2.C.1
Scoring and interpreting standardized tests
ASPPB's competency statement 2.C.1: Administer, score, and interpret a range of frequently used standardized assessment instruments based on psychometric properties, available normed data and criterion-referenced standards, and address any limitations in the selection of instruments
Standardized scores place a person's performance against a norm group or against a fixed criterion. Interpreting them well means converting accurately between score metrics, reporting the error around each score, choosing norms that fit the question, and recognizing limits such as outdated norms, floor and ceiling effects, and the low scores that turn up by chance across a large battery.
Key ideas
- Norm-referenced versus criterion-referenced
- Norm-referenced scores compare a person with a reference group, such as others of the same age. Criterion-referenced scores compare performance with a fixed standard of mastery, whatever other examinees did.
- Score metrics
- Standard scores (mean 100, SD 15), T scores (mean 50, SD 10), scaled scores (mean 10, SD 3) and z scores are linear transformations of one another. Percentile ranks are not equal-interval: near the mean a few points shift the percentile a lot, at the extremes far less.
- Error bands and change
- Scores are reported with confidence intervals built from the standard error of measurement. Change between testings is judged with a reliable change index, which asks whether a difference is larger than measurement error alone would produce.
- Norms that age
- A meta-analysis of 285 studies found IQ scores rising about 2.3 points per decade, and about 3 points for modern Wechsler and Stanford-Binet tests, so older norms tend to inflate scores. Floor and ceiling effects distort scores at the extremes of a test's range.
- Low scores are common across a battery
- In batteries of 20 or more measures, most healthy adults in normative samples have at least one score more than one standard deviation below the mean, so a few isolated low scores are not, alone, evidence of impairment.
Worked example
Ms. Brandvold, 34, obtains a standard score of 120 on a reading comprehension test with a mean of 100, a standard deviation of 15 and a reliability of .96. She asks what the score means and how exact it is.
- z = (120 minus 100) divided by 15 = 1.33, so her score is one and a third standard deviations above the mean.
- Under the normal curve, a z of 1.33 falls at about the 91st percentile; the same standing is a T score of about 63 and a scaled score of 14.
- The standard error of measurement is 15 times the square root of (1 minus .96), which is 15 times .2, or 3 points. A 95 percent interval is about 1.96 times 3, roughly 6 points either side: about 114 to 126.
- She is told that she scored higher than about 9 in 10 people in the norm group, and that her true score very likely lies between 114 and 126.
Convert carefully between metrics, and always state the error band around a single score.
Check yourself
Two pairs of examinees each differ by 10 percentile points: one pair is at the 50th and 60th percentiles, the other at the 89th and 99th. On a standard score scale (mean 100, SD 15), which statement is true?
Sources
- Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014), Chapter 2, Reliability/Precision and Errors of Measurement; Chapter 5, Scores, Scales, Norms, Score Linking, and Cut Scores
- Jacobson and Truax (1991), Clinical significance: A statistical approach to defining meaningful change in psychotherapy research, Journal of Consulting and Clinical Psychology (PMID 2002127), Journal of Consulting and Clinical Psychology 59, 12-19 (reliable change index)
- Trahan, Stuebing, Fletcher and Hiscock (2014), The Flynn effect: A meta-analysis, Psychological Bulletin (PMID 24979188), Psychological Bulletin 140, 1332-1360 (2.31 points per decade overall; 2.93 for modern Stanford-Binet and Wechsler tests)
- Binder, Iverson and Brooks (2009), To err is human: 'Abnormal' neuropsychological scores and variability are common in healthy adults, Archives of Clinical Neuropsychology (PMID 19395355), Archives of Clinical Neuropsychology 24, 31-46 (batteries of at least 20 measures)