What is an ANOVA?
An ANOVA is an analysis of the variation present in an experiment. It is a test of the hypothesis that the variation in an experiment is no greater than that due to normal variation of individuals' characteristics and error in their measurement.
To get a grasp of statistics, the researcher must realize that statistics is based on philosophy and the testing of hypothesis. Too often the researcher reverts back to his schoolroom daze, when old Mr Westerkamp leaning over him was ready to pour down verbal abuse when the student did not immediately grasp the concept of decimals points.
...the researcher no longer needs to fear Mr. Westerkamp, although some reviewers with Westerkampian tendancies still exist. Instead the researcher should know that there really is no WRONG analysis. The researcher just might not be testing what he thinks he is. In an ANOVA, variation will come from a number of sources depending upon the layout of the experiment. The concept behind experimental design and the formulation of an ANOVA model is to identify the sources of variation and construct the proper tests to compare them.
Statisticans love to tests hypothesis. The basis for every statistical test is to phrase the question in terms of a null hypothesis, essentially that everything is equal, and then to test whether that can be accepted within a certain probability. If the null hypothesis is rejected that allows the researcher to say that "significant differences were found in ... with a probability <0.05."
The tests in an ANOVA are based on the F-ratio: the variation due to an experimental treatment or effect divided by the variation due to experimental error. The null hypothesis is this ratio equals 1.0, or the treatment effect is the same as the experimental error. This hypothesis is rejected if the F-ratio is significantly large enough that the possibility of it equaling 1.0 is smaller than some pre-assigned criteria such as 0.05 (one in twenty).
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