THE ROLE OF RELIABILITY IN CRITERION-REFERENCED TESTS

In discussion of the properties of criterion-referenced tests, it is often assumed that traditional reliability indices, particularly those based on internal consistency, are not relevant. However, if the measurement errors involved in using an individual's observed score on a criterion-referenced test to estimate his or her universe scores on a domain of items are compared to errors of an a priori procedure that assigns the same universe score (the mean observed test score) to all persons, the test-based procedure is found to improve the accuracy of universe score estimates only if the test reliability is above 0.5. This suggests that criterion-referenced tests with low reliabilities generally will have limited use in estimating universe scores on domains of items.     

AN INTERPRETATION OF LIVINGSTON'S RELIABILITY COEFFICIENT FOR CRITERION-REFERENCED TESTS

An alternative interpretation of Livingston's reliability coefficient is based on the notion of the relation of the size of the reliability coefficient to the range of talent. It is shown that the (generally) larger Livingston coefficient does not imply a smaller standard error of measurement and consequently does not imply a more dependable determination of whether or not a true score falls below (or exceeds) a given criterion value.     

THE ISSUE OF ITEM AND TEST VARIANCE FOR CRITERION-REFERENCED TESTS: A CLARIFICATION

This note contends that item or score variability is an unnecessary characteristic of criterion-referenced tests as they have been traditionally conceived, namely, as measures of well defined classes of examinee behaviors.     

CRITERION-REFERENCED TESTING: COMMENTS ON RELIABILITY1

Currently there is concern among some educators regarding the reliability of criterion-referenced (CR) measures. In this comment, a recent attempt to develop a theory of reliability for CR measures is examined, and some considerations for determining the reliability of CR measures are discussed. Conventional reliability statistics (e.g., coefficient alpha, standard error of measurement) are found appropriate for CR measures satisfying the assumptions of the measurement model underlying classical test theory. For measures with underlying multidimensional traits, conventional reliability statistics may be used at the homogeneous subscale level. When the confidence interval about a student's “below criterion score” includes the criterion, additional evidence about the student should be obtained. Two-stage sequential testing is suggested as one method for acquiring additional evidence.     

THE ISSUE OF ITEM AND TEST VARIANCE FOR CRITERION-REFERENCED TESTS: A REPLY

It is a necessary condition that items and tests have variance and discrimination in the range of interest (population of observations) for which they are calibrated and selected. The basis for selection of the calibration sample determines the kind of scale which will be developed, A random sample from a population of individuals leads to a norm-referenced scale, and a sample representative of abilities of a range of a characteristic leads to a criterion-referenced scale.     

THE ISSUE OF ITEM AND TEST VARIANCE FOR CRITERION-REFERENCED TESTS1

It has been argued that item variance and test variance are not necessary characteristics for criterion-referenced tests, although they are necessary for normreferenced tests. This position is in error because it considers sample statistics as the criteria for evaluating items and tests. Within a particular sample, an item or test may have no variance, but in the population of observations for which the test was designed, calibrated, and evaluated, both items and tests must have variance.     

TOWARD AN INTEGRATION OF THEORY AND METHOD FOR CRITERION-REFERENCED TESTS1,2

In this paper, an attempt has been made to synthesize some of the current thinking in the area of criterion-referenced testing as well as to provide the beginning of an integration of theory and method for such testing. Since criterion-referenced testing is viewed from a decision-theoretic point of view, approaches to reliability and validity estimation consistent with this philosophy are suggested. Also, to improve the decision-making accuracy of criterion-referenced tests, a Bayesian procedure for estimating true mastery scores has been proposed. This Bayesian procedure uses information about other members of a student's group (collateral information), but the resulting estimation is still criterion referenced rather than norm referenced in that the student is compared to a standard rather than to other students. In theory, the Bayesian procedure increases the “effective length” of the test by improving the reliability, the validity, and more importantly, the decision-making accuracy of the criterion-referenced test scores.     

EFFECTS OF DIFFERENT SAMPLES ON ITEM AND TEST CHARACTERISTICS OF CRITERION-REFERENCED TESTS

Although many have rejected classical test construction and analysis procedures for criterion-referenced tests, the present study was concerned with the possibility that classical procedures are both applicable and appropriate when samples of both mastery and nonmastery examinees are employed. A rationale for using these samples was presented, and empirical evidence was gathered which supported the practice of combining samples to increase the variance of test scores and thereby permit the proper estimate of reliability and item validities.     

ESTIMATING THE RELIABILITY OF MULTIPLE TRUE-FALSE TESTS

This study was designed to examine the level of dependence within multiple true-false (MTF) test item clusters by computing sets of item intercorrelations with data from a test composed of both MTF and multiple choice (MC) items. It was posited that internal analysis reliability estimates for MTF tests would be spurious due to elevated MTF within-cluster intercorrelations. Results showed that, on the average, MTF within-cluster dependence was no greater than that found between MTF items from different clusters, between MC items, or between MC and MTF items. But item for item, there was greater dependence between items within the same cluster than between items of different clusters.