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How To's: How to Develop Local Norms
Norms provide a useful frame of reference for interpreting test scores. Determining whether a candidate's score is high or low is made possible by comparing his or her score to the scores obtained by other examinees in a relevant group. This comparison can be "built-in" by converting raw scores to percentile scores.
Percentile scores indicate the percentage of other candidates who scored below a given score. For example, a percentile score of 70 is well above average; it indicates the candidate scored better than 70% of candidates in the comparison group. Percentiles range from 1 to 99, with a percentile score of 50 being average.
While PSI provides norms for each of the tests we publish, users often wish to develop their own norms reflecting the characteristics of their local populations. Norms may be developed by following the simple steps outlined below.
- Administer the test to a meaningful sample of persons in the desired comparison group (e.g., current employees in the target job; applicants for the position; or a relevant recruiting source such as college students.) For attitude tests, use applicants rather than current employees. Current employees are not seeking entry into the organization and therefore tend to perform differently than prospective employees. Employees, applicants or others may be used as a norm group for ability tests. Participants in the norming should be instructed to perform their best, as they would on any employment test.
- The norm group should be as large as possible. The minimum number of examinees depends upon the number of percentile points that are to be computed (e.g., percentiles 1-99, deciles, quintiles). As a general rule, the norm sample should contain several hundred examinees, although satisfactory results may be obtained with as few as 100 examinees.
- Tabulate the scores. This may be done via computer by simply generating a frequency distribution of scores, indicating for each score its frequency, cumulative frequency, and cumulative percentage of the total sample. This is further described below and illustrated in Table 1.
- Step 1:
- Tabulate the number (frequency) of people who obtained each possible score on the test, sorted in descending order of test score (see columns 1 and 2 in the Table);
- Step 2:
- Calculate the "running total" (cumulative frequency) of people obtaining each test score (see column 3);
- Step 3:
- Calculate the cumulative percentage of examinees obtaining each score by dividing the cumulative frequency by the total number of examinees, then multiplying by 100 (see column 4);
- Step 4:
- Calculate the percentile value corresponding to each test score by subtracting the cumulative percentage from 100, then rounding to the nearest integer.
For example, in Table 1, the cumulative frequency of examinees scoring 17 or higher is 8; the cumulative percentage of examinees scoring at this level is 5.8%, and the corresponding percentile is 94 (100 - 5.8 = 94.2, which rounds to 94). In other words, for this norm group, a person obtaining a raw score of 17 has performed better than 94% of the examinees.
Table 1
Example of Percentile Computation
| (1) | (2) | (3) | (4) | (5) |
| Score | Frequency | Cumulative Frequency | Cumulative Percent | Percentile |
| 20 | 1 | 1 | 0.7 | 99 |
| 19 | 2 | 3 | 2.2 | 98 |
| 18 | 2 | 5 | 3.6 | 96 |
| 17 | 3 | 8 | 5.8 | 94 |
| 16 | 9 | 17 | 12.3 | 88 |
| 15 | 16 | 33 | 23.9 | 76 |
| 14 | 21 | 54 | 39.1 | 61 |
| 13 | 23 | 77 | 55.8 | 44 |
| 12 | 20 | 97 | 70.3 | 30 |
| 11 | 16 | 113 | 81.9 | 18 |
| 10 | 7 | 120 | 87.0 | 13 |
| 9 | 8 | 128 | 92.8 | 7 |
| 8 | 5 | 133 | 96.4 | 4 |
| 7 | 3 | 136 | 98.6 | 1 |
| 6 | 2 | 138 | 100.0 | — |
