Error in the Estimation of Intellectual Ability in the Low Range Using the Wisc-iv and Wais- Iii By

The error, both chance and systematic, in the measure of true intellectual ability in the low IQ range is quantified and combined to find an overall confidence interval. The chance error was due to: lack of stability, scorer error and lack of internal consistency. The systematic error was due to: the Flynn effect, a floor effect and that error apparent from the lack of agreement between the WISC-IV and WAIS-III. For low Full Scale IQs the WAIS-III can only be considered accurate to within 18 points above the measured IQ and 28 points below, and the WISC-IV to 16 points below the measured IQ and 25 points above it. The implications for the diagnosis of intellectual disability are considered. Key word: WISC-IV, WAIS-III, Low IQ, Test error. Introduction A diagnosis of intellectual disability (ID) or as it was previously known, mental retardation (MR), can have a major effect on people’s lives. On the positive side it can provide services, finance, help in schools, and even prevent the recipient from being executed (Flynn 2006; Flynn 2007; Schalock et al 2007). On the negative side it may be regarded as a stigmatizing label that an individual may seek to avoid (Baroff 1999). Currently, a necessary though not sufficient part of the diagnosis of ID is having an IQ below a specified figure, usually 70, or two standard deviations (SDs) below the norm (American Association on Mental Retardation 2002; American Psychiatric Association 2000; Department of Health 2001; British Psychological Society 2001). This specification of a specific IQ figure implies that an individual has a “true intellectual ability” that can be measured and quantified in terms of an IQ score. True intellectual ability can be defined as the IQ score that an individual would obtain if he/she was assessed using a perfectly standardized IQ test with no measurement error. It is acknowledged that current tests do not measure IQ to a level of accuracy of one point: there is a margin of error, usually considered to be about five points either side of the obtained IQ, which should be taken into account when making a diagnosis of ID (The American Association on Mental Retardation 2002). However, Whitaker (2003, 2008a) has suggested that the margin of error in the low IQ range is much greater than five points and is indeed so large that it is unreasonable to have a specific IQ figure as part of the diagnostic criteria of ID. The purpose of this paper is to quantify the various sources of error in the measurement of low intellectual ability in order to derive a margin of error of the assessment of true intellectual ability using current IQ tests. Most of the examples given will relate specifically to the measurement of Full Scale IQ (FS IQ) on the Wechsler assessments, the Wechsler Adult Intelligence Scale third edition (WAIS-III Wechsler 1997) and the Wechsler Intelligence Scale for Children fourth edition (WISC-IV Wechsler 2003). This is because the Wechsler assessments are the most widely used assessments of low intellectual ability and the bulk of research has been done using these assessments. However, the same arguments apply equally well to other assessments. Errors in the measurement of IQ Error in the measurement of IQ is due to non-intellectual variables that affect an IQ score and can be considered to be of two broad types: chance errors and systematic errors. Chance Error in the Measurement of IQ Chance errors are usually due to a large number of relatively small factors that may occur during an assessment. According to Anastasi and Urbina (1997) three broad types can be detected and quantified. Firstly, there is error derived from a lack of internal consistency. This is the degree to which items on a subtest are measuring the same psychological factor. The degree of error due to a lack of internal consistency is derived by subtracting the split-half reliability coefficient from one. A second type of chance error is temporal error due to variation in the conditions under which assessments are administered. For example, factors such as the level of distraction, how the client felt on the day and the way the assessment was administered will all vary to some extent between assessments and will all affect the score. An estimate of temporal error is given by a test re-test reliability coefficient, or stability coefficient, obtained by correlating the scores of the same individuals when given the same assessment on two occasions. The degree of error is then obtained by subtracting this test re-test reliability coefficient from one. Thirdly, there is scorer error, which is due to inconsistency in scoring the assessment. An estimate of this is obtained by correlating the results of two independent scorers scoring the same assessments and subtracting this correlation coefficient from one. According to Anastasi and Urbina (1997), as well as other theorists in psychometrics such as Crombach, Gleser, Nanda and Rajaratnam (1972) and Shavelson and Webb (1991), errors due to a lack of internal consistency, temporal changes and scorer error are mutually exclusive. Therefore, in order to get an estimate of the total error in the assessment of true intellectual ability all three errors should be summed. Standard Error of Measurement and 95% confidence interval An estimate of error in an IQ assessment is usually given by the standard error of measurement (SEM), and the 95% confidence interval. SEM is the theoretical SD of test scores that would be expected to occur if the tests were repeatedly given to the same client or if different combinations of possible test items were used. Anastasi and Urbina (1997) give the following formula to calculate SEM: