ME Abstract. Keywords: multidimensional reliability, instrument of students satisfaction as an internal costumer, confirmatory factor analysis

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1 Proceedng of Internatonal Conference On Research, Implementaton And Educaton Of Mathematcs And Scences 014, Yogyakarta State Unversty, 18-0 May 014 MULTIDIMENSIONAL RELIABILITY ESTIMATION IN INSTRUMENT OF STUDENTS SATISFACTION AS AN INTERNAL COSTUMER Gaguk Margono Unverstas Neger Jakarta, Kampus UNJ, Jl. Rawamangun Muka, Rawamangun, Jakarta 130, Emal: Abstract The purpose of ths paper s to compare multdmensonal and undmensonal relablty toward students satsfacton as an nternal costumer. Multdmensonal relablty measurement s rarely used n the feld of research. Multdmensonal relablty s estmated by usng Confrmatory Factor Analyss (CFA) on the Structural Equaton Model (SEM). Measurements and calculatons are descrbed n ths artcle usng measurng nstrument students satsfacton as an nternal costumer. Survey method used n ths study and samplng used smple random samplng. Ths nstrument has been tred out to 99 students. The result of the calculaton s concluded that the measurng nstrument of students satsfacton as an nternal costumer by usng multdmensonal relablty coeffcent has hgher accuracy when compared wth a undmensonal relablty coeffcent. Expected n advanced research used another formula multdmensonal relablty, ncludng when usng SEM. Keywords: multdmensonal relablty, nstrument of students satsfacton as an nternal costumer, confrmatory factor analyss ME - 7 INTRODUCTION Accordng to the Latan (01) Structural Equaton Modelng (SEM) s a secondgeneraton multvarate analyss technque that combnes factor analyss and path analyss that allows researchers to smultaneously test and estmate the relatonshp between exogenous and endogenous multple varables wth many ndcators. Joreskog research results n the 1970s brought on the statstcal theory of lnear structural analyss that s better known as structural equaton modelng or SEM. Important source s used n analyzng the covarance structure so that ths approach s sometmes called the covarant structure model (CSM). The model ncludes mmeasurable varables called latent constructs. Ths construct created by a set of measurable varables, namely measureable construct. Error of measurement whch reflects score relablty s seen as a unque construct and become an mportant part of SEM analyss. The error nclude of measurement n the SEM becomes a beneft for usng SEM compared to other analyss technques (Capraro and colleagues, 001). SEM can estmate error varance whch actually estmates relablty. Accordng to Geffen and colleagues (001), SEM s a multvarate statstcal technque that combnes multple regressons. Ths technque dentfes relatonshps between constructs and factor analyss also recognze mmeasurable concept through some manfest ndcators. Both multple regressons and factor analyss are used smultaneously. The frst approach s attenuaton correlaton correcton whch caused by measurement error. The second approach s a structural equaton model n context of confrmatory factor analyss. Lee and Song (001) sad that SEM s one approach to confrm the measurement model. SEM measurement model lnks latent constructs wth emprcal construct. Emprcal ME-195

2 Gaguk Margono / Multdmensonal Relablty Estmaton ISBN constructs expressed by a combnaton of latent constructs. SEM can process generalzablty and tem response theory. It s also able to compare measurement models and facltates the accuracy of accurate model nvestgaton. SEM has two basc components. Frst, the measurement model s defned as the relatonshp between latent varables and a group of explanatory varables that can be measured drectly. Second, the structural model s defned as the relatonshp between latent varables that cannot be measured drectly. These varables also dstngushed as ndependent varables and dependent varable. Geffen and colleagues (001) sad that the measurement model s submodels n SEM whch dentfes latent construct wth ts ndcators. Ths dentfcaton can be used to determne whch shown through loadng tems produced. Based on the SEM perspectve construct relablty can be calculated through the followng equaton: CR Descrpton: CR = Construct relablty = Factor loadng of standardzed ndcators to- = Standard error of measurement McDonald (1981) formulates a relablty coeffcent whch later named as McDonald composte score relablty coeffcent whch also called omega ( ). Relablty coeffcent s based on confrmatory factor analyss that s part of the menu SEM modelng. Ths composte score explans the amount of ndcators proporton of ndcators whch explans measurement construct. The formula for construct relablty coeffcents s: Descrpton: = Factor loadng of standardzed ndcators to- Construct relablty or McDonald composte score relablty wll gve the same result as 1. Hancock and Mueller (000) develop construct relablty coeffcents whch show how well nstrument ndcators could reflect the construct whch s gong to be measured. Ths coeffcent s a modfcaton of McDonald construct relablty coeffcent. It cannot accommodate dfferent weghts of nterdmensons. The result of the modfcaton called weghted coeffcents relablty, t can be shown as: p l 1 (1 l ) w p l 1 1 (1 l ) Descrpton: ME-196

