Estimation Comparison of Multidimensional Reliability Coefficients Measurement of Senior High School Students Affection towards Mathematics

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1 Amercan Journal of Educatonal Research, 015, Vol. 3, No. 11, Avalable onlne at Scence and Educaton Publshng DOI: /educaton Estmaton Comparson of Multdmensonal Relablty Coeffcents Measurement of Senor Hgh School Students Affecton towards Mathematcs Wardan Rahayu 1,*, Dogol Harjono 1 Mathematcs and Scence Department, Unverstas Neger Jakarta, Indonesa Research and Educatonal Evaluaton Program Study, Unverstas Neger Jakarta, Indonesa, Kampus UNJ, Jl. Rawamangun Muka, Rawamangun, Jakarta *Correspondng author: wardan.rahayu@unj.ac.d Abstract The purposes of ths study were to develop nstrument of hgh school students affecton towards mathematcs. It also compared estmaton of multdmensonal relablty coeffcents of the nstrument,.e. McDonald relablty and Maxmum relablty coeffcent. The research used mult-stage random samplng technque. Conceptually, construct of the affecton nstrument conssts of 5 dmensons, namely: atttude, nterest, self-concept, values, and morals. Inter-rater relablty coeffcent whch were obtaned for the fve dmensons move from 0.73 to 0.80 and produce 86 selected tems. These results were acheved from the tems whch have been selected through expert study and panelsts valdaton. Emprcally, frst and second trals (try out) testng whch used confrmatory factor analyss (CFA) wth Maxmum Lkelhood method (ML) receved loadng factor value above 0,3. In the frst and second trals, the multdmensonal relablty coeffcent calculaton showed that the value of McDonald and Maxmum relablty coeffcents were more than 0.9, whch means that the level of relablty of the affecton nstrument towards mathematcs of hgh school students classfed n a very hgh level. Hypothess testng of McDonald and Maxmum relablty coeffcent used t-pared test on bootstrappng methods samples. The result s McDonald relablty coeffcent s lower than Maxmum relablty coeffcent. Keywords: nstrument development, affecton towards mathematcs, McDonald relablty coeffcent, Maxmum relablty coeffcent Cte Ths Artcle: Wardan Rahayu, and Dogol Harjono, Estmaton Comparson of Multdmensonal Relablty Coeffcents Measurement of Senor Hgh School Students Affecton towards Mathematcs. Amercan Journal of Educatonal Research, vol. 3, no. 11 (015): do: /educaton Introducton A success mathematcs lesson n cogntve and psychomotor aspects s affected by the affectve condton of students. Well motvated and postve behavor students affecton towards mathematcs wll make them enjoy the lesson, so that they can get optmal achevement. Teacher has to concern about affectve characterstcs of students n desgnng learnng program and actvtes n order to reach an optmal learnng outcome. There are 5 characterstcs to evaluate students affectve whch nclude observaton sheets, namely: (1) behavor, () nterest, (3) self-concept, (4) value, and (5) moral. Affecton s a general term that refers to a partcular mood and emoton (Schunck, Pntrch, and Meece, 008: 375). The ams of affecton are: (1) entertanments: fun experences, passons, boredom preventon, stress control, () serenty: relax and comfortable senses, overstress avodence, (3) happness: joyfulness, satsfacton, emotonal pressure preventon, (4) physcal senses: enjoyment that requres physcal sensaton, movement, or contact, avod unpleasant thngs, and (5) physcal benefts: feelng healthy, energetc, fatgue or sckness avodence. The mpact of affecton s usually generalzed as behavor controllng. The purpose of controllng has been related to postve atttude towards learnng assgnments, as well as beleves n values. [1] Affectve doman whch s exposed by Krathwhol, Bloom, and Masa quoted n Smth (009) covers conscous behavors, nterest, concerns, responsblty, lstenng ablty, responsveness, nteracton, and an ablty to demonstrate a proper atttude n a test or lesson stuaton. [] Affectve doman relates to emoton, atttude, apprecatons, and some values such as comfort, preserve, respect, and support. Accordng to Bloom, characterstc of affecton s a combnaton of concerns, atttudes and self-esteem. Such affecton can be related to lesson, school and learners academc self-concept. [3] Affecton doman s classfed nto: (a) recevng, (b) respondng, (c) rewardng (valung), organzng, and (e) characterng. [4] The fve categores of affecton has an nternaly contnuous range whch covers nterest, atttude, value, apprecaton, and adjustment. Such elements are ntersectng to each other n a vew of an ndvdual process. The affectve aspects n mathematcs educaton covers: belef, atttude, and emoton. The dea of belef and

2 Amercan Journal of Educatonal Research 1445 atttude towards mathematcs s connected to teacher s and students value. Belef and atttude n math educaton gve more concern to a fact that there s an affecton behavor aspect, named as value. Behavor aspect becomes a sgnfcant focus of study on atttude, belef, and value development. [5] Students success n learnng process can t always be measured wth a test tool, snce there are stll many aspects of students ablty whch are dffcult to be measured quanttatvely and objectvely. For example, mathematcs affectve aspects cover atttude, nterest, dlgence, honesty, responsblty, tolerance, soldarty, belef or optmsm, and so forth. Therefore, an approprate and qualfed evaluaton tool s necessary n order to measure such aspects. One of the measurement tools whch can be used to measure students affectve aspects on mathematcs lessons s a non-test nstrument. The developments of Senor Hgh School students mathematcal affecton nstruments are usually use a sngle dmenson (un dmentonal) nstrument. Ths measurement conceptually formulated to a type of atttude or factor of nterest whch s measured by one measurement nstrument. However, many researchs show that such sngle dmenson assumpton s hard to be reached due to some appearence of some new factors whch are also measured n one nstrument. In other words, mathematcal affecton nstrument has a mult dmensonal characterstc. [6] Some studes were done n order to measure dmensonalty. For example, a research was done by Wdharso (009). [6] The research dscusses about estmaton of alpha coeffcent whch has a sngle dmenson. Alpha coeffcent resulted n a hgh relablty coeffcent on all tems. In ths case, estmaton of alpha coeffcent goes from α = 0,836 up to α = 0,961. In the case of mult dmensonal data wth small number of tems (less than 15), alpha coeffcent produced a low coeffcent relablty. In contrary, data wth bg number of tems (more than 15) resulted n a hgh relablty alpha coeffcent. The result of the research shows that alpha coeffcent s less senstve towards data dmensonalty when the numbers of tems are more than 15. It can be seen from a qute hgh relablty value (more than 0.7) on varous numbers of dmensons. Most researchers use relablty coeffcent monotonously wthout consderng assumpton based coeffcent. It s expected that the relablty study s not only fxed wth one coeffcent only. It also nvolves relablty whch s lkely to draw more optmal results. Most researchers only focus on usng Alpha Cronbach coeffcent to estmate relablty wthout frstly comprehends the assumptons that underle such coeffcent. Many researchers do not realze that alpha coeffcent requres partcular assumpton to be flled. If ths assumpton s not flled, then the relablty coeffcent whch s resulted from such assumpton s the lowest estmaton lmt (underestmate). [7] One assumpton that estmates alpha coeffcent s sngle dmensonalty (un dmentonal) data. If alpha coeffcent s appled to mult dmensonal measurement, t wll produce an underestmate result. Therefore, a research whch s gong to dentfy mult dmensonal measurement relablty should use relablty coeffcent whch can accommodate multdmensonal characterstcs. [6] Relablty coeffcent for Structural Equaton Model (SEM) based- mult dmensonal measurement s started wth confrmatory factors analyss, such as maxmum relablty coeffcent, McDonald s construct relablty coeffcent and Raykov s composte relablty coeffcent. A queston arses from ths fact s whch relablty coeffcent s accurate for mult dmensonal measurement model. Ths research wll expose some relablty coeffcents whch can be appled on mult dmensonal measurement model, namely McDonald s constructve relablty coeffcent and maxmum relablty coeffcent, and also compares the estmaton accuracy of each coeffcent.. Method Ths research appled survey method by gvng questonnares to respondents. Survey was used for data collecton whch was ntended to reveal facts based on the ndcatons that was receved from correspondents answers. The questonnares were psychology attrbute whch were related to math. Lkert scale was used wth fve categores of answers, namely strongly agree, agree, neutral, dsagree, and strongly dsagree. The method whch was orented on stmulus or responses from respondents used to determne poston of contnuum. The resulted scores wll be the score of the agreed tem. The scores, whch were obtaned from tral, were analyzed n order to emphasze construct valdaton as well as ther relablty coeffcent by usng confrmatory factor analyss wth ML (Maxmum Lkelhood) method. Hypothess testng of mult dmensonal relablty coeffcent dfferences between McDonald and Maxmal methods were performed through t-pared test on bootstrappng method sample. Table 1. Research Desgn on Bootstrappng Data Sample Sze McDonald s Relablty Coeffcent Maxmal Relablty Coeffcent 350 ω1 ρ max1 400 ω ρ max 450 ω3 ρ max ω14 ρ max14 Affecton towards math s a psychology response n form of somebody s feelng or emoton towards math. Postve statement can be expressed n form of respect, enjoyment, or sympathy. Negatve statement can be

3 1446 Amercan Journal of Educatonal Research expressed n form of fear, refusal, hate or dslke. Dmenson and ndcator of affecton constructon towards math whch s gong to be measured s receved from theoretcal study. Dmenson and ndcator from affecton constructon towards math can be seen on Table below. Dmenson Atttude Interest Self-Concept Values Moral 3. Research Fndngs Table. Dmenson and Indcator of Affecton Instrument towards Math Indcator Atttude towards the content of math lesson, Atttude towards the purpose of math learnng, Atttude towards the way to study math, Atttude towards attempt to explore math, and Atttude towards math teacher Tryng to understand math, Partcpatng n math learnng, Own math book, State many thngs clearly and conscously, and Tryng to take logcal actons Strength, Weakness, and Independence Optmsm towards math, Beleve to be success n learnng, Beleve n self- ablty, Beleve n teacher s ablty, and Beleve n frends and school Commtment towards assgnments, to Respect teacher, honesty, and care towards frends Based on analyss of experts, they gve relatvely smlar evaluaton n regards to construct the affecton performance test towards mathematcs for senor hgh school students. Generally, the arranged ndcators have been consdered as a representaton of dmenson of affectons construct towards math. The arranged ndcators are the representatons of defned construct. In other words, the tem constructon s n accordance wth the ndcator. The experts gve some nputs to the tems statements whch are arranged based on each ndcator. There are some tems of statements whch are overlappng, for example, the tem should be ncluded n behavoral dmenson, yet t stll appears n dmenson of nterest or even n other dmensons. Therefore, the experts need to gve suggeston to make changes to the constructon of tems statements so t wll adjust to ndcator and dmenson. It s done by pckng such tem to be ncluded nto the most approprate, domnant, and representatve dmenson to measure the ndcator. The result of experts analyss towards non test nstrument, whch s the gudelnes for fllng out the questonnare, shows that generally the non-test nstruments are suffcent when are notced from grammar and wrtng usage. Experts consdered that language that was used n non test nstruments s communcatve. However, there are some sentences whch are suggested to be changed because they are dffcult to be understood, confusng and they may cause msnterpretaton. Besdes that, the experts have to gve some nputs for refnement, such as: by avodng contnous words from left to the rght, lke often, always, very ; avod tems whch can be msnterpreted as facts when they are not; avod tems whch can be nterpreted n many dfferent ways, t s usually found n tems that contan conjuncton of and, but ; avod tems whch answers wll lkely to be smlar from every respondent or tems whch wll not be chosen by any respondent; to draft the tems wth a smple, clear, and drect language; make the tems shorts, not more than 0 words; one tem only contans one dea/man dea; avod double negatve statement; and avod tems whch may create ambguty for respondents. In accordance to experts suggestons whch concerned on construct valdty and readable factor of tems n statements, grammar use, and wrtng. As a result, there are 3 tems whch should be canceled and excluded from the analyss. The tems are actually already ncluded n other tems so that they are overlapped. Therefore, there are 86 tems whch have fulflled requrements on affecton measurement performance test towards math for senor hgh school students. Ths measurement s gong to be used for valdty and relablty test analyss. The result of mprovement and refnement on non test nstrument was then rechecked by 0 panelsts on a ratonal test. The purpose of ths test was to determne ftness and relabltes of the tems statements between raters. CVR (Content Valdty Rato) from Lawshe was appled for ftness test of tems statements whch nvolved 0 panelsts (rater). It can be seen that all tems statements on each dmenson already matched wth and adjusted to ts dmenson constructon. It can be seen from the calculated