Variance

Explanation

The variance is the mean of the squared deviations, and serves as a measure of spread. A deviation is the difference between a value (score) and the mean of the sample. The reason to square the deviations is to get rid of negative values (deviations may be negative). Since the variance is expressed in squared units, one takes its square root to arrive at the standard deviation, a unit of spread to be understood in the original units.

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

1. In reliability analysis, the variance is effectively split up into a true score component and an error component;
2. 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), and by specificity (unique to one particular test);
3. In heredity analysis, the variance is split up into heritability, non-genetic effects, and error.

The variance of a psychometric test is also equal to the sum of the individual item variances of the test, although that is not how it is typically computed.

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 exact reason for that one may find explained in some books on statistics. It can be shown mathematically that n - 1 provides the correct compensation to infer from sample to population. Only when the sample actually is the population, one should divide by n; in all or most other cases, use n - 1.