3 Proceedng of Internatonal Conference On Research, Implementaton And Educaton Of Mathematcs And Scences 014, Yogyakarta State Unversty, 18-0 May 014 l = Coeffcent of the -th standardzed dmensons The relablty coeffcent can be nterpreted as the square of the correlaton between dmensons wth optmal lnear compostes score. Because of ths some experts call the coeffcent as maxmum relablty. Students satsfacton s measured by usng subjectve or soft measurement appled as qualty ndcators. It s called soft because ths measurement focuses on atttudes and perceptons, not concrete thngs (objectve crtera). Therefore, the nstrument utlzed for ths could be student s satsfacton questonnare whch dscusses about servce qualty of the nsttuton. Qualty s a term that s constantly moves dynamcally; f t moves forward, the qualty s sad to be better, otherwse t moves backward t s defned deterorate. Qualty can be understood as superorty or excellence that exceeds the general standard. Somethng sad to be qualfed f there s a match between the requrements of the desred object or servce wth the purpose of the person who wants t. Accordng to Idrus and colleagues (000) "... the purpose of ftness as perceved by the customer." For example, the qualty of the learnng process matches wth what s expected by the students; the better t s served, the hgher qualty t s stated. The frst step to measure servce qualty s dentfyng characterstcs of servce qualty. Lst of these characterstcs can be generalzed n many dfferent ways usng varous resources, for nstance, by studyng lterature such as journal that may contan dmensons of servce qualty. Researchers such as Parasuraman, Zethaml, and Berry (1985) stated that the qualty of servces can be descrbed on nto 10 dmensons. When t s studed, respondents can only dstngush 5 dmensons of servce qualty (servqual). Parasuraman (1988) comments that the 10 orgnal dmensons are overlapped. The fve dmensons of servce qualty are materalzed (tangble), relablty, responsveness, assurance, and empathy. More nformaton about ths can be read from the publcaton about servce qualty, wrtten by Zethaml, Parasuraman, and Berry (1990). Servce s untouchable and nvsble, so the tangble dmenson becomes more mportant. Frst, tangble s the ablty to provde physcal facltes of campus and equpments adequate lectures concernng the appearance of employee/faculty and offcals as well as publc facltes. For example: the avalablty of space concernng the completeness and avalablty of equpments, comfortable and sophstcated campus, computer and nternet facltes, lbrary, lecture halls, semnar rooms, faculty rooms, meda lectures, laboratores, unts of producton, canteen, career gudance centers, health servces, places of worshp, rest areas and parkng lots, as well as means of transport. Students wll see and judge qualty of all facltes. Second, relablty dmenson s a dmenson that measures the relablty of hgher educaton n provdng servces to students. There are two aspects of ths dmenson, they are: (1) the ablty of unverstes to provde servces as nformed to students, and () how far college provdes correct and accurate servce. In other words, relablty s the ablty of ts offcers, employees/faculty n provdng servces on tme, relevant and accurate to satsfy students. These ams are done by developng good admnstraton, currculum and courses whch produce sklls, professon and meet job requrement. The lectures run smoothly as scheduled and the assessment s arranged well also encourage students to ncrease ther ablty. Thrd, responsveness s a wllngness to help students and provde servce quckly. Students expectatons to the speed (fast) servce wll almost certanly change over tme. Responsveness s the wllngness of offcals, faculty/staff to assst and provde servces accordng to students needs. For nstance, offcals easly found for help, lecturers easly met for consultaton, there s nteractve class n learnng whch allows students to develop ther capacty and creatvty for gettng better future. ME-197

