Norms and the Meaning of Test Scores

psychological testing

1. NORMS The obtained scores on the test themselves convey no meaning regarding the ability or trait being measured. But when these are compared with the norms, a meaningful inference can immediately be drawn. Scores on psychological tests are most commonly interpreted by reference to norm that represent the test performance of the standardization sample. In order to ascertain more precisely the individual’s exact position with reference to the standardized sample, the raw score is converted into some relative measure.

2. NORMS These derived scores serve two purposes. 1.They indicate the individual’s relative standing in the normative sample and facilitate evaluation of performance. 2.They provide comparable measures that permit a direct comparison of the individuals’ performance on different tests.

3. NORMS Statistical Concepts A major objective of statistical method is to organize and summarize quantitative data in order to facilitate their understanding. Frequency Distribution It is prepared by grouping the scores into convenient class intervals and tallying each score in the appropriate interval. When all scores are centered, tallies are counted to find out frequencies in each class interval.

4. NORMS Histogram – the height of the column erected over each class interval corresponds to the number of persons scoring in that interval.

5. NORMS Frequency Polygon – the number of persons in each interval is indicated by a point in the center of the class interval and across from the appropriate frequency. Successive points are then joined by straight lines.

6. NORMS Normal curve Normal curve has important mathematical properties and provides the basis for many kinds of statistical analyses. Curve indicates that large number of cases cluster in the center of the range and that the number drops off gradually in both directions as the extremes are approached. The curve is bilaterally symmetrical, with a single peak in the center. Most distribution of human traits, height, weight, personality characteristics are approximate the normal curve. In general, the larger group, the more closely will the distribution resemble the theoretical normal curve.

7. NORMS Central tendency Variability (range, variance, standard deviation) Further description of a set of test score is given by measures of variability or extent of individual differences around the central tendency. The most obvious and familiar way for reporting variability is in terms of range between highest and lowest score. Range is extremely crude and unstable and insufficient description of test score. A more precise method of measuring variability is based on the difference between each individual’s score and the mean of the group.

8. NORMS The SD provide the basis for expressing an individual’s scores on different tests in terms of norms. The interpretation of the SD is clear cut when applied to a normal curve. Percentages of cases fall between Mean-1 and Mean +1 is 68.26%, Mean-2 and Mean +2 is 95.44%, Mean-3 and Mean +3 is 99.72%.

9. NORMS Developmental Norms One way in which meaning can be attached to test score is to indicate how far along the normal developmental path the individual progress. An 8-year-old child who performs as well as the average 10-year-old on an intelligence test may be described as having mental age of 10. They are very helpful for descriptive purpose but they are not compatible to precise statistical treatment.

10. NORMS Developmental Norms The types of developmental norms are Mental Age Norms, Grade Equivalent Norms and Ordinal Scale Norms.

11. NORMS Mental Age Mental age norm is mainly employed to the age tests like intelligence tests. A measure of an individual’s performance on an intelligence test expressed in terms of years and months. A child’s mental age on the test is the sum of basal age and the additional months of credit earned at higher age levels.

12. NORMS Mental Age Mental age norms also have been employed with tests that are not divided into year levels. The mean raw scores obtained by the children in each year group within the standardization sample constitute the age norms for such test.

13. NORMS Grade Equivalents Scores on educational achievement tests are often interpreted in terms of grad equivalents. We use this norm to describe students’ achievement as equivalent i.e. 7 th grade performance in spelling, 8 th grade in reading, 5 th grade in arithmetic. Grade norm are found by computing the mean raw score obtained by children in each grade.

14. NORMS Grade Equivalents If the average number of problems solve correctly on an arithmetic test by 4 th graders in the standardized sample is 23, then a raw score of 23 corresponds to a grade equivalent of 4. Garde norms generally applicable only common subjects those are taught thorough out grades.

15. NORMS Ordinal scales Ordinal scales are designed to identify stage reached by the child in the development of specific behavior functions. The ordinality of such scales refers to the uniform progression of development through successive stages. Although scores may be reported in terms of approximate age levels, such scores are secondary to qualitative description of the children characteristics behavior. These scales typically provide information about what the child actually able to do in successive stages.

