# ANOVA Algorithm

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An ANOVA algorithm is a population mean difference analysis algorithm by partitioning the data into components attributable to different sources of variation.

**AKA:**Analysis of Variance, ANOVA.**Context:**- It attempts to eliminate variance that is due to other factors.
- It is closely related to Student's t-test.
- It can range from being, depending on the number of factors, a One-way ANOVA (used for a single-factor) to being a Two-way ANOVA (with or without interactions).

**Counter-Example(s):****See:**Statistical Inference, MANOVA, ANCOVA, Hypothesis Testing.

## References

### 2013

- (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/Analysis_of_variance
**Analysis of variance**(ANOVA) is a collection of statistical models used to analyze the differences between group means and their associated procedures (such as "variation" among and between groups). In ANOVA setting, the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are equal, and therefore generalizes*t*-test to more than two groups. Doing multiple two-sample t-tests would result in an increased chance of committing a type I error. For this reason, ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance.

### 2009

- (WordNet, 2009) ⇒ http://wordnetweb.princeton.edu/perl/webwn?s=analysis%20of%20variance
- S: (n) analysis of variance, ANOVA (a statistical method for making simultaneous comparisons between two or more means; a statistical method that yields values that can be tested to determine whether a significant relation exists between variables)

- http://www.statistics.com/resources/glossary/a/anova.php
- QUOTE: Analysis of Variance (ANOVA): A statistical technique which helps in making inference whether three or more samples might come from populations having the same mean; specifically, whether the differences among the samples might be caused by chance variation.

### 2008

- (Upton & Cook, 2008) ⇒ Graham Upton, and Ian Cook. (2008). “A Dictionary of Statistics, 2nd edition revised." Oxford University Press. ISBN:0199541450
- QUOTE: ANOVA (analysis of variance): The attribution of variation in a *variable to variations in one or more explanatory variables. The term was introduced by Sir Ronald Fisher in 1918.
A measure of the total variability in a set of *data is given by the sum of squared differences of the *observations from their overall *mean This is the

**total sum of squares (TSS)**. lt is often possible to subdivide this quantity into components that are identified with different causes of variation. The full subdivision is usually set out in an**analysis of variance**table ...

- QUOTE: ANOVA (analysis of variance): The attribution of variation in a *variable to variations in one or more explanatory variables. The term was introduced by Sir Ronald Fisher in 1918.

### 2006

- (Starbird, 2006) ⇒ Michael Starbird. (2006). “Meaning from Data: Statistics Made Clear.” The Teaching Company
- QUOTE: analysis of variance (ANOVA): A procedure of statistical analysis by which differences in means of two or more groups can be assessed after eliminating variance that is due to other factors.

### 1991

- (Efron & Tibshirani, 1991) ⇒ Bradley Efron, and Robert Tibshirani. (1991). “Statistical Data Analysis in the Computer Age.” In: Science, 253(5018). 10.1126/science.253.5018.390
- QUOTE: Most of our familiar statistical methods, such as hypothesis testing, linear regression, analysis of variance, and maximum likelihood estimation, were designed to be implemented on mechanical calculators.