Preface to the second edition |
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xi | |
Preface to the first edition |
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xiii | |
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1 Introduction to scientific data analysis |
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1 | (39) |
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1 | (1) |
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1.2 Scientific experimentation |
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2 | (3) |
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1.3 The vocabulary of measurement |
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5 | (1) |
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6 | (7) |
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1.5 Picturing experimental data |
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13 | (8) |
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1.6 Key numbers summarise experimental data |
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21 | (5) |
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1.7 Population and sample |
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26 | (7) |
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33 | (2) |
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1.9 Modern tools of data analysis - the computer based spreadsheet |
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35 | (1) |
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35 | (5) |
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36 | (4) |
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2 Excel and data analysis |
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40 | (50) |
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40 | (1) |
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2.2 What is a spreadsheet? |
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41 | (1) |
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2.3 Introduction to Excel |
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42 | (20) |
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2.4 Built in mathematical functions |
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62 | (2) |
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2.5 Built in statistical functions |
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64 | (4) |
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68 | (2) |
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70 | (7) |
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77 | (7) |
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84 | (6) |
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84 | (6) |
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90 | (56) |
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90 | (1) |
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91 | (2) |
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3.3 Probability distributions |
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93 | (5) |
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3.4 Distributions of real data |
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98 | (3) |
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3.5 The normal distribution |
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101 | (10) |
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3.6 From area under a normal curve to an interval |
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111 | (8) |
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3.7 Distribution of sample means |
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119 | (2) |
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3.8 The central limit theorem |
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121 | (5) |
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126 | (7) |
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3.10 The log-normal distribution |
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133 | (2) |
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3.11 Assessing the normality of data |
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135 | (2) |
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3.12 Population mean and continuous distributions |
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137 | (2) |
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3.13 Population mean and expectation value |
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139 | (1) |
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140 | (6) |
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140 | (6) |
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146 | (22) |
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146 | (1) |
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4.2 The binomial distribution |
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146 | (11) |
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4.3 The Poisson distribution |
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157 | (8) |
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165 | (3) |
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165 | (3) |
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5 Measurement, error and uncertainty |
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168 | (58) |
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168 | (3) |
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5.2 The process of measurement |
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171 | (3) |
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174 | (2) |
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5.4 Precision and accuracy |
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176 | (1) |
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5.5 Random and systematic errors |
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177 | (1) |
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178 | (11) |
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5.7 Uncertainty in measurement |
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189 | (10) |
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5.8 Combining uncertainties |
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199 | (9) |
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208 | (5) |
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5.10 Relative standard uncertainty |
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213 | (1) |
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5.11 Coping with outliers |
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214 | (4) |
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218 | (3) |
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221 | (5) |
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221 | (5) |
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226 | (71) |
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226 | (1) |
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6.2 The equation of a straight line |
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227 | (13) |
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6.3 Excel's LINEST() function |
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240 | (3) |
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6.4 Using the line of best fit |
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243 | (9) |
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6.5 Fitting a straight line to data when random errors are confined to the x quantity |
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252 | (1) |
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6.6 Linear correlation coefficient, r |
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253 | (8) |
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261 | (5) |
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266 | (4) |
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6.9 Transforming data for least squares analysis |
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270 | (7) |
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6.10 Weighted least squares |
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277 | (7) |
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284 | (13) |
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285 | (12) |
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297 | (38) |
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297 | (1) |
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7.2 Extending linear least squares |
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298 | (2) |
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7.3 Formulating equations to solve for parameter estimates |
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300 | (2) |
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302 | (6) |
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7.5 Fitting equations with more than one independent variable |
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308 | (4) |
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7.6 Standard uncertainties in parameter estimates |
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312 | (4) |
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316 | (2) |
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7.8 Coefficients of multiple correlation and multiple determination |
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318 | (2) |
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7.9 Estimating more than two parameters using the LINEST() function |
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320 | (2) |
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7.10 Choosing equations to fit to data |
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322 | (5) |
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327 | (8) |
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328 | (7) |
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8 Non-linear least squares |
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335 | (47) |
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335 | (3) |
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8.2 Excel's Solver add-in |
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338 | (14) |
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8.3 More on fitting using non-linear least squares |
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352 | (6) |
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8.4 Weighted non-linear least squares |
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358 | (8) |
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366 | (4) |
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370 | (12) |
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371 | (11) |
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382 | (46) |
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382 | (1) |
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383 | (9) |
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9.3 Comparing χ with μ0 when sample sizes are small |
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392 | (2) |
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9.4 Significance testing for least squares parameters |
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394 | (3) |
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9.5 Comparison of the means of two samples |
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397 | (8) |
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9.6 Comparing variances using the F test |
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405 | (5) |
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9.7 Comparing expected and observed frequencies using the Χ2 test |
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410 | (8) |
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418 | (5) |
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423 | (5) |
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423 | (5) |
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10 Data Analysis tools in Excel and the Analysis ToolPak |
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428 | (16) |
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428 | (1) |
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10.2 Activating the Data Analysis tools |
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429 | (2) |
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10.3 Anova: Single Factor |
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431 | (1) |
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432 | (1) |
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10.5 F-test two-sample for variances |
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433 | (1) |
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10.6 Random Number Generation |
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434 | (1) |
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435 | (4) |
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439 | (1) |
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440 | (3) |
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443 | (1) |
Appendix 1 Statistical tables |
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444 | (9) |
Appendix 2 Propagation of uncertainties |
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453 | (2) |
Appendix 3 Least squares and the principle of maximum likelihood |
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455 | (6) |
Appendix 4 Standard uncertainties in mean, intercept and slope |
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461 | (5) |
Appendix 5 Introduction to matrices for least squares analysis |
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466 | (5) |
Appendix 6 Useful formulae |
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471 | (4) |
Answers to exercises and end of chapter problems |
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475 | (27) |
References |
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502 | (4) |
Index |
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506 | |