4 Gaguk Margono / Multdmensonal Relablty Estmaton ISBN Fourth, assurance dmenson whch relates to the company's ablty and front-lne staff professonalsm to provde a good servce. Assurance ncludes competence, knowledge, sklls, behavor and characterstcs, professonalsm n work, owned by lecturers, admnstrators, and staff. For example, the lecturers delver lectures n areas of ther expertse/experence, add ther nsght by readng, attendng semnars, tranng, further study, do research, have a good atttude and behavor, and all the persons of the nsttuton have professonalsm and regulated n the rule or standard. Ffth, empathy s the ablty of offcers, employees/faculty, and academc advsors to gve good servce, good communcaton, personal attenton, awareness and understand students specfc needs. It can be llustrated as lecturers know the name of the students, faculty academc advsor truly act as a counselor and as a supervsor rather than just as a language edtor, and offcals can easly be reached ether n the offce, va phone, emal and so on. Ths empathy relates to the development of human needs theory of Maslow. At the hgher level, human needs are no longer as prmary thngs such as physcal and socal needs, but also needs of ego and self-actualzaton. Later, the last two needs become the dmenson of empathy. Furthermore, Kotler (1994) stated that customer satsfacton s "... the level of a person 's felt state resultng from comparng a product 's perceved performance (outcomes) n relatons to the person 's expectaton." Thus, the level of students satsfacton depends on match of between achevement level of servce qualty or servce purchased wth students expectaton. In educaton, psychology, economcs, busness, and management, good judgment requres relable measurement or trustworthy. Accordng to Naga (199) educatonal and psychologcal measurement ncludes several thngs, they are: frst, measure the latent trat whch s nvsble to the respondent. Secondly, to measure the characterstcs of the latent form, respondents gven stmulus or approprate measurng nstruments. Thrd, the stmulus responded by respondents should correctly reflects the latent trat. Fourth, the response can be scored and nterpreted adequately. One thng whch s mportant s how far the score acheved shows the latent trat? Does the stmulus express the characterstc of the latent trat? Are the responses gven by partcpants relable for scorng psychologcal attrbutes that? Those questons regard to valdty and relablty of the measurement. Accordng to Wersma (1986), relablty s the consstency of an nstrument to calculate somethng to be measured. Relablty ndcates how far the nstrument and ts results can be trusted. Therefore, relablty s an ndex that ndcates a measurement s relable or not. If the use of an nstrument s repeated for couple of tmes for the measurng the same symptoms, then the nstrument could be relable. In other words, the measurement results are expected to be the same f the measurements repeated. Generally, there are three major categores of measurement relablty, they are: (1) type of stablty (e.g. retest, parallel forms, ad alternatve forms), () type of homogenety or consstency nternal (e.g., splt half, Kuder-Rchardson, Cronbach's alpha, theta and omega), and (3) type of equvalent (e.g. parallel to alternatve forms and nter-rater relablty). The nstrument was gven to one group of subjects once, and then the relablty s estmated. Ths knd of measurement approach generates nformaton about the nternal consstency of the nstrument. Internal consstency reflects the same aspect of homogenety statement. The hgher the relablty coeffcent, the closer the value of observaton scores wth actual scores. So the observaton score can be used as substtute for the real component of the score. Hgh or low relablty coeffcent s not only determned by the value of the coeffcent. The nterpretaton of hgh and low coeffcent value obtaned through computaton and also standards of dscplnes nvolved n the measurement. The hgher the coeffcent of relablty of an nstrument, the smaller errors occur n decsons. Commonly, the measurement of affectve characterstcs provde lower relablty coeffcent than the cogntve measurement, because the cogntve characterstcs tend to be ME-198

