First matlab codes for statistics

statistics/lecture/descriptivestatistics.tex

@@ -89,108 +89,190 @@
   \tableofcontents
 \end{frame}
 
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Descriptive statistics}
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{types of data}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Statistics of ratio data}
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-
-\begin{frame}
-  \frametitle{data scales}
-  \framesubtitle{What data types are distinguished in statistics?}
-  \Large
-  {\bf Why are data types important?}
-  \pause
-  \begin{itemize}
-  \item selection of statistics 
-  \item selection of plots
-  \item selection of correct tests
-  \end{itemize}
-\end{frame}
 %-------------------------------------------------------------
-
 \begin{frame}
-  \frametitle{data scales}
-  \framesubtitle{nominal/categorial scale}
+  \frametitle{Statistics of ratio data}
   \begin{itemize}
-  \item properties like cell type, experimental group (i.e. treatment
-    1, treatment 2, control)
-  \item each observation/sample is put into one category
-  \item there is no reasonable order among the categories
-  \item  example: [rods, cones] vs. [cones, rods]
-  \end{itemize}
-\end{frame}
-%-------------------------------------------------------------
-
-\begin{frame}
-  \frametitle{data scales}
-  \framesubtitle{ordinal scale}
-  \begin{itemize}
-  \item like nominal scale, but there is an order
-  \item {\bf but:} there is no reasonable measure of {\em distance}
-    between the classes
-  \item examples: ranks, ratings
-  \end{itemize}
-\end{frame}
-%-------------------------------------------------------------
-
-\begin{frame}
-  \frametitle{data scales}
-  \framesubtitle{interval scale}
-  \begin{itemize}
-  \item quantitative/metric values
-  \item reasonable measure of distance between values but no absolute zero
-  \item examples: temperature in $^\circ$C
-  \end{itemize}
-\end{frame}
-%-------------------------------------------------------------
-
-\begin{frame}
-  \frametitle{data scales}
-  \framesubtitle{absolut/ratio scale}
-  \begin{itemize}
-  \item like interval scale but with absolute zero
-  \item example: temperature in $^\circ$K
-  \end{itemize}
-  \pause
-  %\begin{emphasize}{relationsships between scales}
+  \item Location, central tendency
     \begin{itemize}
-    \item scales exhibit increasing information content from nominal
-      to absolute
-    \item conversion  ,,downwards'' always possible
+    \item arithmetic mean
+    \item median
+    \item mode
     \end{itemize}
-  %\end{emphasize}
+
+  \item Spread, dispersion
+    \begin{itemize}
+    \item variance
+    \item standard deviation
+    \item interquartile range
+    \item coefficient of variation
+    \item minimum, maximum
+    \end{itemize}
+
+  \item Shape
+    \begin{itemize}
+    \item skewnees
+    \item kurtosis
+    \end{itemize}
+
+  \item Dependence
+    \begin{itemize}
+    \item Pearson correlation coefficient
+    \item Spearman's rank correlation coefficient
+    \end{itemize}
+
+  \end{itemize}
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\subsection{Data types}
+
+%-------------------------------------------------------------
+\begin{frame}
+  \frametitle{Data types: nominal scale}
+  \begin{itemize}
+  \item Binary
+    \begin{itemize}
+    \item ``yes/no'',
+    \item ``true/false'',
+    \item ``success/failure'', etc.
+    \end{itemize}
+  \item Categorial
+    \begin{itemize}
+    \item cell type (``rod/cone/horizontal cell/bipolar cell/ganglion cell''),
+    \item blood type (``A/B/AB/0''),
+    \item parts of speech (``noun/veerb/preposition/article/...''),
+    \item taxonomic groups (``Coleoptera/Lepidoptera/Diptera/Hymenoptera''), etc.
+    \end{itemize}
+  \item Each observation/measurement/sample is put into one category
+  \item There is no reasonable order among the categories.\\
+    example: [rods, cones] vs. [cones, rods]
+  \pause
+  \item Statistics: mode, i.e. the most common item
+  \end{itemize}
 \end{frame}
 
