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\rhead{Earth, Moon, and Planets Lab (Wed 6-9pm)}
\chead{}
\lhead{Lab 2: Measurement and Error}
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\lfoot{Roban Hultman Kramer} \cfoot{\thepage} \rfoot{Fall 2006}

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\begin{document}
\begin{center}
\huge Measurement and Error: The Height of Pupin
\end{center}

\section*{Introduction}

One of the primary activities of a scientist is comparing theories
with empirical data. Scientists use theories to make predictions,
which can be compared with experimental or observational results. In
astronomy, theories are often (though not always) mathematical, and
observations usually consist of quantitative measurements to be
compared with theoretical calculations.

Repeating an observation several times often gives several slightly
different results, even with the same method. The situation is even
more confusing when different techniques give quite different results
for the same quantity. How does a scientists determine which is the
``real'' answer, or whether their set of varying measurements for a
quantity agree with a predicted value? This lab gives you a chance to
explore these questions while performing your own measurements.

\section{Precision, accuracy, and evaluating measurements}

A couple of definitions that might be useful to you:

\begin{description}
\item[Precision:] how close a measurement is to other measurements
  performed the same way.
\item[Accuracy:] how close a measurement is to the ``true'' value.
\end{description}
Examples: Lets say you measure the distance between two points several
times. You get the following results: $2.15\mathrm{cm}$,
$2.10\mathrm{cm}$, $2.11\mathrm{cm}$, $2.20\mathrm{cm}$,
$2.13\mathrm{cm}$. We might choose the average value $2.14\mathrm{cm}$
as our estimate of the true distance. The most discrepant measurement
from the average was $2.20\mathrm{cm}$. This differs from the average
by $0.6\mathrm{cm}$, so we might say the precision of our measurement
is $0.6\mathrm{cm}$. There are other ways to calculate the precision
of a measurement, so it's important to specify how to determined
precision when you report a value.

Now lets say that the ruler we used was poorly manufactured, and the
true distance was $3\mathrm{cm}$. We would then say that the accuracy
of the measurement was only $0.86\mathrm{cm}$. Note that it is usually
impossible to know how accurate a measurement is, since all you have
to compare it with may be other measurements.

Now discuss the following questions with your group and
\textbf{briefly record your answers in your notebook}. 

\begin{enumerate}
\item How would you define ``experiment'' (the noun)? How does an
  experiment differ from a measurement?
\item Let's say you have two different methods of measuring a quantity
  and can repeat each one many times. How would you determine which
  method was ``better'' and what are your criteria? 
\item Lets say you have the value of a quantity as predicted by a
  theory and a set of measurements of that value from an
  experiment. How would you go about determining if the experimental
  results agree with the theory?
\end{enumerate}

\section{Designing an experiment/measurement}

\subsection*{Materials} meter sticks, rulers, twine, scissors, tape,
  etc.

\subsection*{Instructions}

With your group come up with three methods of measuring the height of
Pupin with the materials you have been provided, and \textbf{record
the procedure for each in your notebook. Which methods do you expect
to work best and worst? How will you determine the precision of your
measurements?} Show your methods to a lab instructor before
proceeding. 

\section{Measure the height of Pupin}

\subsection*{Materials} whatever you have selected

\subsection*{Instructions}

Once you have our approval, use each of your measurement techniques
several times. You should end up with at least four numbers
\textit{per technique}. \textbf{For each technique determine a single value
for the height of Pupin and the precision of that measurement.}

\textbf{Answer in your notebook:}
\begin{enumerate}
\item Which
technique do you thing worked best, and why? 
\item How did you decide which technique worked best? 
\item Determine a final value of the height of Pupin
and the precision of that value.
\end{enumerate}

\end{document}