16. NORMS Within-Group Norms Such type of norms helps in comparing the individual’s performance with the most nearly comparable standardized group’s performance. For example – a child’s raw score is compared with that of children of same chronological age or in the same school grade. Within group norms have a uniform and clearly defined quantitative meaning and can be appropriately employed in most types of statistical analyses. Nearly all standardized tests provide some form of with-in group norms.

17. NORMS Percentiles Percentile scores are expressed in terms of the percentage of persons in the standardization sample who fall below a given raw score. A percentile indicates the individual’s relative position in the standardized sample. It can be regarded as ranks in a group. Lower the percentile, the poorer the individual’s standing.

18. NORMS Percentiles The 50 th percentile (P 50 ) correspond to median. Percentiles above 50 represent above-average performance and below 50 signify inferior performance. Adv. – Percentiles are easy to compute and can be readily understood. It is universally applicable. It can be used equally well with adults and children and suitable for any type of test.

19. NORMS Percentiles The chief drawback of percentile scores arises from marked inequality of their units, especially at the extremes of the distribution. It is apparent that percentile show each individual’s relative position in the normative sample but not the amount of differences between scores.

20. NORMS Standard Scores Standard scores are most satisfactory type of derived score from most point of view. It expresses the individual’s distance from the Mean in terms of the Standard Deviation of the distribution. They are obtained by linear or nonlinear transformation of the original raw scores.

21. NORMS Standard Scores When found by linear transformation, they retain the exact numerical relations of the original raw scores. Because they computed by substracting a constant from each raw score and then dividing the result by another constant. All properties are duplicated in the distribution of these standard scores. Standard scores are often termed as z-score.

22. NORMS Standard Scores To compute z-score, we find the differences between raw score and the mean of normative group and then divide the difference by SD of the normative group. Any raw score that is equal to mean is equivalent to a z-score of 0. For occurrence of negative values and decimals, some further linear transformations are usually applied.

23. NORMS Standard Scores For example, scores on the Scholastic Assessment Test (SAT) are standard scores adjusted to mean 500 and SD 100. Thus , standard score -1 on the test would be expressed as 500-100*1=400 . Scores on separate subtests of the Wechsler Intelligence Scales are converted to a distribution of mean 10 and SD 3.

24. Relativity of Norms Interest Comparison Test scores cannot be properly interpreted in abstract; these must be referred to particular tests. An individual’s relative standing in different functions may be grossly misinterpreted through lack of comparability of test norms. There are three principal reasons account for systematic variations among the scores obtained by the same individual on different tests.

25. Relativity of Norms Interest Comparison - Tests may differ in content despite their similar labels - Scale units may not be comparable - Composition of the standardized samples used in establishing norms for different tests may vary.

26. Relativity of Norms The Normative Sample Any norm is restricted to the particular normative population from which it was derived. Psychological norms are in no sense absolute, universal, or permanent. Norms merely represent the test performance of the persons constituting the standardization sample. In the development and application of test norms, considerable attention should be given to the standardization of sample.

27. Relativity of Norms The Normative Sample It is apparent that the sample on which the norms are based should be large enough to provide stable values. Norms with a large sampling error would be of little value in the interpretation of test scores. Requirements of selecting representative sample from the population under consideration are also important. Subtle selective factors that might make the sample unrepresentative should be carefully investigated. It is far better to redefine the population more narrowly than to report norms on an ideal population that is not adequately represent by standardized sample.

28. Relativity of Norms National Anchor Norms One solution for the lack of comparability of norms is to use an anchor test to work out equivalency tables for scores on different tests. Such table are designed to show what score in Test A is equivalent to each score in test B. This can be done by the equipercentile method. In this method, scores are considered equivalent when they have equal percentile in a given group.

29. Relativity of Norms Specific Norms Another approach to the nonequivalence of existing norms is to standardized tests on more narrowly defined populations. In such case, the limits of the normative population should be clearly reported with the norms. For many testing purposes, highly specific norms are desirable. Even when representative norms are available for a broadly defined population, it is often helpful to have separately reported subgroup norms . The subgroup may be formed with respect to age, grade, type of curriculum, sex, geographical region, urban, or rural environment, socioeconomic level, and many other variables.