Behavior Research Methods, Instruments, & Computers 1996,28 (2),209-213 A two-score composite program for combining standard scores LARRY D. EVANS University ofArkansasfor Medical Sciences, Little Rock, Arkansas It is often desirable for mental health practitioners to combine standard scores from different tests, raters, or times into a single composite standard score. Most often the result is a more reliable and ac­ curate standard score. This paper describes a computer program that uses two standard scores, score reliability and correlation with a third variable, to yield a composite standard score, reliability and cor­ relation. Trends, limitations, optimum benefits, and examples are discussed. References are provided for calculating composites based on more than two scores. Composite scores are routinely used by test publishers Wang and Stanley (1970) reviewed various methods to to derive an overall scale score from two or more subtests. derive weights, but basic techniques may be based on re­ The Full Scale IQ (FSIQ) of the Wechsler Intelligence liability coefficients, test length, optimal correlation with Scale for Children-Third Edition (Wechsler, 1991), the a criterion, or subjective judgments ofthe importance of Basic Reading Skills Cluster of the Woodcock-Johnson each test's contribution to a composite. Psychoeducational Battery-Revised (Woodcock & John­ There are specific instances in which composite scores son, 1989), and the Adaptive Behavior Composite ofthe may be highly desirable. First, practitioners may give a VinelandAdaptive Behavior Scales (Sparrow,Balla, & Cic­ second test to confirm an initial test's results, then need chetti, 1984) are common examples ofcomposite scores. to combine the scores to reflect the best indication ofover­ While often used by test publishers, composite scores are all performance in a particular domain. Indeed, federal less frequently derived by mental health practitioners. and most state special education guidelines discourage This is unfortunate, as an understanding of composite reliance on a single score or procedure during decision scores enhances the interpretation of composite scores, making. The State ofArkansas, for example, requires that such as the FSIQ, and provides a tool that may be re­ after an initial achievement test has been administered to quired to synthesize psychological results. a student suspected ofhaving a learning disability, a sec­ Combining two or more same-domain scores into a sin­ ond achievement test must be given to further assess the gle composite score offers several advantages over inter­ area ofsuspected disability (Arkansas Department ofEd­ pretation ofindividual scores. First, one conceptualization ucation, 1993). Second, after assessing a subject, a prac­ of a composite score is a score from a single test com­ titioner may wish to obtain results ofa recent evaluation posed ofthe items ofseveral individual tests (Thorndike, in some other setting, either incidentally or as a blind sec­ Cunningham, Thorndike, & Hagen, 1991). This "longer" ond opinion, and to combine same-domain scores to obtain test generally results in a more reliable score. Second, com­ a more accurate picture ofthe subject's overall abilities. posite scores avoid loss of information. For example, Third, practitioners may use screening or abbreviated test when two tests measure the same domain and yield dif­ batteries, then later provide more comprehensive evalu­ ferent scores, practitioners often try to determine which ation for failed screenings. It is often desirable to then score is more accurate, often by comparing scores with combine the results ofthe screening and comprehensive an overall profile, selecting the more reliable or compre­ scores (generally weighting the comprehensive score hensive score, or relating subject behavior, during testing, more heavily) so as not to lose the time and expense re­ to each score. Regardless ofwhat single score is thought quired for the screening. Fourth, comprehensive behav­ to be the more accurate, the net effect of using only one ioral assessment may include subject ratings from sev­ test is loss ofinformation. Because the composite score eral individuals, times, or settings. A composite score is based on the scores ofboth tests, there is no sacrificing may then be needed to summarize the ratings and in­ oftest data. Third, composite scores offer great flexibility crease overall reliability. in test result interpretation. Weights can be assigned to scores on the basis ofthe purpose ofthe composite score. Statement ofthe Problem Most practitioners would benefit from being able to combine scores into a composite score. The resulting com­ A copy ofthe compiled program is available from the author upon re­ posite score would often provide a more reliable and valid ceipt ofa self-addressed, postage-paid mailer and one DOS- formatted, high-density floppy disk. Correspondence should be addressed to Larry summary score. Better understanding ofcomposite scores Evans, Dennis Developmental Center, 1612 Maryland Street, Little would also aid in interpreting the composite scores pro­ Rock, AR 72202 (e-mail: [email protected]). vided by tests. Unfortunately, the equations needed to 209 Copyright 1996 Psychonomic Society, Inc. 210 EVANS calculate composite scores are not readily available to where SDx is the composite's standard deviation, SDx 1and most practitioners and are not reliably performed by SDx are thCe standard scores' standard deviations, and r12 hand calculations. is the Pearson product-moment correlation coefficient for the standard scores. If the obtained standard scores Response to the Problem are initially expressed as z scores and equal weights of This paper describes a computer program designed to 1.00 are assigned, then Equation 3 simplifies to calculate a standard score composite based upon two standard scores. A two-score composite may be the most (4) common composite and, as the simplest composite, pro­ Equations 3 and 4 indicate that, for obtained scores with vides a basis for assessing the relative benefits ofmultiple­ the same standard deviation, as the correlation increases score composites. toward 1.00, the composite standard deviation approaches COMPOSITE SCORE PROGRAM twice the obtained scores' standard deviation. The final step is to convert the composite score to a standard score with the same mean and standard devia­ A program was written using Version 1.0 ofMicrosoft tion as one or both ofthe obtained scores. This involves Visual Basic for MS-DOS. After an initial start-up screen first converting the composite score to a z score, then to ofinstructions, the program displays a single screen with a standard score in the same metric as one or both ofthe edit fields that allow the user to enter data for two test obtained scores. Using the above equations, the z score scores (standard score, reliability, correlation with a crite­ for the composite score is rion, and score weight) and the correlation between the two scores. After a push button is clicked, the calculations Xc - M, z = c (5) are performed and the composite standard score, its relia­ XC SD bility, and its correlation with a criterion are shown at the XC bottom ofthe screen. A single, pull-down menu allows the The z score for the composite (z, ) can be multiplied by results to be printed, entered data to be erased, or exiting the the standard deviation ofan obtained score and the prod­ program. uct then be added to the same obtained score's mean in The program is intentionally straightforward, with an order to produce a composite standard score that is in­ emphasis on application. A key to successfully using the terpretable relative to the obtained scores. program is an understanding of the equations and out­ One synthesis of the above equations is that, as the put. Therefore, the following equations and examples, correlation rl 2 increases toward 1.00, the composite stan­ which are intended to help the user understand and uti­ dard score approaches the (weighted) average of the lize the program results, are provided. obtained scores. As the correlation decreases, the com­ posite standard score increasingly deviates from this av­ Calculating the Composite Standard Score erage, with the direction of deviation being away from The first calculation involves determining a compos­ the (weighted) mean. ite score: (1) Calculating the Composite's Reliability The composite standard score, as with any standard where Xc is the composite score, bl and b2 are weights, score, should not be interpreted without taking the error and X I and x2 are the obtained standard scores. If equal ofmeasurement into account (Salvia & Ysseldyke, 1991). weights of1.00 are assigned to each obtained score, then The composite's reliability is therefore important for de­ Equation 1 simplifies to the sum ofthe obtained scores. termining the standard error ofmeasurement and the es­ The composite score of Equation 1 is not a standard timated true composite score. The composite's reliability score in the same metric as the obtained scores, and re­ may also be important to determine if the score differs quires that the composite's mean and standard deviation significantly from another standard score (Payne & Jones, be calculated before it can be interpreted. The equation 1957) or ifthe composite score is to be entered into a soft­ for the composite score's mean is ware analysis program such as regression software for learning disabilities (e.g., Evans, 1994). The composite's