CVR scores whch exceeds CVR tables crtcal scores of on 5% sgnfcance test wth 0 raters, whch s 0.4. Thus, all tems can be consdered as approprate and ft to be used to measure senor hgh school students affectve constructon of towards math. Hoyt formula was used to calculate the measurement of construct relablty from the panelsts towards the affecton wth non test nstruments. The result of coeffcent relablty from nter rater relablty calculaton from panelsts for each dmenson moves from 0.73 to These scores are classfed as a hgh level relablty so that the affecton nstrument towards math for Senor Hgh School students are consdered as a relable nstrument. The emprcal test calculaton shows that there are three tems of statements whch are not vald and need to be dropped because they have r calculaton value whch are less than 0.. The relablty test by usng coeffcent relablty formula from Alpha Cronbach s the next step to be done for each dmenson. The result shows that relablty coeffcent scores for each dmenson have an alpha Cronbach score whch s moved from 0.71 to Based on the crtera that expressed by Naga (01), t can be stated that measurement tool whch s used n ths research s approprate and relable. [8] Snce ths affecton nstrument s mult dmensonal, the measurement of coeffcent relablty s also performed wth mult dmensonal coeffcent relablty formula. One of the formula s stratfed wth alpha coeffcent. The result of the calculaton produces a score of stratfed alpha coeffcent, that s α s = 0,794. Such relablty coeffcent score s consdered as a hgh relablty. As a result, the affecton nstrument towards math for Senor Hgh School

4 Amercan Journal of Educatonal Research 1447 students whch has multdmensonal characterstc can be used as a relable measurement tool. Composte score s generated from the addton of each tems that sut to ts ndcator. After that, by usng confrmatory factor analyss, such ndcators are confrmed to be known f they have been n accordance to ts' basc dmenson of affecton towards math. Goodness of ft n SEM can t be drectly performed lke other multvarate technques. SEM does not have best statstc test whch can explan the strength of model predcton. Therefore, some measurements of goodness of ft whch can be used supportvely need to be developed. Ths test s conducted n order to evaluate the goodness of ft (GOF) between data and model. Generally, model ftness test for nvolves structural and ntegrated model are dvded nto three groups of test: absolute ft measures, ncremental ft measures, and parsmonous ft measures. Table 3. Total Scores of Model Goodness of Ft Measurement on 1 st Tral Goodness of Ft Measurements Scores Defntons A. Absolute Ft Measures Ch Square 371,8 Less Ft GFI 0,85 < 0,90 Margnal Ft RMSEA 0,069 < 0,08 Good Ft RMR 0,6 > 0,05 Less Ft B. Incremental Ft Measures AGFI 0,81 0,80 AGFI < 0,90 Margnal Ft NFI 0,9 0,90 Good Ft TLI / NNFI 0,95 0,90 Good Ft CFI 0,96 0,90 Good Ft IFI 0,96 0,90 Good Ft RFI 0,90 0,90 Good Ft C. Parsmonous Ft Measures AIC 494,93 < 506,00 (Saturated) and < 4467,14 (Independence Model) Good Ft CAIC 705,55 < 1593,47 (Saturated) and < 4561,70 (Independence Model) Good Ft ECVI,49 <,54 (Saturated) and <,45 (Independence Model) Good Ft PGFI 0,68 > 0,60 Good Ft Table shows that there are GOF measurements that shows a not really good compatblty result, whch are Ch Square and RMR. There are GOF measurements whch are margnal ft, GFI and AGFI, and 10 GOF measurements whch show good ft. The result ndcates that even though there are some GOF measurements whch show a not really good ft, most of GOF measurements shows a good ft. Therefore, t can be concluded that the most model s good ft. Evaluaton of measurement model ftness s done to each construct by lookng at the valdty and evaluaton of ts construct relablty. Measurement model testng s done through convergent valdty and relablty testng. Convergent valdty shows that measurement ndcators (manfest varables) from a latent construct should have hgh correlaton. Relablty testng s needed to know the nstrument accuracy, consstency, and precson n measurng construct. Convergent valdty can be seen from loadng factor value of ndcators from each dmenson wth an acceptable loadng factor value above The loadng factor value and t-value of each ndcator n every dmenson can be seen as the followng fgure. Fgure 1 shows that all ndcators are sgnfcant because the loadng factor value s > 0.3. Therefore, t can be stated that construct ndcators for each dmensons can explan latent construct very well. The result of valdty test by concernng loadng factor s also relevant wth the t-test. Ths shows t calculated > t crtcal. t-crtcal value wth 95% sgnfcant level s t calculated value can be seen from Fgure below. Fgure 1. Loadng Factor value of each ndcator for every dmenson n Frst Tral Model Fgure shows that all t- calculated value on each ndcator s more than 1.96, so that all ndcators are sgnfcant. It means that all ndcators gve sgnfcant nformaton towards latent varable. Construct relablty value cannot

