

\subsection{\bf Interpretation of Value of $\chi^2$}

\begin{slide}
\begin{itemize}
\item Thus, if value of $\chi^2$ is many (say $>3$) standard deviations
away from its mean, then the theoretical form is in doubt.

\item The usual maximum likelihood method does not have this
advantage: remember $L$ was unnormalized and so its value had no
significance for the goodness of fit.

\item This is quite a difficult problem and an elementary discussion is
given in MacDonald notes, page~14 onwards.

\item The only way to get a feeling for $\chi^2$ is to use it:  so I
won't dwell here on the important techniques used to minimize $\chi^2$
to get good theoretical parameters and estimate errors in the same.  We
will come back to this later in the notes.

\item Mathews and Walker solve the simplest problem, i.e., $\xi_i$ are
linear in theoretical parameters.

\item We do an example of this below.  

\item Bevington or similar book should be read before tackling a real
problem.
\end{itemize}
\end{slide}

