تأثيرُ حجمِ العيِّنة وتدريج الاستجابةِ في تقديراتِ مُعامل ثباتِ ألفا العام للمحْرزي لأنواعِ الدَّرجات المحولة

Abstract

The study aimed to examine the effect of sample size and response rating scales on estimating Almehrizi generalized alpha reliability coefficient for different scaled scores using real data for students' attitudes towards mathematics in TIMSS2019 for test administration in 2019. The sample consisted of 5117 male and female fourth-grade students in Sultanate of Oman. To achieve study objectives, three data sets were created through manipulating the response rating scales to obtain three types of response rating scales (four response categories which was the original scale – three response categories - two response categories). For each response rating scale, 100 subsamples were randomly selected using three sample sizes (30 for small sample size – 200 for medium sample size – 1000 for large sample size). In addition, five scaled scores were computed for the three types of rating scales: raw scores, standardized scores, percentile scores, and two TIMSS scaled scores. Almehrizi's generalized Alpha Coefficient was computed for each of these scaled scores for all data sets. Finally, these reliability coefficients were compared to answer research questions using descriptive statistics, bias and RMSE. Results revealed that the Almehrizi’s Generalized Alpha Coefficients for all data sets showed high accuracy, as they were very close to the reliability coefficient values for the original data set for all scaled scores. Both bias and RMSE values were very close to zero indicating accurate estimation even for small sample size (30). The study recommended utilization of this coefficient to estimate reliability for different scaled scores in research and assessment tools.