Module Identifier | PH24010 | ||

Module Title | DATA HANDLING AND STATISTICS | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr Geraint Vaughan | ||

Semester | Semester 1 | ||

Other staff | Dr James Whiteway, Dr Geraint Thomas | ||

Pre-Requisite | Core Physics Modules at Level 1 | ||

Co-Requisite | PH25010 | ||

Course delivery | Lecture | 8 lectures (first half of semester) | |

Seminars / Tutorials | 3 workshops | ||

Laboratory | 36 Hours 12 laboratory sessions (3 hours each) | ||

Assessment | Exam | End of Semester Examinations | 20% |

Course work | Young's Modulus experiment | 30% | |

Course work | Random Measurement Experiment | 15% | |

Course work | Photometry Experiment | 15% | |

Course work | MathCad exercises | 10% | |

Course work | Theory exercises | 10% |

**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. An introduction to 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.

**Additional learning activities**

Use of STOMP CAL package.

Simple modelling using MathCad.

**Outline syllabus**

Introduction to MathCad 8

Theory of measurement (STOMP Measurement and Uncertainty package)

Units 0.1,0.2,0.3 Introduction to STOMP

Unit 1.2 Random and systematic errors

Unit 2.2 Accuracy and precision

Unit 2.3a Mean and standard deviation

Units 2.4 and 2.4a Gaussian, Poisson and Binomial distribtions

Units 2.5a, 3.1 and 3.1a Combining uncertainties

Units 3.2, 4.1 and 4.2 - The Least Squares Principle, graphing data and fitting a straight line to data.

Experiments

1. Random Measurements

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.

Photometry experiment. Exercise in taking and transforming measurements.

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.

**Reading Lists**

**Books**
**** Recommended Text**

Roger Barlow.
*Statistics*. Wiley ISBN 0-471-92295-1
**** Reference Text**

D. Donnelly.
*MathCad for Introductory Physics*. Addison-Wesley ISBN 0-201-54736-8

P.M. Morse.
*Vibration and Sound*.