5 Proceedng of Internatonal Conference On Research, Implementaton And Educaton Of Mathematcs And Scences 014, Yogyakarta State Unversty, 18-0 May 014 more stable than affectve characterstcs. Accordng to Gable (1986) cogntve relablty coeffcent of the nstrument usually about 0.90 or more, whereas affectve nstrument relablty coeffcent s less than Relablty coeffcent of 0.70 or generally accepted as a good relablty (Ltwn, 1995). In addton, Naga (199) says that the adequate relablty coeffcent should be above Psychologcal measurement always apples valdty and relablty test. But n psychometrcs, there were no agreement among the experts about the relablty coeffcent or formula for relablty among researchers. The problems are: frst, many researchers who consdered competent but do not report the relablty of ther measurement (Thompson, 1994). Second, relablty coeffcents are used monotoncally by researchers wthout consderng assumptons that underle the coeffcent. The researchers use alpha coeffcents were also wthout realzng that for ths coeffcent requres assumptons that are dffcult to fulfll. If the assumptons are not acheved, so resultng alpha coeffcent s the lowest value of estmaton. Many researchers only focused on the use of coeffcent alpha to estmate relablty. The popularty of Cronbach's alpha coeffcent caused by some factors such as: 1) ts computatonal technque s relatvely easy, as t only requres nformaton such as the total score varance, and ) samplng dstrbuton s already known so the determnaton of confdence ntervals on populaton s very possble ( Feld and colleagues, 1987). Thrd, the problems assocated wth assumpton whch becomes requrement for estmatng relablty. In the emprcal realsm, nstead of parallel characterstc requrement, tau-equvalent becomes a challenge for researchers n developng measurement nstruments. Ths s supported by Kamata and colleagues (003) who found that the assumpton of equalty, the power of dscrmnaton between test components, and undmensonalty measurement s relatvely dffcult to acheve. If tau-equvalent assumpton cannot be ganed then the coeffcent alpha relablty values whch produced s very small. It s below the estmated coeffcents. Fourth, the problem s dealng wth undmensononalty measurement. Undmensonalty s an mportant aspect n estmatng relablty. Result of psychologcal undmenson measurement s very dffcult to acheve, especally n the context of the personalty doman that contans broad varances area trats. Socan (000) wrtes that most of factor analyss n several studes conducted are multdmensonal case, not undmensonal. Assumpton s not major ssue n developng a model of nternal consstency, but t becomes subject of study of many researchers n relablty assessment. Lke research done by Vehkahlat (000) that concluded that unrealstc assumptons n classcal theory s assumpton of purty scores of undmensonal whch practcally s dffcult to prove. It makes study of multdmensonal measurements grow because many cases found that correlaton between dmensons of tems hgher than the correlaton between tems n test. Most of educaton measurement use undmenson. Ths measurement conceptually process one capablty factor, personalty, trat, and atttude whch measured by one measurng nstrument. However, many studes shown that the undmenson assumpton s dffcult snce there s another new factor measured n one nstrument. In other words, the nstrument that s often used n psychologcal research tends to be multdmensonal. Some mportant reasons why multdmensonal measurement relablty s mportant suggested by Wdharso (009). He descrbes some reasons, they are: Frst, the general characterstcs of the psychologcal construct s multdmensonal. Second, any nvolvement n preparaton of psychologcal aspect nstruments are usually preceded by havng tem from theoretcal aspects and ts tendency s multdmensonal. The thrd reason s the number of tems n the nstrument. Too much tems may add more error varance potental n tem and ths wll encourage new dmensons. The total of the ME-199

6 Gaguk Margono / Multdmensonal Relablty Estmaton ISBN tems and forms the scale affect respondents' atttudes toward tems whch then affect ther response to the nstrument. The fourth reason s tems wrtng technques. Spector and colleagues (1997) found that tem wrtng technque whch has reversed drecton between postve (favorable) and negatve (unfavorable) drecton could form a new dmenson. In fact many psychologcal scales usng dfferent tem wrtng technques wth reversed drecton n collectng data. Dfferent measurement unts become the ffth reason. Psychologcal measurement tends to have dfferent measurng unts between one tem wth another tem and t has dfferent capablty as measurement construct ndcator. Ths condton wll cause the measurement results tend to be multdmensonal. Wdharso and Mardap (010) dd research on multdmensonal model. It has hgher accuracy relablty coeffcent than undmenson model. Therefore, n ths study, researchers focused only on nternal consstency coeffcent lke untuk undmensonal relablty and, CR dan w. Ths study ams to test the accuracy of relablty coeffcent multdmensonal compared to relablty coeffcent of undmenson. Based on the descrptons above, some questons arse: What s the nternal consstency relablty of multdmensonal nstrument measurng student satsfacton as an nternal customer? How s the comparson between multdmesonal relablty and undmensonal relablty? Whch one s more accurate to measure relablty? RESEARCH METHOD The method used n ths study was a survey method. There was no treatment n ths survey. The survey reveals the fact based on symptoms found from students or respondents. In ths tral obtaned a sample of 103 respondents students from Yogyakarta State Unversty (UNY) n October 013. The nstrument has scale, t s dvded nto two columns: frst column s a realty or the fact perceved by students about servce qualty. There are fve alternatve answers rangng from Very dssatsfed (Vd) values of 1, s Dssatsfed (D) values of, Neutral (N) values of 3, Satsfed (S) values of 4, and Very satsfed (Vs) values of 5. The scale was for the performance nstrument. For the second column, the expectatons of students to nsttutons wth an alternatve fve-pont scale based on the level of student nterest wth answers rangng from Very unmportant (Vu) values of 1, Somewhat unmportant (Su) values of, Neutral (N) values of 3, Importance (I) values of 4, and Very mportant (V) values of 5. The scale was for expectaton nstrument. RESULTS OF RESEARCH AND DISCUSSION 1. For Performance Instrument The performance of the nstrument conssts of a 30 tems questonnare statement of students satsfacton as an nternal customer. Thrteth tems of the nstrument are the result of research that has been valdated by researchers usng factor analyss. The nstrument conssts of 30 tems, dvded nto: 6 statements for tangble dmenson, 7 statements for relablty dmenson, 5 statements for responsveness dmenson, 7 statements for assurance dmenson, and 5 statements for empathy dmenson. Frst, for undmenson Cronbach alpha relablty obtaned drectly usng SPSS, that s Secondly, for whch the relablty of McDonald omega composte relablty n ME-00

