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In educational settings researchers and practitioners are interested in students’ attributes suchas achievement, intelligence, aptitude, ability, skills, attitudes, interests and motivation. Theseattributes are defined as psychological constructs since they could not be observed andmeasured directly. Psychological constructs are measured by observing the behaviors whichare accepted as indicators of these constructs (Lord & Novick, 1968; Embretson & Reise,2000). Therefore, information is obtained about the individuals in terms of the relatedattributes obtained through psychological measurement tools such as tests, scalesquestionnaires. A test is a measuring tool that describes numerically the degree of amount ofthe interested construct individuals have under standardized conditions. Tests contain a set oftest items to measure the related constructs and they are used for many purposes ineducational settings. According to the results obtained from these tests, many decisions aremade about the students such as admission and placement to some programs. Therefore it isimportant to get valid and reliable measures (Haladayna, 2004). Regardless of the purpose ofmeasurement, tests are required to have the psychometric properties as validity and reliability.For example, if a test intents to discriminate among examinees over a wide range of ability, itneeds to be composed of items of medium difficulty. On the other hand, if a test aims toidentify areas of specific weaknesses for low-ability students, it needs to include a substantialnumber of items which are relatively easy for the students as a whole (Crocker & Algina,1986). As it is understood, through the intentions of measurement, tests to be used arediffering in terms of ability levels. Therefore, it is important to know which test is moresuitable for the measurement purposes. IRT has an important advantage in terms of item andtest information functions which clarify the effectiveness of the test according to ability levelsof individuals by taking account the amount of information provided by these functions. Itemresponse theory is an effective way of describing items and tests, selecting test items andcomparing tests. Preparing the suitable test design involves the use of item and testinformation functions. Item information function has an important role in item evaluation andtest development. Since a test is a composition of items, the test information at a given abilitylevel is computed by summing the item information at that level. As a result, the amount ofinformation provided by the test will be much higher than the amount of information providedby a single item. Hence, a test estimates the ability more precisely than a single item(Hambleton, Swaminathan, & Rogers, 1991; Baker, 2001). It could be determined at whichpoints on the theta scale the test provides the most information. Moreover, selecting theappropriate model for the related study is crucial in educational and psychologicalmeasurement for dealing with measurement errors. Since, it clarifies the relationships amongtest items and ability scores to achieve the best test design (Hambleton & Jones, 1993).Therefore it is considered that comparison of dichotomous IRT models for different abilitylevels in terms of the item and test information functions would yield more information aboutreliability of measures. For this reason at this study it is aimed to compare dichotomouslyscored one-parameter, two-parameter, and three-parameter logistic item response theorymodels in terms of the test information function at the three ability levels as low, middle andhigh, separately. Therefore, the method of this study is survey research. Data was collected byusing the test that aims to measure students’ achievement levels on the subject of “educationalmeasurement and evaluation”. This test was developed by researcher and administered to thestudents in the Gazi University at the Faculty of Education at the spring term of 2014-2015academic year. Obtained data includes 264 participiants’ responses. Then, this data issimulated in R studio by package of Latent Trait Models under IRT by taking the sample size1000. Similarly, this simulated data was analyzed in the program of R studio. The analyseswere carried out by the R package of Latent Trait Models under IRT. The results show thatone and two-parameter logistic models provide the highest information at the middle abilitylevel, and the lowest information at the high ability level. Moreover, three-parameter logisticmodel provides the highest information at the middle ability level although it provides thelowest information at the low ability level. Also, three-parameter model provides the highestinformation among these models in terms of total information (%95.19), which explains 64.39percent of total information at the middle ability level. This findings show that guessingparameter is an important factor for this achievement test. Therefore, use of three-parameterlogistic model is the most suitable one for this test, and also this test could be used forparticipants at the middle ability level. For the future researches, it is recommended tocompare the dichotomously scored models in terms of ability estimation at different abilitylevels. |
