525Chapter 9
Essential Statistics for Data Analysis
Statistics is perhaps the most powerful available technique for analyzing experimen-
tal data. However its proper use requires careful attention not only to the techniques
used but also to the system being analyzed. The advent of modern but very compli-
cated radiation detection and measurement systems has shifted the experimenter’s
intention from merely taking averages of data to the more complicated tasks of full
scale statistical analysis. Most of the modern statistical techniques are labor in-
tensive and are almost impossible to perform without using computers. A modern
experimenter, therefore, uses statistical analysis software to analyze the data, a task
that is easy to perform but prone to errors if not carefully done. Unfortunately
these software work as black boxes; they take data in and produce the final results.
No matter what is fed in, something comes out as the result. Whether it makes
sense or is correct is up to the person doing the analysis to decide. Therefore it
is imperative that an experimenter fully understands the statistical techniques and
their underlying theories before using statistical software.
Statistics is a vast field and it should not be expected that the reader becomes
familiar with all of its intricacies after going through this chapter alone. However it
will provide enough information that would enable the reader to analyze the data
more efficiently.
Before we begin, let us see what our main objective should be in terms of draw-
ing reasonable inferences from the outcome of an experiment. Suppose we want to
measure the half life of a radioactive isotope. To do this, we use a suitable detector
and measure the activity of the sample at several time intervals. However, there is a
problem with this scheme; each of these measurements has some uncertainty associ-
ated with it. This uncertainty could be a combination of several effects such as the
random nature of the radioactive phenomenon, the randomness in the conversion
process of incident radiation into charge pairs, and the errors in the measurement
system. Now we have a huge problem here; we have a number, namely the mea-
surement at a point in time, but do not know how much faith we should put into it.
The best and the easiest solution to this problem is to take several measurements
instead of one and then report the average of these with a range within which any
subsequent measurement isexpectedto lie, that is
A=A ̄±
A.
The calculation of the averageA ̄and the dispersion Aand their interpretation is
the task from where we start this chapter.