Kolmogorov-Smirnov: Compares data to a theoretical distribution
$$
F_n(x) := \frac{1}{n} \sum_{i=1}^n I_{[x_i,\infty)} (x) \textrm { for } x\in \mathbf{R}
$$
$$
H_0: \text{The data follows the reference distribution.}
$$
$$
H_1: \text{The data does not follow the reference distribution.}
$$

The statistic:
$$
D := \sup_x|F_n(x) - F(x)|.
$$
The Null-hypothesis should be rejected if p-value<$\alpha$.

Normal probability plot:
If the data are normal the points should lie close to the line on the plot.

{\bf Example - beer} \\
We perform the Kolmogorov-Smirnov test using the ks.test() in R.
\begin{verbatim}
ks.test(resid) # resid are the residuals
\end{verbatim}

We make a normal probability pot using the qqnorm() function in R. We add a line to the plot using the qqline() function.
\begin{verbatim}
qqnorm(resid)
qqline(resid)
\end{verbatim}