From Psychology Wiki

Community portal · Tasks to do · News · Help

Clinical · Educational · Ind&Org · Other fields · Professional · Transpersonal · World

Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Personality | Philosophy | Research Methods | Social | Statistics

Statistics: Scientific method · Research methods · Experimental design · Undergraduate statistics courses · Statistical tests · Game theory · Decision theory

---

In descriptive statistics, statistical dispersion (also called statistical variability) is quantifiable variation of measurements of differing members of a population within the scale on which they are measured.

[edit] Measures of statistical dispersion

A measure of statistical dispersion is a real number that is zero if all the data are identical, and increases as the data becomes more diverse. An important measure of dispersion is the standard deviation, which is the square root of the variance (which is itself a measure of dispersion).

Other such measures include the range, the interquartile range, and the average absolute deviation, and, in the case of categorical random variables, the discrete entropy. None of these can be negative; their least possible value is zero.

A measure of statistical dispersion is particularly useful if it is location invariant, and linear in scale. So if a random variable X has a dispersion of S_X then a linear transformation Y = aX + b for real a and b should have dispersion S_Y = aS_X. One of the forms in which statistical variability is realized in the empirical sciences is that of differences in repeated measurements of the same quantity.

[edit] Sources of statistical dispersion

In the physical sciences, such variability may result only from random measurement errors: instrument measurements are often not perfectly precise - i.e., reproducible. One may assume that the quantity being measured is unchanging and stable, and that the variation between measurements is due to observational error.

In the biological sciences, this assumption is false: the variation observed might be intrinsic to the phenomenon: distinct members of a population differ greatly. This is also seen in the arena of manufactured products; even there, the meticulous scientist finds idiosyncrasy of sampled items.

The simple model of a stable quantity is preferred when it is tenable. Each phenomenon must be examined to see if it warrants such a simplification.

See also summary statistics.de:Streuung (Statistik)

This page uses content from the English-language version of Wikipedia. The original article was at Statistical_dispersion. The list of authors can be seen in the page history. As with Psychology Wiki, the text of Wikipedia is available under the GNU Free Documentation License.