THE STATISTICAL ANALYSIS OF THE QUALITY OF A TEST FROM A COURSE OF HIGHER MATHEMATICS ON THE TOPIC "LIMITS. DERIVATIVES"

In article the mathematical and statistical analysis of the quality of a test on a subject "Limits. Derivatives" is carried out. The most important characteristics at quality check of a test are reliability and validity. Three ways of calculation of coefficients of reliability are considered. In the first case the coefficient of reliability of a test pays off on a variation of test tasks on a formula KR-20. The second way of determination of the coefficient of reliability of a test is connected with the use of the average coefficient of the correlation of all tasks; thus the formula of calculation of coefficients of correlation was applied to dichotomizing data. The third way of determination of coefficient of reliability is based on splitting of a test on even and odd tasks and the determination of coefficient of correlation between these groups with the subsequent correction on Spirmen-Brown's formula. In the analysis of the turned-out results it appeared that the coefficients of correlation of all tasks meet the requirements of high quality of tests. As for coefficients of reliability, they aren't high enough. It means that it is necessary either to change tasks, or to increase quantity of tasks in the test. In the article, it is offered to change the test length. In this connection the size of frequency rate of such change is defined. In the analysis of a validity of a test as an assessment of coefficient of a validity of separate tasks the coefficient of correlation of each task with test mark of the student (the individual mark) - dot biserial coefficient of correlation was used. Its values, and also the value of the general coefficient of the validity of a test is estimated as averages therefore by way of recommendation it is offered to exclude certain tasks, having replaced them with others. In general the conclusion is that this test can be used as means for control of the level of knowledge of students of a subject "Limits. Derivatives" after the completion.

test, reliability coefficient, validity coefficient, correlation coefficient