7 Proceedng of Internatonal Conference On Research, Implementaton And Educaton Of Mathematcs And Scences 014, Yogyakarta State Unversty, 18-0 May 014 multdmensonal, usng LISREL 8.8 and Excel programs, t s obtaned: , so (17.00) (17.00) (19.870) and 1 Thrd, for the relablty of the multdmensonal construct relablty, t s obtaned the same results as follows: CR (17.00) and 1 (17.00) (19.930) , so Fourth, relablty of multdmensonal maxmum relablty, by usng LISREL 8.8 and p l Excel programs, t s obtaned: 1.584, so t can be calculated as follows: 1 (1 l ) w For Expectaton Instrument The amounts of the tems are the same as the performance nstrument. The expectaton nstrument conssts of 30 tems. Frst, for relablty alpha Cronbach undmenson obtaned drectly usng SPSS, that s Secondly, for whch the relablty McDonald omega composte relablty multdmensonal, usng the LISREL 8.8 and Excel program, t s obtaned: and , so obtaned (19.060) (19.060) (17.489) Thrd, for the relablty of the multdmensonal construct relablty obtaned the same results as follows: and , so 1 1 (19.060) CR (19.060) (17.750) Fourth, for maxmum relablty, usng LISREL 8.8 and Excel program, t s obtaned: p l , and so t can be calculated as follows: w (1 l ) From the results above t can be summarzed as table 1 below: ME-01

8 Gaguk Margono / Multdmensonal Relablty Estmaton ISBN Table 1. Summary of Research Fndngs Relablty CR w Performance Expectaton The calculatons for the above two nstruments are the multdmensonal relablty coeffcent obtaned relatvely hgher relablty coeffcent than undmensonal model. Stll there s not agreement among experts psychometrcs about ths. But for Indonesa researchers there should be change n usng way to fnd out relablty after knowng the most approprate, correct and adequate tools. Indeed, most researchers among the faculty and post graduate students (of both S and S3)) do not know the formula for calculatng the coeffcent of relablty construct, omega or maxmum relablty. Ths s the tme to ntroduce and use the formula because many psychologcal constructs, personalty, educaton, and socal are multdmensonal. So researchers and students can develop and grow nsght and nformaton about other relablty coeffcent. Educaton measurement s somethng that s qute complcated. It s hoped that varous wrtngs n journals provde vald, relable, and accurate result. Experts try to brng educatonal measurement far nto the area of mathematcs. Wthout masterng hgh level and complcated mathematcs calculaton, we cannot understand the varous journals of educaton measurements. So far, we left behnd n the feld of educatonal measurement. Only few scence educaton experts who understand the content of educatonal measurement journals. These journals consst of hgh level mathematcs. Therefore, the amount of scence educaton experts n educatonal measurement should be ncreased. The frst effort to do t s by changng our percepton that educaton and psychology measurement do not requre math. Educators need to change ther percepton of mathematcs. Educators need to be aware that there s a part of educaton whch hardly uses mathematcs such as the example above uses multvarate statstcs that requre hgh mathematcal sklls. CONCLUSION AND SUGGESTION Based on the test results of ths study t can be concluded that multdmensonal relablty coeffcent s more precse or accurate when compared to relablty coeffcent n undmensonal. There are some suggestons for ths: frst, estmaton of the nstrument need to be tested further by usng another formula whch s not based on SEM. Second, because ths study used a fve-pont scale, t s necessary to contnue to use varety of dfferent scales, such as the semantc dfferental scale, dchotomous scale, Thurstone scale, and so on. Thrd, these nstruments need to be tested usng a larger populaton sample and the wder settng and nvolves several provnces at the same tme, also the school level and dfferent type of unversty or college. Thank statement. Thanks to the Drectorate of Hgher Educaton, Mnstry of Educaton and Culture. Research Insttute of UNJ for Fundamental Research grants for Fscal Year 013, and all students who have been wllng to be the respondents; the data of ths paper s part of Fundamental Research fndng. ME-0

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