Anova Essay

ANOVA Essay

The analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation. ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes t-test to more than two groups. ANOVAs are helpful because they have an advantage over a two-sample t-test. By doing ANOVA, we can eliminate the chance of committing a type I error. This is why ANOVAs are useful in comparing two or more means.

ANOVA was invented by Sir Ronald Fisher around 1920. Sir Ronald Fisher was a statistician and geneticist. As stated above, the ANOVA are similar to the t-test but unlike the t-test, they can compare multiple groups. There are several types of ANOVA, the one-factor (one-way) ANOVA, two-factor (two-way) ANOVA, and also repeated measures ANOVA. The factors in this type of test are the independent variables and each one of the variables must be measured on a categorical scale – which means that levels of the independent variable must define separate groups. An example of a one way ANOVA would be taking the average test scores for students exposed to three different teaching techniques (three levels of a single independent variable).

The null hypothesis for ANOVA is that the mean is the same for all groups. The alternative/research hypothesis is that the average is not the same for all groups. The ANOVA test can also be used to compute the F-statistic, named after Fisher. The F-statistic is also used to calculate the p-value. With the computation of ANOVA, if the null hypothesis is rejected, then all we know is that at least 2 groups are different from each other.

References:

Dr. Lange, Robert (March 25, 2004) ANOVA http://www.beckyfiedler.com/edf6481/instruments/anova.pdf

Dr. Markham, Shelby (2001) Analysis of variance...