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ANOVA: Analysis of Variance

ANOVA, or analysis of variance, is a statistical procedure you will often see mentioned and used in scientific literature. But what is it? Arun Kumar offers a nice look at this technique in a blog post from 2013 (http://blog.minitab.com/blog/statistics-in-the-field/understanding-anova-by-looking-at-your-household-budget). He begins by noting that in order to understand ANOVA, you need to grapple with some other terms, such as sum or squares, degrees of freedom and F-ratio. This is true. But for the moment, let’s forget those terms and consider the technique.

ANOVA is all about variation, and variation is part of whatever we do. Your temperature varies over the course of the day, how much you spend varies, your patient’s pain score can vary. What ANOVA does is try to look at the components that may affect that variation. It asks how much those components contribute to the variation. Kumar uses a monthly budget to illustrate this point- how much each month do we spend on food, entertainment, insurance, etc.? How much is miscellaneous and not easily classified? This last category is akin to an “error” category. Thus, we can ask, how much does each category relate to the total expenses for the month? How do they compare to the miscellaneous (error) category?

These factors are what we call a model. For reasons I will not discuss here, we look at the sum of squares due to error as the unexplained variation, while our model uses the sum of squares as the explained model. Typically, we would like to see the explained variation be greater than the unexplained. In ANOVA, we can assess this with the F-ratio. And here we need to consider degrees of freedom, by which we adjust the sum of squares. This is then called the mean square. Our F-ratio is then the mean square of a factor divided by the mean square of error. The higher the F-ratio the more significant the factor is. In the end, this is the important thing for you to know.

I am sure this a bit confusing. A youtube clip, located at https://www.youtube.com/watch?v=-yQb_ZJnFXw, does a nice job of providing additional explanation and examples.


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