\setcounter{ExampleCounter}{1}
\paragraph{Observational Study:} the investigators don't actively affect the subjects of the study; they simply observe what they do and what happens to them (ex: tobacco studies)

\paragraph{Experimental Study:} the investigators assign subjects to different groups and vary the conditions for each group, observing the results (ex: pharmaceutical studies)

\subsection{Experimental Study Terms}
\begin{itemize}
\item \textbf{Experimental unit:} the individuals being studied (people, animals, objects, etc.)

\item \textbf{Response:} what we measure about these individuals (ex: blood pressure based on new medication)

\item \textbf{Explanatory variable:} a variable that causes a change in the response; the goal is to identify an explanatory variable and see how much of a change it causes (ex: dosage of new medication)

\item \textbf{Treatment:} the different values of the explanatory variable that we give to the experimental units; we divide them into treatment groups

\item \textbf{Lurking variable:} an additional variable that can obscure the results of a study (ex: men tend to have higher blood pressure than women)

\item \textbf{Control group:} a treatment group to which nothing is done (except a placebo)

\item \textbf{Placebo:} a fake treatment

\item \textbf{Blinding:} ensuring that those involved in the study don't know what treatment group they belong to (hence the use of placebos); double-blind: even the researchers don't know
\end{itemize}
\vfill
\pagebreak

\begin{example}{Experimental Design}
Researchers want to investigate whether taking aspirin regularly reduces the risk of heart attack.  Four hundred men between the ages of 50 and 84 are recruited as participants.  The men are divided randomly into two groups: one group will take aspirin, and the other group will take a placebo.  Each man takes one pill each day for three years.  At the end of the study, researchers count the number of men in each group who have had heart attacks.\\

Identify each of the following in this study:\\

\begin{itemize}
\item \textbf{Population:} All men aged 50 to 84
\item \textbf{Sample:} The 400 men selected for the study
\item \textbf{Experimental units:} The individual men in the study
\item \textbf{Control group:} The group taking the placebo
\item \textbf{Explanatory variable:} The medication
\item \textbf{Treatments:} Aspirin or placebo
\item \textbf{Response variable:} Whether or not a subject had a heart attack
\end{itemize}
\end{example}