Variance

Variability is a numerical description that refers to the spread values within a given distribution. Variability can be described using four common measures: range, the mean deviation score, standard deviation, and variance. Variance is most useful in determining the overall spread of a data set. Range simply takes two data points, the lowest and highest values, and measures the space between them. The interquartile range also interprets the amount of spread within a set of data by using only the middle 50% of scores. Unlike range, variance takes into account every data point within the set and measures each distance from the mean. Variance is calculated using a number of values from data and the associated distribution. Specifically, variance requires raw data scores and the sample size of the data.

The sum of squares (or sum of squared errors) is also used as a method to determine total spread or dispersion. The problem with sum of squares is this value cannot be compared across samples that differ in size. Variance deals with average spread, which is comparable across groups that may change sizes.

Variances are most impactful when comparing multiple distributions. Furthermore, this statistic becomes the basis for various statistical comparisons, including an analysis of variance (ANOVA). In experiments, people or groups undergo treatments to potentially elicit various responses. If all scores, or responses, are different, variability will be large. If all scores are exactly the same, variability will be zero.

Variance is used in many different experimental designs. After discussing a brief history, variance is described not only by its formulae but also by its conceptual properties. Variance is then applied to statistical testing, including ANOVA and multiple regression.