Norms and the Meaning Test Score PDF

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Norms and the Meaning Test Score The Nature of Norms Norming is basically a procedure that facilitates the test user’s interpretation of test scores. - In the absence of additional interpretive data, a raw score on any psychological test is meaningless. -Scores on psychological tests are most commonly interpreted by reference to norms that represent the test performance of the standardization sample. -The norms are thus empirically established by determining what persons in a representative group actually do on the test. -Any individual’s raw score is then referred to the distribution of scores obtained by the standardization sample, to discover where he or she falls in that distribution.

Purposes of norms 1. They indicate the individual’s relative standing in the normative sample, and thus permit an evaluation of his performance in reference to other persons. 2. They provide comparable measures that permit a direct comparison of that individual’s performance in different tests.

The Nature of Norms Derived scores (norms) are expressed in one of two major ways: 1. Developmental level attained 2. Relative position within a specified group

The Nature of Norms Normative sample –that group of people whose performance on a particular test is analyzed for reference in evaluating the performance of individual test takers. ●Members of the normative sample will all be typical with respect to some characteristic(s) of the people for whom the particular test was designed. ●A test administration to this representative sample of test takers yields a distribution (or distributions) of scores. These data constitute the norms for the test.

Sampling to Develop Norms -The process of administering a test to a representative sample of test takers for the purpose of establishing norms is referred to as standardization or test standardization.

Sampling Methods -In the process of developing a test, a test developer has targeted some defined group as the population for which the test was designed. For practical reasons, the test developer obtains a distribution of test responses by administering the test simply to a sample of the population.

1. Stratified sampling – considers certain characteristics that must be proportionately represented in the sample (helps prevent sampling bias and ultimately aids in the interpretation of the findings).

2. Stratified random sampling –when members from the identified strata are obtained randomly

3. Purposive sampling –if we arbitrarily select some sample because we believe it to be representative of the population

4. Incidental / Convenience sampling – often used for practical reasons, utilizes the most available individuals. Generalization of findings from incidental samples must be made with caution.

Developing norms for a standardized test ◆ The test developer administers the test according to the standard set of instructions that will be used in the test, including the recommended setting (for the test).

◆ The test developer summarizes the data using descriptive statistics, including measures of central tendency and variability. Developing norms for a standardized test ●The test developer also provides a precise description of the standardization sample itself.

● In order to best assist future test users, test developers are encouraged to “describe the population(s) represented by any norms or comparison group(s), the dates the data were gathered, and the process used to select the sample of test takers” (Code of Fair Testing Practices, 1988, p. 3).

Types of Norms 1. Percentile norms -An expression of the percentage of people whose score on a test or measure falls on a particular raw score. -A ranking that conveys information about the relative position of a score within a distribution of scores. -A converted score that refers to a percentage of test takers -Percentage correct: refers to a distribution of test scores –the number of items that were answered correctly divided by the total number of items and multiplied by 100.

■Disadvantage: real differences between raw scores are minimized near the ends of the distribution, and exaggerated in the middle of the distribution. ◆ Differences between raw scores that cluster in the middle may be too small, yet even the smallest differences will appear as differences in percentiles. ◆At the ends of the distribution, differences in raw scores may be great, but these are reflected as relatively small differences in percentiles. ◆ Percentiles show each individual’s relative position in the normative sample, but not the amount of difference between scores.

2. Standard Scores - Express the individual’s distance from the mean in terms of the standard deviation of the distribution. ●Computing z-scores ● Conversion of standard scores

3. Age norms -Also known as age-equivalent norms ▪Indicate the average performance of different samples of test-takers who were at various ages at the time the test was administered ▪ In practice, a child of any chronological age whose performance on a valid test of intellectual ability indicated that he or she had intellectual ability similar to that of an average child of some other age was said to have the “mental age” of the norm group in which his or her test score fell. -The use of “mental age” can be problematic. A six-year old who performs intellectually like a 12-year old, may be said to have that mental age. But the six-year old is likely not to be similar at all to the average 12-year old socially, psychologically, and in many other key respects.

●IQ standard deviations are not constant with age. At one age, an IQ of 116 might be indicative of performance at 1 standard deviation above the mean, whereas at another age, an IQ of 121 might be indicative of performance at 1 standard deviation above the mean.

● Intellectual development progresses more rapidly at the earlier ages, and gradually decreases as the individual matures.

4. Grade norms - Also known as “grade equivalents”

●Designed to indicate the average test performance of test-takers in a given school grade ● They are found by administering the test to representative samples of children over a range of consecutive grade levels. Then, the mean or median score for children at each grade is calculated. ♢ For example, if the average number of problems solved correctly by fourth graders in the representative sample is 23, then a raw score of 23 corresponds to a grade equivalent of 4.

♢ They have widespread application, especially to children of elementary school age.

♢ Issue: Does a student in twelfth grade who scores “6” on a grade-normed spelling test have the same spelling abilities as the average sixth grader?

♢The answer is . . . NO.

♢What this finding means is that the student and a hypothetical, average sixth grader answered the same fraction of items correctly on that test.

♢ Grade norms DO NOT provide information as to the content of type of items that a student could or could not answer correctly. ♢ The primary use of grade norms is as a convenient, readily understandable gauge of how one student’s performance compares with that of fellow students in the same grade.

5. Other types of norms: a. National norms –derived from a normative sample that was nationally representative of the population at the time the norming study was conducted. Variables of interest include age, gender, ethnic background, socioeconomic strata, geographical location, etc.

b. National anchor norms –an equivalency table for scores on two nationally standardized tests designed to measure the same thing. They provide some stability to test scores by anchoring (comparing) them to other test scores.

c. Subgroup norms –norms for any defined group within a larger group.

d. Local norms –normative information about some limited population, frequently of specific interest to a test user.

■ Relativity of Norms

~ Intertest Comparisons

~ Why test scores can be misinterpreted

The Normative Sample ◆ Any norm, however expressed, is restricted to the particular normative population from which it was derived.

◆ Psychological test norms are not absolute, universal, or permanent. They merely represent the test performance of the persons constituting the standardization sample. The Normative Sample -In the development and application of test norms, considerable attention should be given to the standardization sample.

◆ It should be large enough to provide stable values;

◆ Similarly chosen people of the same population should NOT yield norms that diverge appreciably from those obtained;

◆ Should be representative of the population under consideration

● Be careful of institutional samples (schools,prisons, mental patients)

◆ Define the specific population to which norms can be generalized....