English abstract
This study aimed to use Rasch's Dichotomous Model to construct and calibrate a Mathematical Skills Test, and to ensure that Rasch Model's assumptions were fulfilled in the data. It also aimed to estimate Rasch model parameters (Items difficulty, and person's ability). To conduct the study, the researcher constructed a test measuring basic mathematical skills for tenth grade. The test consisted of 80 items; 40 multiple-choice items, and 40 short answer items. It was conducted on a sample of 494 male and female students from Grade 10 in Muscat region schools in 2009/2010. The SPSS, WINSTEPS and ITEMAN programs were used for statistical analysis of the data. Classical psychometric parameters were obtained and factor analysis was carried out in order to investigate Unidimensionality in the test. In addition, model-fit analysis was performed by WINSTEPS in order to examine the unfit items and persons. The results indicated that the assumptions of Rasch Model were not violated in the Mathematical Skills Test for Tenth Grade in the Sultanate of Oman. The test results satisfied unidimensionality and local independence of measurement. Unfit Items and persons were deleted according to model-fit analysis. These indicators showed that the average of item difficulties for this test was greater than the average of the ability estimates of the study sample, Moreover, the values of the standard error of ability estimates were low, which gave an indication of the accuracy of the ability estimates of the study sample and locating the persons positions on the ability scale. The researcher utilized the information function in choosing the best items to select the top 10% of students, which were 40 Items after taking into consideration the relative weights for each domain in order to preserve the structure of the test and its content validity. The researcher concluded that the model which is applied in this study was the Rasch Model; and its assumptions wereinvestigated in the data of Skills' Test in Mathematics for the grade tenth in the Sultanate of Oman.Consequently, the researcher reached the worthiness of Rasch model on test's data and the model assumptions, and utilizing this model to construct a test has a certain specification depend on its purpose.
