The reliability and validity of certain arithmetic tests

In studying the achievement of pupils in the elementary school it is important to know the reliability of our measuring instruments. It is obviously worth very little to measure school achievement and judge the merit of instruction thereby unless the reliability and validity of our measuring instruments are known. During the school year 1926-1927 the writers gave a number of arithmetic tests to the pupils of the sixth and seventh grades in the Peabody Demonstration School. The papers were each checked by two different persons so as to eliminate errors in scoring. When the scores were finally tabulated, it was found that seventy-three pupils had taken all the tests. The scores made by these pupils were accordingly taken for the purpose of this study. In handling the data the scores from the two grades were thrown together so as to somewhat lighten the statistical work. For several of the tests it was necessary to reduce the scores for the pupils of each grade to standard scores before this was done. Correlations were found between the different forms of the same test and between each test and a composite score. This composite score was secured by first converting all test scores into standard scores and then adding these for each pupil. By using this method each test received equal weight in the composite. This composite was used in finding the validity of each test. It is realized that there is a certain amount of self-correlation involved, and that this would tend to raise the size of the correlation. Also the fact that the scores from the two grades were thrown into one distribution would tend in most cases to raise the correlation. The correlation of one form of a test with another form of the same test was taken as a measure of reliability. Since several of the tests are not published in more than one form, it was necessary to repeat the same form in order to secure a measure of reliability. This was true in the case of the Courtis Arithmetic Test and the Cleveland Survey Arithmetic Tests. The coefficient of reliability and the coefficient of alienation are given in Table I for the several tests. The coefficient of reliability, as previously stated, was found by correlating one form of a test with

Achievement test · Arithmetic · Mathematics education · Psychometrics · Pupil · Reliability (semiconductor · Standardized test · Statistics · Test (biology · Test validity · Educational Assessment and Pedagogy · Mathematics · Psychology

• Remedial cases in arithmetic

  William A Brownell•Peabody Journal of Education•1929

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