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The basic idea behind analysis of variance (also called ANOVA) is that it can tell you whether a set of statistical results can properly be divided into categories in some particular way.
For example, let us say that you have statstics telling you how well all the students in a given population did on a test. You want to find out what sorts of groups did better or worse on the test. You want to determine, for example, if men did better than women or if students majoring in math did bettter than those majoring in physics.
What ANOVA can tell you is whether the scores achieved by these different groups are truly different (in a statistical sense) from one another. It can tell you if the groups' results were different enough to be meaningful.
Analysis of variance, often called ANOVA is a statistical technique for testing the hypothesis that sample means of several groups are derived from the same population. For example consider a company outsources a particular type of bush, used by it in assembly of its final product, from four different vendors. If the company wants to ascertain if the quality of bushes procured from different vendors are similar, it can do so by examining if the differences (variance) in bushes supplied by each vendor are large as compared to differences (variance) in the means for bushes supplied by different vendors.
The computation of ANOVA consists of comparing the variances among the means to the variances within the samples. In this comparison what difference is considered to be statistically significant depends on the sample sizes and the amount of certainty that we desire in our testing.
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