Data acquisition and error analysis are integral parts of any
quantitative experiment or survey. In our introductory lab assignment
we were required to analyze the statistical properties of a
computerized experiment used to count photons from an LED. The end
objective was to examine how errors from varying the parameters of the experiment,
mainly the number of samples and the count rate, could be analyzed
using statistical methods. We found that Poisson statistics provided
the best fit to our data. By overlaying the Poisson distribution of
the estimated parent population over the sample population, we were
able to see the correlation between the samples acquired during the
experiment and the theoretical Poisson probability distribution
function. The Gaussian also provided a good fit to the data as we
increased the number of counts that we were receiving. The
Gaussian approximation got increasingly better as the number of counts went
up. These approximations provided us with a way to quantify some of the
physical limitations of our experiment. We found that our
approximations improved by a factor of
where N is the
number of experiments we ran for each data set.
