The theoretical aspects of the data analysis part of the course are discussed in lectures. There are some Excel exercises which emphasise some of the material. There is also an accompanying set of files (in WORD or PDF format) giving additional notes and derivation of formulae etc.
Firstly, in the course, there is a general discussion on the "experimental method", followed by comments on the difference between random and systematic errors, and precision and accuracy in experimental work. These topics are discussed in the file DA-1.
A brief review of the normal probability distribution is followed by the practical matter of finding suitable measures to describe the distribution of repeated measurements, i.e. the mean and standard deviation. The standard error on the mean is shown to be the quantity to quote when reporting your results. The details are in file DA-2. One of the Excel exercises illustrates this material (see task 2)
It is rare that the aim of an experiment is to measure directly a single quantity e.g. the length of a piece of string! Usually many quantities are measured, e.g. lengths, times, masses etc. and then compounded by some formulae to give the quantity that is the aim of the experiment. Thus we need to know how to incorporate the uncertainties of measurement of the individual quantities into the final result. This process is known as error propagation. These methods are discussed in DA-3. It is expected that these methods will be used routinely in all your practical work. They are also the subject of task 3.
You are encouraged to present your data in graphical form as many
experimental
data make a greater visual impact if presented in this way rather than
as a huge table of numbers. If the functional form of the
equation that
is thought to describe the data is known then statistical ideas can be
used to extract parameters and to test the hypothesis. In this
introductory
course we only examine the case of a straight line fit to the
data.
However
this is one of the commonest forms as, with a little mathematical
rearrangement,
many formulae describing phenomena investigated in your practical work
can be converted to a linear relationship. The principle of least
squares
is used to find expressions for the slope and intercept of the
line.
The
formulae for calculating the errors on these quantities from either the
errors on the the points or from the spread of the points about the
line
are quoted only - not derived. The details are in
DA-4.
These formulae are implemented in task 4.
You are
also expected to apply these results in all your analyses of
experiments
which result in the production of straight line plots.
The notes in DA-5 discuss briefly the problem of identifying and dealing with suspect data.