i.e. 1 L Variace of te sample mea for equal allocatio is give b; ) (1 ) ( 1 L f V (13) Te ema allocatio is a special case of optimum allocatio. If co per sample uit is te same for all rata, te optimum allocatio for fixed co reduces to fixed sample size. Accordigl, (14) ad te variace of sample mea uder ema allocatio is give b, ( ) V ) ( (15)

5 amplig Tecique to Eimate te Examiatio Performace REULT AD DICUIO Populatio atiics Te basic atiics of marks for subject-1, subject- ad subject-total are sow i Table. Te populatio mea of te subject-1 durig varied from 41 to 48. For subject mea varied from 6 to 31. It is clear tat marks for subject-1 was greater ta tat of subject-. Te maximum marks for subject-1 was 100 i all four ears ad for subject- te maximum was aroud 97. Te populatio mea of subject-total was aroud 75. Te maximum marks for subject-total varied 191 to 193. Overall populatio atiics were cosiet i all four ears. Table. Populatio atiics of grade 5-scolarsip examiatio results. Year Variable Mea Media CV Miimum Maximum 001 ubject ubject ubject Total * ubject ubject ubject Total * ubject ubject ubject Total * ubject ubject ubject Total * ote: CV-Coefficiet of variatio, * out of 00 Basic atiics of marks b geder Te basic atiics of marks (subject total) accordig to geder is give i Table 3. Mea mark ad varied from 69 to 73 for male udets, wereas for female it ad varied from 78 to 80 durig te period of Mea marks of bot subjects were iger for female udets ta tat for te male couterparts i all four ears. However, subject-total maximum was iger for male udets i 001 ad 004.

6 Kumari & amita Table 3. Basic atiics of te results b geder. Year Geder Mea Media CV Miimum Maximum 001 Male Female Male Female Male Female Male Female Basic atiics of marks b medium Te grade five-scolarsip examiatio is eld i bot iala ad Tamil media. Basic atiics of marks of subject-total is give i Table 4. Te mea marks of subjecttotal varied from 77 to 79 ad 63 to 67 for iala ad Tamil media respectivel durig four ears. I additio mea marks for eac subject were also iger for iala medium ta tat of te Tamil medium for all ears. Table 4. Basic atiics of results b medium. Year Medium Mea Media CV Miimum Maximum 001 iala Tamil iala Tamil iala Tamil iala Tamil Mea ad variace of subject total b dirict Te mea ad variace of subject-total b dirict is give i Table 5. Te ige mea of subject-total was recorded i Colombo i 001 ad 00 ad Gampaa i 003 ad 004. Te lowe mea of subject total was recorded i Killiocci dirict i all four ears.

7 Tropical Agricultural Researc Vol. 18 Table 5. Basic atiics of marks b dirict Dirict Total Total Total Total Mea Variace Mea Variace Mea Variace cout cout cout cout Mea Variace Colombo Gampaa Kulutara Kad Matele _elia Galle Matara Hamba Jaffa Killioc Maar Vuwia Mulatie Baticoloa Ampara Tricomal Kuruegal Putlam Aurada Poloaru Badulla Moraga Ratepura Kegalle

8 Tropical Agricultural Researc Vol. 18 Precisio of eimates from simple radom samplig Figure 1 sows te V () agai te sample size (samplig percetage) from te populatio. Te variaces are almo similar i all ears but decreased wit te icrease of sample size as expected. V ( ) % % 4% 6% 8% 10% amplig % Fig. 1. Cage of V () agai samplig percetage. Te variace reductio wit differet sample sizes relative to 1% samplig is give i Table 6. It is clear tat we te sample size icreased from 1% to %, te variace reductio was approximatel 50%. Terefore, gai i precisio from 1% to % samplig is about 100%. imilarl, we te sample size was icreased furter up to 10% V () graduall decreased leadig to gradual gai i precisio. Table 6. Variace reductio wit respect to 1% samplig. ample size Reductio i variace (%) relative to 1% samplig % samplig % samplig % samplig % samplig % samplig

9 amplig Tecique to Eimate te Examiatio Performace Precisio of eimates from ratified radom samplig tratificatio of te populatio was doe b dirict, geder, medium ad b bot dirict ad geder togeter. umber of rata i eac ratificatio was 5,,, ad 50 respectivel. V ( ) obtaied uder proportioal allocatio, equal allocatio ad ema allocatio for a fixed sample size (1% samplig) is give i Table 7 ad Figure. ( Table 7. V ) obtaied uder differet tpes of allocatios wit eac tratificatio variable ratificatio at 1% samplig. Year Proportioal allocatio ( Variace of sample mea V ) Equal allocatio ema allocatio Dirict Geder Medium Dirict ad geder Te relative precisio of eimates b tpes of allocatio is discussed uder eac ratificatio criterio. tratificatio b geder ice, tere was equal male to female ratio i te populatio, ratificatio b geder resulted i equal ratum size. Tus te proportioal allocatio is equivalet to equal allocatio. Tis was reflected i te precisio of eimates obtaied uder proportioal ad

