require(mosaic)
require(Stat2Data)
require(agricolae)
cols <- trellis.par.get()$superpose.symbol$col

#### Motivation to Correct for Multiple Testing

Let $$X,Y$$ be two random vectors, and consider the model $$Y \sim \beta_0 + \beta_1 \cdot X$$. The null hypothesis is that $$\beta_1 = 0$$. In our hypothesis test, we compute the $$t$$-statistic associated with the likelihood of observing the data ($$\hat{\beta_1}$$) under the assumption that the true slope is 0 (e.g. $$\beta_1 = 0$$). If the probability of $$\hat{\beta_1}$$ is sufficiently small (e.g. less than $$\alpha = 0.05$$), then we say that we have found a statistically significant association.

But what if we have 20 variables $$X_1,X_2, \ldots, X_{20}$$ in our model? Remember the jelly beans!