 %-------------------------------------------------------------
 \begin{frame}
-  \frametitle{examples from neuroscience and psychology}
+  \frametitle{Data types: ordinal scale}
   \begin{itemize}
-  \item {\bf nominal:}\pause 
+  \item Like nominal scale, but with an order
+  \item Examples: ranks, ratings
     \begin{itemize}
-    \item treatment group
-    \item stimulus class
-    \item cell type
+    \item ``bad/ok/good'',
+    \item ``cold/warm/hot'',
+    \item ``young/old'', etc.
+    \end{itemize}
+  \item {\bf But:} there is no reasonable measure of {\em distance}
+    between the classes
+  \pause
+  \item Statistics: mode, median
+  \end{itemize}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}
+  \frametitle{Data types: interval scale}
+  \begin{itemize}
+  \item Quantitative/metric values
+  \item Reasonable measure of distance between values, but no absolute zero
+  \item Examples: 
+    \begin{itemize}
+    \item Temperature in $^\circ$C ($20^\circ$C is not twice as hot as $10^\circ$C)
+    \item Direction measured in degrees from magnetic or true north
+    \end{itemize}
+  \pause
+  \item Statistics:
+    \begin{itemize}
+    \item Central tendency: mode, median, arithmetic mean
+    \item Dispersion: range, standard deviation
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}
+  \frametitle{Data types: absolute/ratio scale}
+  \begin{itemize}
+  \item Like interval scale, but with absolute origin/zero
+  \item Examples: 
+    \begin{itemize}
+    \item Temperature in $^\circ$K
+    \item Length, mass, duration, electric charge, ...
+    \item Plane angle, etc.
+    \item Count (e.g. number of spikes in response to a stimulus)
+    \end{itemize}
+  \pause
+  \item Statistics:
+    \begin{itemize}
+    \item Central tendency: mode, median, arithmetic, geometric, harmonic mean
+    \item Dispersion: range, standard deviation
+    \item Coefficient of variation (ratio standard deviation/mean)
+    \item All other statistical measures
+    \end{itemize}
+  \end{itemize}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}
+  \frametitle{Data types}
+  \begin{itemize}
+  \item Data type selects
+    \begin{itemize}
+    \item statistics 
+    \item type of plots (bar graph versus x-y plot)
+    \item correct tests
+    \end{itemize}
+  \item Scales exhibit increasing information content from nominal
+    to absolute.\\
+    Conversion  ,,downwards'' is always possible
+  \item For example: size measured in meter (ratio scale) $\rightarrow$
+    categories ``small/medium/large'' (ordinal scale)
+  \end{itemize}
+\end{frame}
+
+%-------------------------------------------------------------
+\begin{frame}
+  \frametitle{Examples from neuroscience}
+  \begin{itemize}
+
+  \item {\bf absolute:}\pause
+    \begin{itemize}
+    \item size of neuron/brain
+    \item length of axon
+    \item ion concentration
+    \item membrane potential
+    \item firing rate
+    \end{itemize}
+
+  \item {\bf interval:}\pause
+    \begin{itemize}
+    \item edge orientation
     \end{itemize}
 
   \item {\bf ordinal:} \pause 
     \begin{itemize}
+    \item stages of a disease
     \item ratings
-    \item clinical stages of a disease
+    \end{itemize}
+
+  \item {\bf nominal:}\pause 
+    \begin{itemize}
+    \item cell type
+    \item odor
     \item states of an ion channel
     \end{itemize}
-  \item {\bf Absolut-/Ratioskala:}\pause
-    \begin{itemize}
-    \item firing rate
-    \item membrane potential
-    \item ion concentration
-    \end{itemize}
+
   \end{itemize}
 \end{frame}
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\subsection{Real-valued data}
+\end{document}