10 Kumari & amita equal allocatios. Bot allocatios sowed more or less similar precisio compared to ema allocatio. tratificatio b medium Te populatio was ratified ito two rata based o te medium. ice te iala to Tamil ratio was 4:1, te rata were ot equal i size. It was observed tat te ige precisio was obtaied uder ema allocatio followed b te proportioal allocatio. Te lowe precisio was resulted uder equal allocatio. tratificatio b dirict ice, tere are 5 diricts i te coutr, te ratificatio b dirict resulted 5 rata tat were uequal i size. Te ema ad proportioal allocatios gave almo similar ad iger precisio ta te equal allocatio. Two-wa ratificatio Two-wa ratificatio b dirict ad geder ratified te populatio ito 50 rata. It was observed tat precisio obtaied uder ema ad proportioal allocatios were almo similar ad sowed iger precisio ta equal allocatio. Te relative precisio observed uder differet allocatios wit eac ratificatio was cosiet i all four ears (Fig. ). Dirict Geder 0.6 Variace of sample mea Medium Two-wa Year Allocatio Equal ema Proportioal V ( over ear uder Fig.. Te cage i variace of sample mea ) differet allocatios ad ratificatio at 1% samplig.

11 amplig Tecique to Eimate te Examiatio Performace Accordig to results obtaied uder eac ratificatio metod, (Table 7 ad Fig..) ema ad proportioal allocatios were better ta te equal allocatio. ice tere is o muc differece betwee proportioal allocatio ad ema allocatio ad also sice te proportioal allocatio is easier to implemet, it ca be recommeded for samplig. Precisio of ratified radom samplig relative to simple radom samplig Te percetage gai i precisio i ratified radom samplig wit respect to simple radom samplig is sow i Figure 3. It was clear tat tere was -10% gai i precisio from simple radom samplig to ratified radom samplig, except i equal allocatio ratified b medium, dirict ad, dirict ad geder. Te reaso for te gai i precisio i equal allocatio ratified b geder is tat it is equivalet to proportioal allocatio. Dirict Geder % gai i precisio Medium Two-wa Year Allocatio Equal ema Proportioal 004 Fig. 3. Percetage gai i precisio i tratified Radom amplig relative to simple radom samplig over ear at 1% samplig. It is importat to ote tat te ige gai i precisio was obtaied uder twowa ratificatio. Tus it is possible tat furter gai i precisio could be obtaied wit more ta two-wa ratificatio.

12 Kumari & amita Effect of sample size o precisio of eimates uder ratified radom samplig wit differet allocatios Figure 4 sows te cage i V ( ) agai sample size i ear 001. It clearl sows tat precisio icreases wit te icrease of sample size uder all ratificatio metods ad tpes of allocatio. However, it ca be observed tat te precisio obtaied at large sample sizes (10%) for all allocatio metods give almo similar precisio. imilar patter was observed i all four ears Dirict Geder 0.45 Variace of sample mea Medium Two-wa amplig % Allocatio Equal ema Proportioal 10 0 Fig. 4. Te cage i variace of sample mea V ( ) agai sample size uder differet allocatios ad ratificatio i ear 001. Altoug tere was ot muc of a differece i precisio amog tese tree tpes of allocatios at 10% samplig, wic were about 30,000 uits, it is ot muc of a use sice 30,000 would be too muc for a ud. Tus, te iformatio wit respect to small sample sizes suc as 1% ad % would be more useful. Accordigl, ratified radom samplig wit proportioal ad ema allocatios are te appropriate samplig teciques for similar udies.

13 amplig Tecique to Eimate te Examiatio Performace COCLUIO urves of tis ature are quite commo but ot ma udies ave bee carried out to determie te mo appropriate samplig procedure for tese udies. Hece tere is a requiremet for suc udies sice samplig metod plas a importat role i precisio of eimates. I te ud, te metodolog looked ito importat aspects suc as tpes of ratificatio criteria, tpes of allocatio ad sample sizes. Hece, fidigs are applicable to possible differet situatios. I geeral, ratified radom samplig was foud to be superior to simple radom samplig. iti ratified radom samplig, proportioal ad ema allocatios gave iger precisio ta equal allocatio. Te differece betwee ema ad proportioal allocatio was margial. ice te proportioal allocatio is more coveiet compared to ema allocatio, proportioal allocatio is recommeded for udies of tis ature. I additio, it ca be cocluded tat two-wa ratificatio produces more precise eimates ta oe-wa ratificatio. ACKOLEDGEMET Te GTZ-Basic educatio sector program of Miir of Educatio troug MG Cosultacies, Colombo is ackowledged for te source of data. REFERECE Barett, V. (1974). Elemet of amplig Teor, Te Uiversities Press Ltd, t. Paul s House, arwick Lae, Lodo. Cocra,.G. (1977). amplig Teciques, ile, d editio, ew York. Miitab. (1991). Miitab tatiical oftware, coprigt Miitab Ic., Texas, UA. Miir of Educatio, ri Laka. [olie] (cited o ). ttp://