5 1448 Amercan Journal of Educatonal Research be ssued through Lsrel output, so t must be counted manually. The result of the calculaton s McDonald coeffcent relablty constructon whch s ω = and maxmum coeffcent relablty whch s ρ max = Ths coeffcent relablty constructon s categorzed as a hgh coeffcent, so that t can be sad that the model s relable. Fgure. t- calculated of each ndcator for every dmenson n the Frst Tral Model Because all ft model of loadng factor value for each ndcator n every dmenson s more than 0.3; so that t- calculated value > 1.96; and ts relablty constructon s hgh. It can be stated that ths model s good and there s no need for revson/modfcaton. The same result s acheved from the second emprcal tral model. The tral (try out) hypothess s done parametrcally, because prerequste test analyss for t-test (parametrc) has fulflled the assumptons of homogenety and normalty. t-pared test sample s appled. Based on the result of the calculaton, t s known that t- calculated value s The value of t- table wth 5% sgnfcance level and 14 sample on one sded test s t 0.05,13 =,1604. Because t- calculated > t- table therefore H 0 s rejected, whch means that mean of coeffcent relablty of McDonald method s lower than mean of maxmum method coeffcent relablty. 4. Dscusson The value of McDonalds coeffcent relablty s lower than Maxmum relablty coeffcent because Maxmum relablty coeffcent formula has a varance error (θ), whch may cause the value of coeffcent relablty hgher. The formula of Mcdonald Relablty Coeffcent [10] Is: k λ = 1 ω = [10] k k λ (1 + λ ) = 1 = 1 The formula of Maxmum coeffcent relablty s: k λ 1 θ ρ max = = [11] k λ 1+ = 1 θ λ = loadng factor, θ = 1 λ = varance error The amount of coeffcent relablty depends on value of λ (loadng factor) and the measurement error. Loadng Factor s a varance contrbuton of ndcators on ts latent constructon. The hgher the varance, the greater the coeffcent relablty. Because Maxmum coeffcent relablty arranges the value of varance error, therefore the value tends to be hgher than McDonald coeffcent relablty. Ths can be proven mathematcally as follows. For the case of loadng factor, k = 1 rate (only 1 component) or some other components whch have same value, for example λ, both coeffcents relablty value are same. It proves that the rato(r) of McDonald and Maxmum coeffcent relablty moves from 0 up to 1. For loadng factor k = rate ( dfferent components), ( λλ 1 1)( λ1+ λ) such as λ 1 and λ, the rato s r =. λ + λ λ λ ( 1 1 ) The vsualzaton of r- equaton can be seen n the followng fgure. ( λλ 1)( λ + λ ) 1 1 Fgure 3. Equaton Graphcs r = ( λ1 + λ1λ λ ) From vsualzaton of graph on fgure 3 above, t can be clearly seen that r- value moves from 0 up to 1, wth 0 λ 1 1 and 0 λ 1 doman, where λ 1 s represented by x and λ s represented by y. Maxmum value of r s 1. It proves that McDonald coeffcent relablty s lower than Maxmum coeffcent relablty ( ω ρ ). max

6 Amercan Journal of Educatonal Research 1449 Ths s n lne wth a study done by Margono (013). In hs study, he estmated that multdmensonal coeffcent relablty on students atttude toward statstcs measurement s conssts of 3 dmensons. The fndng of the study s the estmaton of McDonald coeffcent relablty whch s and maxmum coeffcent relablty whch s [9] It shows that McDonald coeffcent relablty s lower than maxmum relablty coeffcent. Generally, the quanttatve and qualtatve analytc result shows that non test performance devce or affecton nstrument towards math for hgh school students whch s developed based on theores, experts, and panelsts revew already developed emprcally n some hgh schools. It s aproprate and can be appled for affecton assessment n hgh school level. If t s compared to the concept and the prevous draft from non test devce, there are some revsons and developments whch resulted from the ratonal try out by experts and panelsts and also the emprcal trals from respondents, smlar for the frst and second secton. That development covers the compatblty between tem and ndcator, between ndcator and dmenson n ts latent constructon, and the usng of more communcatve language whch can be understood by respondents. Valdty pertans wth the extent n whch a test s capable