Index. Cambridge University Press Data Analysis for Physical Scientists: Featuring Excel Les Kirkup Index More information

Size: px

Start display at page:

Download "Index. Cambridge University Press Data Analysis for Physical Scientists: Featuring Excel Les Kirkup Index More information"

Giles Gardner
5 years ago
Views:

1 χ 2 distribution, 410 χ 2 test, 410, 412 degrees of freedom, 414 accuracy, 176 adjusted coefficient of multiple determination, 323 AIC, 324 Akaike s Information Criterion, 324 correction for small data sets, 325 Akaike s weights, 326 alternate hypothesis, 384 analysis of variance, 418 Analysis ToolPak, 428 correlation, 432 covariance, 441 exponential smoothing, 441 F test, 433 Fourier analysis, 442 moving average, 442 random number generation, 434 rank and percentile, 442 regression, 435 sampling, 443 single factor Anova, 431 t tests, 439 two factor Anova, 441 ANOVA, 418 principle, 419 AVEDEV(), 68 AVERAGE(), 57, 66, 67 Bessel correction, 29 best line through points using least squares, 230 BINOM.DIST(), 150 cumulative probability, 150 binomial distribution, 148 calculation of probabilities, 148 mean and standard deviation, 150 normal distribution approximation, 153 Bureau International des Poids et Mesures, 7 calculator, 233 central limit theorem, 121 Chauvenet s criterion, 215, 267 CHISQ.INV.RT(), 417 combinations, 148 combined standard uncertainty, 202 combined variance, 202 combining uncertainties, 199 confidence interval, 122, 189 CONFIDENCE.NORM(), 125 CONFIDENCE.T(), 132 continuous random variable, 96 CORREL(), 258 coverage factor, 208, 209 coverage interval, 189 intercept, 239 slope, 239 criterion Chauvenet, 215 data comparing fitted equations, 323 distributions, 90, 146 presentation, 13 transformation, 270 variability, 214 data distributions, 90 data rejection, 266 data transformation consequences, 275 design experimental, 4 deviations, 230 distribution 506

2 INDEX 507 χ 2, 410 binomial, 148 F, 405 log-normal, 133 normal, 101 of real data, 98 of sample means, 119 Poisson, 157 rectangular, 196 t, 126 triangular, 198 dynamic effects, 185 effective number of degrees of freedom, 210, 211 equation of a straight line, 227 error, 174 calibration, 181 experimental, 33, 174 gain, 181 loading, 183 offset, 181 parallax, 179 random, 33, 177, 178 reaction time, 180 resolution, 178 systematic, 34, 177, 180 Type I and Type II, 392 error bars, 19 evaluation of uncertainty Type A, 191, 192 Type B, 191, 195 event, 91 Excel absolute referencing, 52 adding a trendline, 72 adding error bars, 73 Add-ins, 77 Analysis ToolPak, 428 auditing formulae, 60 AVEDEV(), 68 AVERAGE(), 57, 66 backstage view, 44 BINOM.DIST(), 150 calculating r, 258 charts, 70 CHISQ.INV.RT(), 417 CONFIDENCE.NORM(), 125 CONFIDENCE.T(), 132 CORREL(), 258 data analysis tools, 77 descriptive statistics, 82 entering data, 45 entering formulae, 48 Excel 2010, 42 F.INV.RT(), 409 getting started, 42 HARMEAN(), 68 histograms, 78 introduction, 40, 42 LINEST(), 240 mathematical functions, 62 matrices, 302 MAX(), 65 MEDIAN(), 66 MIN(), 65 MINVERSE(), 302 MMULT(), 303 MODE.SNGL(), 66 naming cells, 53 NORM.DIST(), 104 NORM.INV(), 116 NORM.S.DIST(), 109 NORM.S.INV(), 118 operator precedence, 54 POISSON.DIST(), 162 precision of numbers, 46 presentation options, 68 range of numbers, 46 referencing cells, 51 Ribbon, 43 relative referencing, 51 saving data, 45 scatter chart, 70 Solver, 338 spreadsheet readability, 54 statistical functions, 64 STDEV.P(), 68 STDEV.S(), 68 SUM(), 65 T.TEST(), 400, 404 TDIST.2T(), 130 TINV.2T(), 130 TRANSPOSE(), 307 Trendline, 235 trigonometrical functions, 63 troubleshooting, 56 weighted least squares, 284 Worksheets and Workbooks, 44 x y graph, 70 expanded uncertainty, 190, 208 expectation value, 139 experimental error, 33 experimental design, 4 experimentation scientific, 2 F distribution, 405 F test, 407 F.INV.RT(), 409 fitting equations to data, 322 formulae, 466, 471 global minimum, 353 graph logarithmic, 20 x y, 18 grouped frequency distribution, 15 Guide to the Expression of Uncertainty in Measurement, 170, 190 GUM, 170

