Estimation of the All Tests Pass Rate When No Examinee Took All of the Tests

Two models are presented in this article for estimating the proportion of students who would pass all of three or more content area tests given that none have actually been tested in more than two of the content areas. The first model allows one to estimate the proportion of students who would pass all of three or more content area tests from the test results of a study in which no student took more than two of the tests; the second model (which requires an outside estimate of the correlations between the different content area tests) allows one to estimate the proportion of students who would pass all of three or more content area tests from the test results of a study (or field test results) in which students took only one content area test. The models were tested on the Texas End-of-Course test battery (which consists of four content area tests) results of students who took all four content area tests prior to or in the spring of 2001, with at least one of the end-of-course content area tests taken in the spring of 2001. The model test results may have particular application to state assessment programs that must perform standard setting on high-stakes exams before the first live administration of the exams.