Comparison of standard error of mixed-format mathematics achievement test among different proportion of mixed-format scoring: An application of partial credit model and generalized partial credit model

Abstract

This research was purposed to (1) develop mixed-format mathematics achievement test with different proportion of scoring format, and (2) compare a standard error of mixed-format mathematics achievement test among different proportion of mixed-format scoring by analyzed a whole 15 sets of tests and each content independently. Five contents comprised of (1) number and operation, (2) measurement, (3) geometry, (4) algebra, and (5) data analysis and probability. Researcher developed 15 sets of mixed-format mathematics achievement test with 3 different proportion of scoring format (60:40, 70:30, and 80:20) applying 1pl and 2pl model. The finding reveled that;

 1) Most of mixed-format mathematics achievement test were acceptable reliability (greater than 0.5). All 15 sets of tests were fitted for moderate level students or learners.

          2) In perspective of 15 sets of tests, there was no interaction between proportion of scoring format and model influencing standard error at statistical significance level of .05. According to main effect study, proportion of scoring format affected mean of standard error (SE) at statistical significance level of .05. Researcher also made paired comparison of means of SE for each proportion of scoring format as (1) 60:40 was lower than 80:20, (2) 70:30 was lower than 80:20 at statistical significance level of .05. Model also affected SE at statistical significance of .05 as mean of SE using 2pl was lower than using 1pl at statistical significance level of .05.

          3) Content of measurement was the sole content that exhibited the interaction between proportion of scoring format and model influencing SE at statistical significance level of .05. Researcher found that (1) mean of SE of 60:40(1pl) was lower than 80:20(1pl), (2) mean of SE of 60:40(2pl) was lower than 80:20(1pl), (3) mean of SE of 70:30(1pl) was lower than 80:20(1pl), and (4) mean of SE of 70:30(2pl) was lower than 80:20(1pl) at statistical significance level of .05. Main effect study revealed that content of number and operation was the only group that proportion of scoring format affected mean of SE at statistical significance level of .05. Paired comparison revealed that (1) mean of SE of 60:40 was lower than 70:30, (2) mean of SE of 60:40 was lower than 80:20 and (3) mean of SE of 70:30 was lower than 80:20 at statistical significance level of .05. Additionally, content of geometry and content of algebra exhibited mean of SE using 2pl was lower than using 1pl at statistical significance level of .05.