3 508 INDEX HARMEAN(), 68 histogram using Excel, 78 histograms, 14 hypersurface, 336 hypothesis testing, 383 analysis of variance, 418 chi-squared test, 410, 412 comparing means, 397 F test, 407 t test for paired samples, 402, 404 identity matrix, 468 input quantities, 170 intercept of a straight line, 228 International Vocabulary of Metrology, 6, 170 inverse matrix, 468 Johnson noise, 179 least squares, 226 coverage intervals, 314 errors in x quantity only, 252 extended, 298 intermediate calculations, 237 local minimum, 344 matrices, 466 more than one independent variable, 308 multiple variables, 309 non-linear, 335 parameter estimates, 300 polynomial fit, 305 principle of maximum likelihood, 455 significance testing, 394 significant figures, 237 uncertainties in parameter estimates, 312 unweighted, 230 weight matrix, 318 weighted, 277, 316 level of confidence, 208 line of best fit use, 243 linear correlation coefficient, r, 253 significance, 259 table of probabilities, 260 LINEST(), 240 local minimum, 344, 352 log-normal distribution, 133 matrices for least squares, 466 using Excel, 302 matrix multiplication, 467 MAX(), 65 mean, 22 weighted, 218 mean deviation, 24 measurand, 170, 171 function of several input quantities, 202 function of single input quantity, 199 measurement, 168 process, 171 uncertainty, 189 median, 22 MEDIAN(), 66 metrology, 5 MIN(), 65 MINVERSE() Excel, 302 MMULT() Excel, 303 MODE.SNGL(), 66 multiple correlation coefficient, 318 multiple determination adjusted coefficient, 323 multiple determination coefficient, 318 multiple regression, 308 non-linear least squares, 335 starting values, 352 weighted, 358 NORM.DIST(), 104 NORM.INV(), 116 NORM.S.DIST(), 109 NORM.S.INV(), 118 normal distribution, 101 normal quantile plot, 135 null hypothesis, 384 outcome, 91, 147 outlier, 14, 214 effect on residuals, 263 p probability of a success, 150 parameter population, 27 parameter estimates coverage intervals, 351 Poisson distribution, 157 applications, 159 normal approximation, 163 standard deviation, 160 Poisson processes, 158 POISSON.DIST(), 162 population, 26 parameters, 27 population mean, 28, 139 continuous distributions, 137 population parameters, 384 populations parameters approximated by sample statistics, 110 precision, 176 predictor, 228 prefixes, 11 principle of maximum likelihood, 232 probability, 91 calculations, 98 distributions, 93 independent events, 93

4 INDEX 509 mutually exclusive events, 92 rules, 92 probability distribution binomial, 148 normal, 101 Poisson, 157 propagation of uncertainties, 453 r, 253 calculating using Excel, 258 significance, 259 table of probabilities, 260 random error, 33, 177, 178 definition, 33 regression, 227 repeatability, 34 reproducibility, 34 residual heteroscedastic, 358 residuals, 230 definition, 261 effect of an outlier, 263 effect of fitting incorrect equation, 262 effect of incorrect weighting, 263 ideal distribution, 262 plots, 262 standardised, 265 sum of squares, 232 response, 228 Ribbon, 43 Home, 43 rounding numbers effect of, 233 s approximation, 32 distribution, 131 sample, 26 statistics, 29 sample space, 91 sample statistics, 384 scientific experimentation, 2 scientific notation, 11 sensitivity coefficient, 200, 202 SI, 7 base units, 8 prefixes, 11 system, 7 units, 7 significance testing comparing two means, 397 significance tests, 382 significant figures, 12 slope of a straight line equation, 232 Solver, 338 automatic scaling, 367 best estimates of parameters, 361 dialog box, 342 example of use, 338 limitations, 347 options, 367 results, 370 weighted fitting, 359 specification of instruments, 181 spreadsheet, 35 what is it?, 41 standard deviation, 24, 193 distribution, 131 weighted, 281 which to use?, 30 standard error, 193 approximation, 124 of the sample mean, 122 standard normal distribution, 106 standard uncertainty, 193 combined, 202 mean and weighted mean, 461 relative, 213 standardised residuals, 265 standards, 6, 10 statistics sample, 29 STDEV.P(), 68 STDEV.S(), 68 Sturge s formula, 16 sum of squares of residuals, 232 system first order, 186 zero order, 186 systematic error, 34, 177 t distribution, 126 t test paired samples, 402 T.TEST(), 400 TDIST.2T(), 130 TEC, 256 tests of significance, 382 one tailed test, 390 small sample sizes, 392 two tailed tests, 390 thermoelectric cooler, 256 TINV.2T(), 130 traceability, 10 TRANSPOSE(), 307 Trendline, 235 trial, 91, 147 true value, 28, 174 Type A and Type B evaluations of uncertainty combined, 204 Type A evaluation of uncertainty, 191, 192 Type B evaluation of uncertainty, 191, 195 standard uncertainty when distribution is rectangular, 196 standard uncertainty when distribution is triangular, 198 uncertainty, 169 expanded, 190, 208 intercept, 235

5 510 INDEX uncertainty, (cont.) significant figures, 193 slope, 235 uncertainty in parameters functions of a and b, 244 uncertainty in slope and intercept weighted, 280 units, 6, 7 arbitrary, 237 unweighted least squares, 230 useful formulae, 466, 471 variable dependent, 18, 228 independent, 18, 228 predictor and response, 18 variance, 24 combined, 202 VIM, 6, 170 weighted mean standard uncertainty, 219 weighted standard deviation, 281 Welch Satterthwaite formula, 209 x y graphs, 18 z test statistic, 385

Data Analysis. with Excel. An introduction for Physical scientists. LesKirkup university of Technology, Sydney CAMBRIDGE UNIVERSITY PRESS

Data Analysis. with Excel. An introduction for Physical scientists. LesKirkup university of Technology, Sydney CAMBRIDGE UNIVERSITY PRESS Data Analysis with Excel An introduction for Physical scientists LesKirkup university of Technology, Sydney CAMBRIDGE UNIVERSITY PRESS Contents Preface xv 1 Introduction to scientific data analysis 1 1.1