Standard Score

Chapter 4 Understanding Assessment Scores

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Meaningful Assessment Scores 

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Scores are often difficult to interpret without some method for creating a baseline. Criterion and norm-referenced interpretations can be used to make sense of individual scores.

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Criterion-Referenced Interpretation 

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Criterion-Referenced interpretation uses some standard of performance to interpret an examinee’s test results. Criterion-Referenced tests are interpreted in absolute terms and often have a cutoff score representing minimum competency. Criterion-Referenced tests are often used in education and professional settings to determine competency.

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Norm-Referenced Interpretation 

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Norm-Referenced tests compare individual scores to the test scores of group of individuals. The group scores to which each individual is compared are referred to as norms.

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Norm group – the group of individuals whose scores were used to norm a test. Norm groups should be representative and current, and have adequate sample size. 

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Representativeness – the degree to which the norm group represents the population for which the test was written. Current – use instruments with the most up-to-date norm groups. Instruments should be revised with new norm groups about every 10 years. Sample size – The larger a sample size the more representative the norm group will be.

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Types of Norm-Referenced Scores  

Percentile Ranks Standard Scores   

Z Scores T-Scores Deviation IQ: “Standard Scores”

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Percentiles 

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Express the examinee’s relative position to a norm-referenced test. Percentile ranks range from 0 to 100 and indicate the percentage of scores that were lower than the examinee’s. Percentiles are not equal-interval measurements.

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Differences between Percentiles and Percentages Percentiles 

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Scores that reflect the rank or position of an individual’s test performance on a continuum from 0 to 99 in comparison to others who took the test. Symbols for percentile rank: PR or %’ile Example: Shari scored in the 80th percentile on the test, meaning that Shari scored better than 80 percent of the other individuals who took the test.

Percentages 

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A form of raw score that reflects the number of correct responses obtained out of the total possible number of correct responses on a test. Symbols for percentage score: % Example: Shari scored 70 percent on her test. This means she answered 70% of the test items correctly.

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Standard Scores 

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Standard Score refers to scores that have been converted to an interpretable scale that has a set mean and standard deviation. Standard scores allow individual test scores to be interpreted in terms of the normal curve.

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Z Scores 

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Z-Scores convert test scores into a standard deviation value, ranging from -3.0 to +3.0. Z-Scores between -1 and 1 fall within the “average” range.

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T Scores 

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T scores use a mean of 50 and a standard deviation of 10. T scores between 40 and 60 fall within the “average” range.

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Other Standard Scores 

Deviation IQs – used in intelligence testing. Mean of 100 and a standard deviation of 15.   

Can be used in other instruments (not just IQ). Average is between 85 and 115. When you go out one more SD (15 more points), you get to 70 [retarded] and 130 [gifted]

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Standard Scores and T Scores with Normal Curve

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Grade and Age Equivalents 

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Grade Equivalents – norm-referenced scoring that represents academic achievement in each grade. Results are easily misunderstood by parents, students, and teachers. Age Equivalents – represent the average age in years and months in which a given total raw score is typical.

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Grade Equivalents in Normative Tests Are Not Equal to CBM Grades 

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Average children produce grade equivalents above and below grade level. Ex: KTEA-II Reading  16 year old teenager  SS = 90; GE = 8.1  SS = 110; GE = 12.0 © 2010 Pearson Education, Inc. All rights reserved.

Criterion and Norm Referenced Interpretation? 

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Generally, mixing criterion and normreferenced interpretations on the same test is not recommended. Some constructs work better with one form of interpretation than the other.

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