# Proportion of Variance: Simple Definition and Examples of Use

## What is Proportion of Variance?

“Proportion of variance” is a generic term to mean a part of variance as a whole. For example, the total variance in any system is 100%, but there might be many different causes for the total variance — each of which have their own proportion associated with them.

## Different Uses

The term proportion of variance is used in a wide range of statistical concepts and procedures. Although it generally means the variance is proportioned between several factors, variables, or effects, it’s exact definition depends on where you’re using it. For example:

• In ANOVA, Eta squared is the proportion of variance associated with one or more main effects, errors or interactions.
• In MANOVA, Wilk’s Lambda is used to tell you how each level of independent variable contributes to the model. The proportion of variance in dependent variables explained by the model’s effect is represented by λ in the formula’s denominator.
• In Factor Analysis, you might use a Kaiser-Meyer-Olkin (KMO) Test to measure suitability of data for Factor Analysis. The KMO statistic is a measure of the proportion of variance among variables that might be common variance. The lower the proportion, the better suited the data is to Factor Analysis.
• In Partial Least Squares Regression, proportion of variance is shown in the statistics output for most major statistical software packages (like SPSS or Minitab). For example, in the following output, the proportion that factor 1 contributes to variance in the predictor variables is 20.9%. Together, factors 1,2, and 3 contribute 00%.
• In Reliability Testing, the reliability coefficient is a measure of how well a test measures achievement. It is the proportion of variance in observed scores (i.e. scores on the test) attributable to true scores (the theoretical “real” score that a person would get if a perfect test existed).

References:
IBM Knowledge Center (SPSS Statistics v 23.0.0). Prop. of Var. Explained. Retrieved May 28th 2017 from: https://www.ibm.com/support/knowledgecenter/SSLVMB_23.0.0/spss/tutorials/pls_carsales_pve.html

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