Çok Boyutlu Testlerde Değişen Madde Öbeği Fonksiyonunun SIBTEST Yöntemiyle İncelenmesi

Abstract

This research aims to analyze the differential bundle functioning in the multi-dimensional tests. In accordance with this aim, the effect is identified through differentiating the location of item with DIF in the test (six conditions designated whether the bundle; all, a part of or none of the item excluding the bundle include DIF or not), the correlation between the dimensions (0.10-0.45-0.80), the sample size (2000-5000) and the ratio of the reference and the focus group (1/3; 1/1; 3/1). The first 10 item of the test that is comprised of 30 item is acknowledged as the bundle. The length of the test, the number of the item that the bundle includes and the ability difference between the reference and the focus groups are constant in all condition. The item parameters are generated via ITEMGAN (Ackerman, 1994b) program. The data in align with the parameters is generated via SAS program through an extended 2PL model which establishes the conditions in the research and is multidimensional. The analysis of the data is completed in SAS program, Differential Bundle Functioning is identified through SIBTEST method. The result of the research is interpreted according to the criteria of the power rate and the type I error which are the standards for determining DIF. When the results is viewed, the analysis of the bundle reveals that the correlation increased between the two dimensions, relatively the less the power rates become. The power rate at its highest in all condition is obtained when the correlation between the two dimensions is the lowest. It is observed that the power rates, which are obtained according to two different sample sizes (N=2000, 5000) in the research, increase as the sample size increases. Another variable examined in the research is the ratio of the focus and the reference groups (R/O=1/3, 1/1 and 3/1). SIBTEST, at the level of the bundle, is capable of determining DIF at its highest when the focus and the reference groups are equal. According to the result of the type I error rate, which is another criterion in the research, the error rate is identified to be relatively decreasing as the correlation between the dimensions increase and it is identified to be increasing as the sample size increases. Also according to the ratio of the focus and the reference groups, largest error rate is obtained when the sample sizes are equal. The conditions when SIBSTEST is at its best to determine DIF belong to the conditions that all item which compose the bundle indicate DIF. When all items in the bundle indicate DIF, in the conditions which include or lack the items with DIF excluding the bundle, SIBTEST at the level of the bundle determines DIF 100% precisely. That the bundle includes items which do not indicate DIF has a relatively decreasing effect on the power rates obtained at the bundle level. When the items in the bundle do not indicate DIF and when DIF is found in some items excluding the bundle and in the conditions when the items with DIF is found neither in the bundle nor in the test, it is observed that the type I error rates which belong to the bundle rather exceeds the nominal alfa level (0.05). This condition is thought to derive from the fact that the items do not indicate DIF when examined one by one, yet they increase the level of DIF when they are examined as groups. Another result of the research is that when no items are found which indicate DIF, in two different conditions when there are and are not items excluding the bundle indicate DIF, it is observed that the error rates belonging to the bundle are at closer levels. In other words, if there are no items which indicate DIF in the bundle, whether there are or are not items with DIF excluding the bundle does not have an obvious effect on the error rates obtained at the bundle level. In addition to that, a variance analysis is conducted in order to find the alteration of the type I error and the power rates accordingly to the research factors. The results show that when DIF indicating and not indicating items are found together in the bundle and when there are no items with DIF excluding the bundle, the power rates of the bundle are significant only for the main effect of the sample size. When the items with DIF and without DIF are found together and when the items with DIF exist outside of the bundle; the power rates of the bundle, the correlation between the dimensions, the size and the sample size ratio as the main effects; and only the interaction between the sample size and sample size ratio as the interaction effects are significant. When the ANOVA results of the error rates are viewed, when the items with DIF is not found in the bundle and the items with DIF are found outside of the bundle, the error rates of the bundle, the correlation between the dimensions, the sample size and the sample size ratio are found significant for the main effects. When the items with DIF is found neither in the bundle nor outside of the bundle, the error rates of the bundle, the sample size and the sample size ratio are significant for the main effects.