Analysis of Variance (ANOVA) is a technique that's used for analyzing the differences between the means from several groups (it is essentially an extension of the t-test to multiple samples). It is deeply tied to a statistical discipline known as experimental design, a discipline that analyzes how to collect the data, how to layout an experiment, and which variables should be measured.
In statistics, correlation is not the same as causality: two phenomena might be correlated, but deducing causality out of that correlation is usually wrong. For example, most animals wake up just before dawn, but we can't deduce that waking up causes the sunlight to appear.
A very important question then, is: how can we determine causality within a statistical framework? The way we identify causality in statistics is by first laying out...
