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Data Analysis

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 Excel-3)

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 Excel exercises Excel-4 and Excel-5.

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 two Excel exercises (Excel-6 and Excel-7).  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 is discuss briefly the problem of identifying and dealing with suspect data.