multivariate-statistics/content/chapters/part1/3.tex

\chapter{Tests Reminders}

\section{\texorpdfstring{$\chi^2$}{chi2} test of independence}


\section{\texorpdfstring{$\chi^2$}{chi2} test of goodness of fit}

Check if the observations is in adequation with a particular distribution.

\begin{example}[Mendel experiments]
	Let $AB$, $Ab$, $aB$, $ab$ be the four possible genotypes of peas: colors and grain shape.
	\begin{tabular}{cccc}
		\toprule
		AB  & Ab  & aB  & ab \\
		\midrule
		315 & 108 & 101 & 32 \\
		\bottomrule
	\end{tabular}
\end{example}

The test statistics is:
\[
	D_{k,n} = \sum_{i=1}^{k} \frac{(N_i - np_i)^2}{np_i} \overunderset{\mathcal{L}}{H_0}{n \longrightarrow \infty} \chi^2_{(n-1)(q-1)??}
\]