# Managers-Net

## Analysis of Variance

A statistical analysis technique in which the variance attributable to individual influences or variables and combinations of influences or variable is isolated, in situations in which a continuous dependant variable is controlled by one or more independent variables and where a series of sets of values of each variable is available.

BSI definition (21091) - the dispersion of a population measured as the mean squared deviation of individual values from the mean

NB: Financial - the difference between planned use of resources and actual results - STATISTICAL VARIANCE ANALYSIS (21002) - the two definitions are not mutually compatible a method of partitioning the total variance of a set of values in order to assess whether the variance attributable to a particular source or sources differs from that attributable to random variance.

Analysis of variance is best explained by means of an illustration.

The variance is a statistical parameter that shows the extent to which a set of values depart from uniformity, e.g. whether the weights of 1000 men are closely clustered around a single value, e.g. around 120 kgs, or whether they are widely dispersed, e.g. from 60 to 180 kgs.

Suppose that we have weight data for 1000 British men and 1000 Canadians. We could calculate the total variance of all the men, but it would be more instructive to split this up into two components - the variance (extent of departure from the mean) between national weights and the variance within each national group, i.e. variance between samples and variance within samples. We could then determine whether it were true that there is a greater variation in the weights of British or Canadian men. The analysis of variance provides answers to this kind of question. Similarly one could determine the extent to which the colour variations of a product were the result of processing temperature variations, processing time variations and inter-relationships between the two.

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