What are norms in psychological scales?
Psychological scales use norms, and without norms, evaluations based on simple absolute or relative scores are usually of questionable validity.
A norm is a standardized measure for comparison, calculated from a standardized sample of test results, i.e., the mean and standard deviation of a standardized sample. It is the standard of reference score used in talent assessment to compare and interpret test results. Test scores must be compared to some standard in order to show what it represents.
A norm is a standardized measure for comparison, calculated from the test results of a standardized sample, which is the reference score standard used for comparison and interpretation of test results in psychometric testing.
According to the size and source of the sample, there are usually national norms, regional norms and special norms, and according to the specific application criteria and score characteristics, there are also percentile norms, standardized score norms and so on.
For the test developer, the choice of norms is based primarily on knowledge of the general population that the test will be administered to, and the norm group must be representative of that population.
An example. To study the values of college students, the general population is college students, and the sample selection must be based on the nature of the population, such as: gender, age, major, family background, etc., to find a representative sample to represent the target population, to meet all the conditions before it can be called the normative model, to be truly representative. This will have a norm score, usually is the administration of the norm sample out of the original scores of the test subjects according to certain rules to convert out of the derived scores.
Norm (norm) usually have the following kinds:
(1) mean: a common form of norm. The results measured by a subject (crude score, or raw score) and standardized samples when compared to the average, in order to determine the level of its performance.
(2) Standardized scores: the mean is still limited in what it can tell us. Looking only at the mean and not paying attention to the dispersion, the information obtained about the subjects is very limited. If the standardized score is used as a norm, it can provide more information. Standard scores indicate where a subject’s test scores fall on the distribution of scores in a standardized sample. Standard Score (Z) = the difference between the subject’s score (X) and the sample mean (x) (i.e., X-x) divided by the standard deviation of the sample scores (SD). This is simplified to Z = (X-x)/SD. In this way, not only is the subject’s performance compared to the sample at the top or bottom of the scale, but also by how many standard deviations.
Many scales use this norm or a norm derived from it. For example, in Wechsler’s scale, the departure IQ = 100 + 15(X-x )/SD is one such model. The difference between the deviant IQ and the standardized scores is that the standardized scores have a mean of 0, while the deviant IQ has a mean of 100, i.e., Z=X is 0 in the standardized scores, but 100 in the deviant IQ; and secondly, the SD of the standardized scores varies according to the sample, whereas in the deviant IQ, the standard deviation is made to be 15 (16 in the case of the Stanford Binet).
(3) T-score: The T-score norm is another common norm derived from the standard score. For example, the MMPI uses this norm. The difference between it and the deviation IQ is that the mean value and standard deviation are different, and the formula for calculating the T-score is:
T=50+10(X-x)/SD
(4) Derived from the standardized score of the other forms of norms; standardized 20 and standardized 10 is in this category, are to change the mean and standard deviation of the values obtained. The formula is as follows;
Standard 20=10+3(X-x)/SD
Standard 10 = 5 + 1.5(X-x)/SD
In the Wechsler scale, there are crude scores, scale scores and deviation IQ measures. The scale score is calculated by the Standardized 20 method.
(5) Percentile rank (PR): This is another commonly used norm, which has been used earlier and is more versatile than the standardized scores. Its advantage is that it can be understood without the essentials of statistics. It is customary to rank poor scores at the bottom and good scores at the top, and to calculate the percentile range of each of the sample scores. The subjects’ scores are compared to the norm. For example, a percentile equivalent of 50 (P50) means that the subject’s score is equivalent to the 50th percentile of the standardized sample. That is, 50 percent of the sample had scores below his (the best of which were at most the same as his) and the other 50 percent had scores better than his. For example, at P25, it means that 25% of the sample is below him (or at best as good as him) and another 75% are better than him. And so on.
(6) cut off score (cut off score): in the screening test is often used in this norm. For example, in education, when using the 100-point system, 60 points to pass, this is the cut-off score. The cut-off score for entrance examinations varies according to the performance of the candidates and the number of admissions. In clinical neuropsychological testing, a cut-off score is established by comparing the test scores of normal people with those of patients with encephalopathy, and this score is used to classify the presence or absence of brain damage. If a test is sensitive to detecting a certain type of brain damage, the cutoff score is valid. Very few, if any, patients would be classified as false negatives, and very few or no normal people would be classified as false positives. If there is no sensitivity, the chances of either false positives or false negatives are increased.
(7) Ratio (or quotient): This type of norm is also more commonly used. For example, the ratio IQ was used before the deviation IQ method. The method of calculation: IQ = MA/CA x 100, which is to set MA (mental age) and CA (actual age) equal to 100 in order to make the IQ into a whole number. Impairment index = number of tests categorized as impaired / number of tests measured.
The above are generalized forms of norms, but there are also norms of various natures. For example, age norms (established by age groups), gender, region and various disease diagnosis norms. In terms of comparability, the more specific the norm is, the more valid it is. In terms of adaptability, norms are easier to use. For example, in the case of intelligence tests, the national norm is used in a wide range of areas, while the regional norm is used in a limited area. However, the latter is more accurate than the former. Although some norms are regional, they can be used in similar areas because the region is representative.
