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• W348671978 abstract "Using the grade equivalent composite scores on the Iowa Tests of Basic Skills of Iowa-fourth grade public school, pupils who took the tests in January 1970, a study was made to determine the relative precision with which anestimate -could be made of the individual percentile norms from different types of cluster sample designs. Five scores ranging from the 14th to the 93rd percentiles were selected, and the proportions below these five scores became the proportions to-be estimated. The variances of the estimates of these five proportions were computed for over 20 different sample designs; results from. seven sample designs are presented. Using the error variances that were computed for each of the seven sample designs, the ratio of the error variance based on a cluster sample to the error variance based on a simple random sample of-pupils was determined. (DB) FILMED FROM BEST AVAILABLE COPY AERA, 1 3 Annual Meeting February, 1973 THE EFFECTS OF CLUSTER SAMPLING IN THE WORMING OF AN ACHIEVEMENT TEST BATTERY by Jane Williams Bergsten U,S. UEPARTMFNT OF HEALTH. EDUCATION A WELFARE OFFICE OF EDUCATION THIS DOCUMENT HAS BEEN REPRO DUCED EXACTLY AS RECEIVED FROM THE PERSON OR ORGANIZATION 'RIG INATING IT POINTS OF VIEW OR OPINIONS STATED' DO NOT NECESSARILY REPRESENT OFFICIAL OFFICE OF ECU CATION POSITION OR POLICY In constructing individual pupil percentile norms for test scores one would typically test a sample of pupils rather than an enare population of pupils. In selecting and testing a sample of pupils it is usually administratively easier and less expensive per pupil to test whole classes, whole buildings or whole systems of pupils than it is to sample and test pupils individually. However, assuming that a given number of pupils are to be tested, the use of any of these types of cluster samples could be expected to decrease the precision of the estimates which could be made. The objective of this study was to determine the relative precision with which one could -estimate the individual pupil percentile norms for pupil achievement test scores of the children in a parti vier grade from different type& of cluster 7, sample designs. ogrThe population studied consisted of the grade equivalent composite scores on the Iowa Tests of Basic-Skills made by Iowa fourth grade public school pupils 1.Nrho took the battery of tests in January of 1970. This consisted of scores for about 95% of a'l fourth grade public school pupils in the state or -approximately. 45,000 fourth graders in 1,800 classes in 1,000-buildings-in 400 systems. The entire population of scores was included in the analysis. Thus, the values of the population proportions to be estimated were actually known, as were the sizes of the various clusters studied. Since from a practical point of view it was not feasible to attempt to estimate proportions below every score, five scores ranging from the 14th to the 93rd percentiles were selected, and the proportions below these five scores became the proportions to be estimated. The variances of the estimates of these five proportions were computed for over 20 different sample designs. The results from seven sample designs will be presented here. These include random samples of entire classes, of entire buildings, and of entire school systems of fourth grade pupils. Using the error variances that were computed for each of the seven sample designs, the ratio of the error variance based on a cluster sample to the error variance based on a simple random sample of pupils was determined. These ratios were measures of the relative inefficiency of the cluster sample design and are commonly referred to as measures of design effects or DEFFs. DEFFs were used to compare the relative precision of estimates based on different sample designs. In addition, DEFFs were used to compute the intraclass correlation coefficients for classes, buildings and systems. The intraclass correlation coefficient provides a measure of the within cluster homogeneity. From the handout you can see that a design involving the selection of whole classes of fourth grade pupils yielded error variances roughly four times those of a simple random sample while the selection of fourth graders by buildings yielded variances about six or seven times those of a simple random sample. When whole systems of fourth graders were selected, variances up to 56 times those of a simple random sample were obtained. There is another ay of looking at these figures. In order to obtain the same error variance as would be obtained from a simple random sample, it would be necessary to test about four times as many pupils if theywere selected by classes, about six or seven times as many pupils if they were selected by buildings, and up to 56 times as many,pupils if they were selected by systems. By partitioning the sy3terns into four strata according to the total K-12 enrollment and selecting clusters separately from ithin each stratum, the error variances were reduced. As compared to a comparable unstratified design, a stratified sample of classes produced a reduction in error variance of about 10%. In the case of sampling buildings, a reduction in error variance of about 15% occurred because of stratification, and in the case of sampling systems, there was a reduction of-about 45%. One of the reasons for the large er -or variances in the case of sampling whole systemE of fourth graders is that some of the syste s had very large enrollment, therefore a large number of -fourth graders. If a mixed . design were used wherein buildings were selected from the stratum containing the largest systems, and systems were selected from each of-the other three" @default.
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• W348671978 date "1973-02-01" @default.
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• W348671978 title "The Effects of Cluster Sampling in the Norming of an Achievement Test Battery." @default.
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