# Variance

© Paul Cooijmans

## Explanation

The variance is the mean of the squared deviations. A deviation is the difference between a value (score) and the mean of the sample. The variance is the square of the standard deviation. The variance of a variable may be visualized as a square, the length of any of its sides representing the standard deviation.

Mental test score variance may be analysed in different ways, resulting in different ways of splitting up the variance:

- In reliability analysis, the variance is effectively split up into a true score component and an error component;
- In factor analysis, the variance is effectively split up into components accounted for by the general factor (= that which is common to all tests), by one or more group factors (common to some but not all tests), by specificity (unique to one particular test), and error;
- In heredity analysis, the variance is split up into heritability, non-genetic effects, and error.

When estimating the total population variance from a sample taken from that population, one computes the variance by dividing the sum of the squared deviations by *n* - 1 instead of simply by *n* (*n* is the number of values in the sample). The reason for that one may find explained in some books on statistics.