The current study aimed to exam the effects of sample size, response scale, and derived scores on
estimating Almehrizi generalized alpha and generalized beta reliability coefficients. To achieve
the aim of the study, a scale of students' attitudes towards mathematics has been used with a test
TIMSS2019 and three copies have been made so that they represent the main samples, the first is
for quadruple scaling, the second is for triangular scaling, and the third is for binary scaling. Also,
five derived scores were extracted in all main samples and the sample of the study consisted of
5117 male and female students from the fourth-grade students in all schools of the Sultanate. The
sub-samples were formed for each of the three scales with different sizes (30, 200, 1000). The
reliability coefficients were calculated for the generalized alpha and the generalized beta in each
of the main samples and random samples for all types of raw and derived scores, and this was done
through the R program. The coefficients in all the raw scores and the derived scores in the main
samples were calculated according to the type of score and grading, then the descriptive statistics
were extracted for the generalized alpha and the generalized beta reliability coefficients in random
samples through 1000 iterations and compared them with the reliability coefficients of the main
sample, and finding the bias and the root mean squares error (RMSE).The study reached a high
score in the level and accuracy of the estimates of Almehrizi generalized alpha and the generalized
beta reliability coefficients in all types of raw and derived scores, through what was shown by the
estimates of reliability coefficients in all types of scale scores in random samples and their
closeness to the reliability of the main sample, as well as what was shown by the bias and the root
mean squares error (RMSE) which are close to zero.