ANOVA: Description and Application

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1. I need some examples on how ANOVA is used in different circumstances like work, personal life, education etc.

An ANOVA (Analysis of Variance), sometimes called an F test, is closely related to the t test. The major difference is that, where the t test measures the difference between the means of two groups, an ANOVA tests the difference between the means of two or more groups. One potential drawback to an ANOVA is that you lose specificity: all an F tells you is that there is a significant difference between groups, not which groups are significantly different from each other. To test for this, you use a post-hoc comparison to find out where the differences are - which groups are significantly different from each other and which are not. Some commonly used post-hoc comparisons are Scheffe's and Tukey's. http://www.georgetown.edu/departments/psychology/researchmethods/statistics/inferential/anova.htm

Example 1: Personal Life

You might guess that the size of maple leaves depends on the location of the trees. For example, that maple leaves under the shade of tall oaks are smaller than the maple leaves from trees in the prairie and that maple leaves from trees in median strips of parking lots are smaller still. To test this hypothesis you collect several (say 7) groups of 10 maple leaves from different locations. Group A is from under the shade of tall oaks; group B is from the prairie; group C from median strips of parking lots, etc. Most likely you would find that the groups are broadly similar, for example, the range between the smallest and the largest leaves of group A probably includes a large fraction of the leaves in each group. Of course, in detail, each group is probably different: has slightly different highs, lows, and hence it is likely that each group has a different average (mean) size. Can we take this difference in average size as evidence that the groups in fact are different (and perhaps that location causes that difference)? Note that even if there is not a "real" effect of location on leaf-size (the null hypothesis), the groups are likely to have different average leaf-sizes. http://www.physics.csbsju.edu/stats/anova.html

Can you think of other group comparisons that you might use the ANOVA for? Perhaps you are trying to determine what University to go too, so you want to compare three Universities on success rates (e.g., how many students graduated). You would use the ANOVA to test if there was a difference.

Example 2: Business

1. You might want to compare the mean distances of four brands of golf balls travel when struck with a five iron to determine what golf balls to carry in stock. Ten balls of each brand are randomly selected, five to be struck by the driver, and five to be struck by the five iron. The four brands would ...