for measurng what supposed to be measured. Performance test whch s developed has suffcent valdty for both valdty constructon whch has assessed by experts and panelsts and also the valdty constructon from emprcal try out. The valdty constructon s seen on the compatblty between tem and ts ndcator. The ndcator that form a dmenson s a latent constructon. Ths non test nstrument s developed based on affecton competences assessment devce n hgh school level and theortcal revew whch supports that competence. The result of the experts assessment shows that ths non test nstrument has suffcent construct valdty. Therefore, ths non test nstruments can be used for hgh school level, both state and prvate schools. The relablty of ths non test nstrument s classfed as a hgh level, whether f t was emphaszed from the panelst assessments result, or from the frst and second emprcal try out. The construct coeffcent relablty from the frst and second emprcal try out s more than 0.9. Ths coeffcent relablty s classfed as a hgh level, eventhough t closes to a perfect level. The measurement relablty of the devce s consstence for the devce to measure what to be measured. The hgher coeffcent relablty, the closer observed score to the real component score. The value of observed score can be used as a substtute of real component score. Therefore, t can be sad that the result of the measurement, usng ths non test devce, shows the partcpants competence whch s close to ther real competence. However, target objects, e.g. students response, become a source of error whch s needed to be evaluated n ths measurement. The varety of students ablty and comprehenson toward questons n the research questonnare nfluence the relablty of ths non test devce. Besdes that, students psychologcal factor should be concerned when they are answerng the questons. Students wth a good mood wll answer the questons well. On contrary, students wth anxousness, restless, or other psychologcal dsturbance tend to answer the questons n desultory. Therefore, to guarantee havng a hgh nstrument relablty, the use of non test nstrument at school must be conducted carefully and consdered the psychologcal state of the students. In ths case, teacher who gves ths questonnare needs to emphasze students readness condton, whether the students are psychologcally ready to answer the questons of non test nstruments gven. 5. Concluson Based on the result of the emprcal try out whch has been conducted, t shows that the nstrument for measurng hgh school students affecton towards math has fulflled valdty and relablty requrements. Ths can be proven by construct valdty analyss usng Maxmum Lkelhood method n confrmatory factor analyss. The calculaton of construct relablty coeffcent by usng McDonald and Maxmum method of multdmensonal relablty formula shows a very hgh relablty coeffcent. The result of try out (tral) hypothess shows that McDonald relablty coeffcent s lower than Maxmum relablty coeffcent. The comparson between McDonald relablty coeffcent and Maxmum relablty coeffcent moves from 0 up to 1 loadng factor. However, there has not been an agreement reached by experts of psychometrc about the most relable coeffcent for a research nstrument. It s expected that other relablty coeffcents from classc test theory or modern test theory/ Item Response Theory (IRT) are used n future research. References [1] Schunk, Dale H., Paul R. Pntrch, dan Judth L. Meece, Motvaton n Educaton: Theory, Research, and Applcatons. Pearson Educaton, New Jersey Inc., 008. [] Smth, Mark K., Teor Pembelajaran dan Pengajaran, terjemahan Abdul Qodr Saleh. Mrza Meda Pustaka, Yogyakarta, 009. [3] Bloom, Benjamn S., Human Characterstcs and School Learnng. New York: McGraw-Hll Book Company, [4] Gronlund, Norman E., Measurement and Evaluaton n Teachng. Macmllan Publshng Company, New York, [5] Clarkson, Phlps dan Norma Presmeg, Crtcal Issues n Mathematcs Educaton. Sprnger Scence+Busness Meda, New York, 008. [6] Wdharso, Wahyu, "Koefsen Relabltas pada Pengukuran Keprbadan yang Bersfat Multdmensonal." Pskobuana, Vol 1 (1), [7] Wdharso, Wahyu dan Djemar Mardap, "Komparas Ketepatan Estmas Koefsen Relabltas Teor Skor Murn Klask." Unpublshed, 009. [8] Naga, Dal S., Teor Skor pada Pengukuran Mental. PT. Nagaran Ctrayasa, Jakarta, 013. [9] Margono, Gaguk, Aplkas Analss Faktor Konfrmator untuk Menentukan Relabltas Multdmens. Statstka, Vol. 13 (1), Me, [10] McDonald, Roderck P., Test Theory: A Unfed Treatment. New Jersey: Lawrence Erlbaum Assocates, Inc., [11] Wahyu Wdharso, "Estmas Relabltas Pengukuran dalam Pendekatan Model Persamaan Struktural," (accessed May 3, 013).