Preface to the second edition .................................. xi
Preface to the first edition ................................. xiii
1 Introduction to scientific data analysis ..................... l
1.1 Introduction ............................................ 1
1.2 Scientific experimentation .............................. 2
1.3 The vocabulary of measurement ........................... 5
1.4 Units and standards ..................................... 6
1.5 Picturing experimental data ............................ 13
1.6 Key numbers summarise experimental data ................ 21
1.7 Population and sample .................................. 26
1.8 Experimental error ..................................... 33
1.9 Modem tools of data analysis - the computer based
spreadsheet ............................................ 35
1.10 Review ................................................. 35
End of chapter problems ..................................... 36
2 Excel and data analysis ..................................... 40
2.1 Introduction ........................................... 40
2.2 What is a spreadsheet? ................................. 41
2.3 Introduction to Excel .................................. 42
2.4 Built in mathematical functions ........................ 62
2.5 Built in statistical functions ......................... 64
2.6 Presentation options ................................... 68
2.7 Charts in Excel ........................................ 70
2.8 Data analysis tools .................................... 77
2.9 Review ................................................. 84
End of chapter problems ..................................... 84
3 Data distributions I ........................................ 90
3.1 Introduction ........................................... 90
3.2 Probability ............................................ 91
3.3 Probability distributions .............................. 93
3.4 Distributions of real data ............................. 98
3.5 The normal distribution ............................... 101
3.6 From area under a normal curve to an interval ......... 111
3.7 Distribution of sample means .......................... 119
3.8 The central limit theorem ............................. 121
3.9 The t distribution .................................... 126
3.10 The log-normal distribution ........................... 133
3.11 Assessing the normality of data ....................... 135
3.12 Population mean and continuous distributions .......... 137
3.13 Population mean and expectation value ................. 139
3.14 Review ................................................ 140
End of chapter problems ............................... 140
4 Data distributions II ...................................... 146
4.1 Introduction .......................................... 146
4.2 The binomial distribution ............................. 146
4.3 The Poisson distribution .............................. 157
4.4 Review ................................................ 165
End of chapter problems ............................... 165
5 Measurement, error and uncertainty ......................... 168
5.1 Introduction .......................................... 168
5.2 The process of measurement ............................ 171
5.3 True value and error .................................. 174
5.4 Precision and accuracy ................................ 176
5.5 Random and systematic errors .......................... 177
5.6 Random errors ......................................... 178
5.7 Uncertainty in measurement ............................ 189
5.8 Combining uncertainties ............................... 199
5.9 Expanded uncertainty .................................. 208
5.10 Relative standard uncertainty ......................... 213
5.11 Coping with outliers .................................. 214
5.12 Weighted mean ......................................... 218
5.13 Review ................................................ 221
End of chapter problems .................................... 221
6 Least squares I ............................................ 226
6.1 Introduction .......................................... 226
6.2 The equation of a straight line ....................... 227
6.3 Excel's LINESTfJ function ............................. 240
6.4 Using the line of best fit ............................ 243
6.5 Fitting a straight line to data when random errors
are confined to the x quantity ........................ 252
6.6 Linear correlation coefficient, r ..................... 253
6.7 Residuals ............................................. 261
6.8 Data rejection ........................................ 266
6.9 Transforming data for least squares analysis .......... 270
6.10 Weighted least squares ................................ 277
6.11 Review ................................................ 284
End of chapter problems .................................... 285
7 Least squares II ........................................... 297
7.1 Introduction .......................................... 297
7.2 Extending linear least squares ........................ 298
7.3 Formulating equations to solve for parameter
estimates ............................................. 300
7.4 Matrices and Excel .................................... 302
7.5 Fitting equations with more than one independent
variable .............................................. 308
7.6 Standard uncertainties in parameter estimates ......... 312
7.7 Weighting the fit ..................................... 316
7.8 Coefficients of multiple correlation and multiple
determination ......................................... 318
7.9 Estimating more than two parameters using the
LINEST() function ..................................... 320
7.10 Choosing equations to fit to data ..................... 322
7.11 Review ................................................ 327
End of chapter problems .................................... 328
8 Non-linear least squares ................................... 335
8.1 Introduction .......................................... 335
8.2 Excel's Solver add-in ................................. 338
8.3 More on fitting using non-linear least squares ........ 352
8.4 Weighted non-linear least squares ..................... 358
8.5 More on Solver ........................................ 366
8.6 Review ................................................ 370
End of chapter problems .................................... 371
9 Tests of significance ...................................... 382
9.1 Introduction .......................................... 382
9.2 Hypothesis testing .................................... 383
9.3 Comparing x with μ0 when sample sizes are small ...... 392
9.4 Significance testing for least squares parameters ..... 394
9.5 Comparison of the means of two samples ................ 397
9.6 Comparing variances using the F test .................. 405
9.7 Comparing expected and observed frequencies using the
χ2 test ............................................... 410
9.8 Analysis of variance .................................. 418
9.9 Review ................................................ 423
End of chapter problems .................................... 423
10 Data Analysis tools in Excel and the Analysis ToolPak ...... 428
10.1 Introduction .......................................... 428
10.2 Activating the Data Analysis tools .................... 429
10.3 Anova: Single Factor .................................. 431
10.4 Correlation ........................................... 432
10.5 F-test two-sample for variances ....................... 433
10.6 Random Number Generation .............................. 434
10.7 Regression ............................................ 435
10.8 t tests ............................................... 439
10.9 Other tools ........................................... 440
10.10 Review ............................................... 443
Appendix 1 Statistical tables ................................ 444
Appendix 2 Propagation of uncertainties ...................... 453
Appendix 3 Least squares and the principle of maximum
likelihood ........................................ 455
Appendix 4 Standard uncertainties in mean, intercept and
slope ............................................. 461
Appendix 5 Introduction to matrices for least squares
analysis .......................................... 466
Appendix 6 Useful formulae ................................... 471
Answers to exercises and end of chapter problems .............. 475
References .................................................... 502
Index ......................................................... 506
|
