Module description
This module will be a laboratory-based course where the handling of data in selected experiments is treated in parallel with a course on the theory of measurement, the nature of experimental errors, random and systematic. The course provides an introduction to the basic statistics encountered in Physics, including the Binomial, Poisson and Normal distributions, and simple least-squares regression. The estimate of standard error, the combination of errors and the optimum design of experiments to reduce the final error in the most efficient way are covered, together with a demonstration of selection effects in compiling a data-base. An introduction to the MathCad programming package will be given.

Module objectives / Learning outcomes
After taking this module students should be able to:

• understand the nature of random error in experimental data
• use the Gaussian distribution and appreciate why it applies in so many cases
• calculate the mean and standard deviation of data following a simple, unbiased Gaussian
• recognise the effect of inter-dependence of measurements and extreme values on data sets
• combine several different errors to derive a final error
• identify the most important source of error in an experiment and concentrate on reducing that error
• appreciate how selection effects introduce a bias into a data sample
• fit a straight line to experimental data and evaluate the standard error in the slopeand intercept.
• write a simple MathCad program to model a physical system.

Additional learning activities
Practical experience of using spreadsheets and plotting routines.
Simple modelling using MathCad.

Outline syllabus
Lectures and Workshops

Experimental Errors. Types of errors: mistakes; rounding errors; noise errors.
Mean and standard error of measurement.
Combination of Errors: multiplication by a constant; addition and subtraction of measurements; multiplication and division of measurements; taking the power of a measurement.
Linear regression for measurements with equal errors in y. Error estimates for m and c.
MathCad: introduction to this programming package and simple exercises.
Probability. Exclusive and exhaustive. Binomial, Poisson and exponential distributions.
Central limit theorem. Gaussian (Normal) distribution.
Distribution function and the 95% and 99% limits.
Errors and the Gaussian distribution.

Experiments

1. Resistors and Dartboard
Measurement of resistors. Median, mean, average deviation and standard deviation. Histogram. Illustration of a simple Gaussian distribution.
Analysis of Dartboard results. Illustration of inter-dependence of data and rejection of extreme data.

2. Herzsprung-Russell diagram.
Comparison of 100 brightest and 100 nearest stars. Illustration of selection effect in determining the mean of a sample.

3. Young's Modulus experiment.
Determination of Young's Modulus, with special care taken to estimate the random uncertainty in the final result. Identification of the parameter contributing most to the final error.