@@ -45,6 +45,87 @@ This forms an \textit{abstract class} of a procedure, which can be represented by a real class, which can then be instantiated through the application of data. +\subsection{Decision} +\label{sec:components:decision} + +By example, consider the t-test as an instance of a procedure, +representing the general class of testing hypotheses surrounding 2 +means. Related would be formal likelihood tests with distributions, +the superspace/classes from regression and ANOVA. +Questions could be: +\begin{itemize} +\item are the 2 means the same? +\item what is the difference? +\item what is the strength of the difference? +\end{itemize} + +\subsection{Core Assessment} +\label{sec:components:assessment} + +This is the construction of the model and parameters that would be +used to form the term used to make the assessment. Here, we could +consider +\begin{equation} + \label{eq:assess:ex:1} + \hat{E}[Y|G=1] - \hat{E}[Y|G=0] +\end{equation} +as the fundamental quantity to compare. This can arise from many +sources such as regression models +\begin{equation} + \label{eq:assess:ex:2} + Y = \mu + \beta G + \epsilon \\ + E[\epsilon] = 0 +\end{equation} +or +\begin{equation} + \label{eq:assess:ex:2} + E[Y|G] = \mu + \beta G +\end{equation} + +\subsection{Normalized Behavior} +\label{sec:components:normbeh} +Let $X=(Y,G)$ from above, the whole data. + +empirical adjustment: +\begin{equation} + \label{eq:norm:ex:1} + \frac{ \hat\mu_1 - \hat\mu_0}% + {\hat{SE}(\hat\mu_1 - \hat\mu_0)} +\end{equation} +or regression-model-based: +\begin{equation} + \label{eq:norm:ex:2} + \frac{ \hat\beta}% + {\hat{SE}(\hat\beta)} +\end{equation} +or likelihood-model-based: (FIXME!) +\begin{equation} + \label{eq:norm:ex:3} + -2 \log \frac{ L(\hat\beta|X)}% + {L(0|X)} +\end{equation} +or score-model-based: +\begin{equation} + \label{eq:norm:ex:4} + \cal{I}^{-1}(\beta=0,X) S(\beta=0,X) +\end{equation} + +\subsection{Conclusion Desired} +\label{sec:component:conclusion} + +Value or Range on the Target Scale (existing parameter describing +data-oriented substantive model) + +Translation of Value/Range on the Decision Scale (what to do, what to +decide about the problem, i.e. in a testing framework). + +\section{Class Implementation} +\label{sec:class} + + +\section{Discussion} +\label{sec:disc} + \end{document} Doc/papers/CLS-philosophy.tex c255a2f85c9a6da51ace13dd9e6ce0af0f1e5a69 AJ Rossini blindglobe@gmail.com http://github.com/blindglobe/common-lisp-stat/commit/782d8075fb9bb241246c561ed7c42fee5abdde82 782d8075fb9bb241246c561ed7c42fee5abdde82 2009-10-29T00:14:51-07:00 2009-10-29T00:14:51-07:00 basic structure of the object model for statistical procedures Signed-off-by: AJ Rossini <blindglobe@gmail.com> b065512d7991f82c3c957d98c6dbc04fbc96b937 AJ Rossini blindglobe@gmail.com