Module Identifier PH24010 Module Title DATA HANDLING AND STATISTICS Academic Year 2001/2002 Co-ordinator Professor Geraint Vaughan Semester Semester 1 Other staff Dr James Whiteway Pre-Requisite Core Physics Modules at Level 1 Course delivery Lecture 8 lectures (first half of semester) Seminars / Tutorials 3 workshops Laboratory 36 Hours 12 laboratory sessions (3 hours each) Assessment Course work MathCad exercises 10% Course work Theory exercises 10% Course work Young's Modulus experiment 30% Course work Photometry experiment 30% Exam 1 Hours End of Semester Examinations 20%

#### Module description

This module is 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. Further instruction on the MathCad programming package will be given.

#### Learning outcomes

After taking this module student should be able to:
• understand the nature of random error in experimental data
• use the Gaussian distribution and apprectiate 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 slope and intercept.
• write a simple MathCad program to model a physical system.

Use of STOMP CAL package.

#### Outline syllabus

Use of Mathcad for statistical problems.

Theory of measurement (STOMP Measurement and Uncertainty package)

Random and systematic errors
Accuracy and precision
Mean and standard deviation
Gaussian, Poisson and Binomial distribtions
Combining uncertainties
The Least Squares Principle, graphing data and fitting a straight line to data.

Experiments
1. Photometry experiment. Exercise in taking and transforming measurements.
2. 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.