Standard value scale
For the calibration and normalization of psychological tests , various standard scales have been developed, which are essentially derived from the z-scale (mean = 0, standard deviation = 1). The selected combination of mean and standard deviation as well as the defined range of values determine the scale. For example, the IQ norm has a mean value of 100 and a standard deviation of 15. A norm value scale based on the z-standardization is an interval scale . Some scales as the Stanine scale or T-Scale based in contrast to percentile ranks .
The following standards are common (high values usually correspond to high characteristics, better performance for performance characteristics):
| Standard scale | Mean value ( M ) | Standard dev. ( s ) | limited range of values |
|---|---|---|---|
| z | 0 | 1 | - |
| IQ | 100 | 15th | - |
| SW (standard values), also Z | 100 | 10 | - |
| T | 50 | 10 | - |
| C (C-values or Centiles) | 5 | 2 | - |
| Deci-C (C with more differentiation) | 50 | 20th | - |
| Stanine (Standard Nine) | 5 | 2 and 1.96, respectively | 1-9 |
| STEN (Standard Ten) | 5.5 | 2 | 1-10 |
| N standard school grades (1–5) according to Lienert (1961) | 3 | -1 | 5–1 in the original |
| L (after good year) | 10 | 5 | - |
| WP (value points) | 10 | 3 | - |
| Performance scale of the PISA studies | 500 | 100 | |
| PR (percentile rank) | 50 (median) | 0-100 |
It does not matter which standard scale is ultimately used. However, it is important that different values are available in the same standard for comparison. For intelligence tests, for example, the IQ standard has largely prevailed. However, some tests also use other standards. B. the Adaptive Intelligence Diagnostic (AID) also back to T values.
The values from a normalization can be converted into the values of another normalization at any time without great effort ( X - the value, M - mean value of the distribution, s - scatter of the distribution):
If the characteristic is normally distributed , as in the case of the standard scales , the calculation of z values is reduced to the formula:
In the case of abnormal distributions (especially for percentile ranks ), on the other hand, a simple z-standardization using this formula leads to distortions. Instead, a normal rank transformation (surface transformation) can be used. The normalization of non-normally distributed value distributions can lead to problems (sham differentiation or leveling of differences).
literature
- Manfred Amelang, Werner Zielinski: Psychological diagnostics and intervention. Springer, Berlin 1994, ISBN 3-540-58084-0 .
- Walter Gutjahr: The measurement of psychological properties. Berlin: Deutscher Verlag der Wissenschaften 1971 (1.A.), 1972 (2.A.), 1974 (3.A.) and Cologne: Kiepenheuer & Witsch 1977.
Web links
- Standard value calculator for converting various standard value scales
Remarks
- ↑ is the abbreviation for English : Standard Nine (standard nine). It corresponds to C, with Stanine no values greater than 9 or less than 1 are possible - greater / smaller values are set to 9 or 1 in this standard.
- ↑ The literature contains both 2 (mainly German-language textbooks) and 1.96 as the standard deviation to be used (see link) 1.96 refers to the error probability of 5% of the z-distribution, i.e. H. the scatter around the mean value m ± 1.96 · z is identical to the confidence interval
- ↑ Standard school grades as a transformation from the z-scale should not be confused with “real” school grades, which are mostly not normally distributed and tend to have only an ordinal scale level; for standard school grades see z. B. here
- ↑ Low counts for z = good performance -> N = 3 - z