Exploratory data analysis, John W. Tukey

The approach in this introductory book is that of informal study of the data. Methods range from plotting picture-drawing techniques to rather elaborate numerical summaries. Several of the methods are the original creations of the author, and all can be carried out either with pencil or aided by hand-held calculator. Cover......Page 1 1 . Break table for two-decimal logs......Page 2 2. Break table for (square) roots......Page 3 3. Main break table--digits of negative reciprocals......Page 4 Title page......Page 5 Copyright......Page 6 Dedication......Page 7 Preface......Page 9 To the Student or Teacher......Page 14 Contents......Page 16 1A Quantitative detective work......Page 21 Comments about the index page......Page 22 1B Practical arithmetic......Page 23 1C Scratching down numbers......Page 26 1D Doing better with stem-and-leaf......Page 27 1E Using the right number of stems......Page 31 1F How to count by tallying......Page 36 1G What does it mean to "feel what the data are like"?......Page 39 1H How far have we come?......Page 40 1K How to use stem-and-leaf to pick up additional information (optional technique)......Page 43 1P Additional problems......Page 45 2 SCHEMATIC SUMMARIES (pictures and numbers)......Page 47 2A Extremes and median......Page 49 2B Hinges and 5-number summaries......Page 52 2C Box-and-whisker plots......Page 59 2D Fences, and outside values......Page 63 2E Schematic plots......Page 67 2F Pros and cons; the Rayleigh example......Page 69 2G Eighths, sixteenths, etc.......Page 73 2H How far have we come?......Page 75 3 EASY RE-EXPRESSION......Page 77 3A Logarithms = logs......Page 79 3B Quick logs......Page 81 3C Comparisons of two batches......Page 84 3D Quick roots and quick reciprocals......Page 89 3E Looking quickly......Page 99 3F Counted data......Page 103 3G Relation among powers and logs (optional)......Page 106 3H How far have we come?......Page 112 3P Additional problems......Page 113 4 EFFECTIVE COMPARISON (including well-chosen expression)......Page 117 4A Alternative forms of display of summaries......Page 119 4B Comparing several batches (continued)......Page 122 4C A more extensive example......Page 125 4E Adjustments, rough and exact......Page 130 4F Residuals......Page 133 4H How far have we come?......Page 135 4P Additional problems......Page 136 5 PLOTS OF RELATIONSHIP......Page 145 5A How to plot y against x......Page 146 5B Looking at subtraction......Page 151 5C Subtracting straight lines......Page 155 5D Plotting the population of the U.S.A.......Page 161 5E Plotting the ratio of births to deaths......Page 168 5F Untilting defines "tilt"......Page 174 5H How far have we come?......Page 176 5P Additional problems......Page 177 6 STRAIGHTENING OUT PLOTS (using three points)......Page 189 6A Looking at three points......Page 191 6B Re-expressing y alone......Page 192 6C Re-expressing x alone......Page 195 6D A braking example......Page 201 6E The vapor pressure of H2O......Page 207 6F Re-expressing the second variable......Page 211 6G Wise change of origin as a preliminary......Page 213 6H How far have we come?......Page 217 6P Additional problems......Page 219 7 SMOOTHING SEQUENCES......Page 225 7A Medians of 3......Page 230 7B Eye resmoothing......Page 234 7C Looking ahead......Page 236 7D Copying-on--and more, usually.......Page 241 7E Blurring the smooth--and setting the fences......Page 243 7F Splitting peaks and valleys......Page 247 7G Hanning......Page 251 7H How far have we come?......Page 255 7I Breaking a smooth......Page 257 7J Choice of expression......Page 267 7K A two-section example......Page 279 7M How much more may we have learned?......Page 284 8A Parallel schematic plots......Page 285 8B Smoothing the cross-medians......Page 294 8C Smoothing broken hinges......Page 296 8D Dealing with the two questions......Page 299 8E Wandering schematic plots......Page 303 8F A more demanding example: Governor's salary and bank deposits......Page 307 8G Further questions/analysis in the example......Page 318 8H How far have we come?......Page 326 8I The need to smooth both coordinates (optional)......Page 327 9A E-traces and D-traces......Page 329 9B Simple delineation--Twin Riyers again......Page 331 9C Reduced and schematic delineations......Page 333 9D What our schematic plots and delineations have missed......Page 339 9E Three variables at once--or more......Page 341 9H How far have we come?......Page 349 10 USING TWO-WAY ANALYSES......Page 351 1OA Two-way residuals; row-PLUS-column analysis......Page 352 1OB The row-PLUS-column fit......Page 357 10C Some points of technique......Page 363 10D Row-TIMES-column analysis......Page 364 10E Looking at row-PLUS-column fits and their residuals......Page 369 10F Fitting one more constant......Page 372 1OG Converting PLUS to TIMES; re-expression......Page 378 10H How far have we come?......Page 380 11 MAKING TWO-WAY ANALYSES......Page 382 11A Taking medians out......Page 383 11B Alternative organizations of the arithmetic......Page 392 11C Making the core of a two-way plot......Page 394 11D Going on with the residuals......Page 398 11E Coding residuals; condensing fits and residuals......Page 402 11F We can combine!......Page 410 11G Guidance for expression......Page 416 11H How far have we come?......Page 419 11I Exploring beyond PLUS-one (extends Chapter 10)......Page 421 11J Taking out any summary......Page 424 11K An example of re-expression--city killings......Page 428 11L An unusual fit......Page 435 11M How much more may we have learned?......Page 439 12 ADVANCED FITS......Page 440 12A PLUS-one fits......Page 441 12B Pictures for "-PLUS-one" fits......Page 444 12C Making those pictures......Page 448 12D Sometimes we can have parallel-line plots, still......Page 451 12E More extended fits......Page 453 12F Simplification is sometimes possible......Page 458 12H How far have we come?......Page 461 13A Three- and more-way analyses: Arrangement and tagging......Page 463 13B An analysis of the psychological example......Page 468 13C Making three-way analyses......Page 472 13D Three-way re-expression......Page 478 13E More about the example......Page 482 13H How far have we come?......Page 485 14 LOOKING IN TWO OR MORE WAYS AT BATCHES OF POINTS......Page 486 14A Coordinates and level traces......Page 487 14B Different middle traces for the same slices......Page 490 14C An explanation......Page 495 14D Changing the slicing coordinate......Page 496 14E What matters?......Page 501 14F Rematching and strength of relationship......Page 502 14H How far have we come?......Page 511 14I The ubiquity of medians (optional section)......Page 512 15 COUNTED FRACTIONS......Page 514 15A Started counts and counted fractions......Page 516 15B Three matched scales for counted fractions......Page 518 15C Quicker calculation......Page 522 15D Examples where careful expression clearly pays off......Page 528 15E Double folding--the 2 x 2 case......Page 533 15F Double folding--Iarger cases......Page 536 15G Easy froots and flogs with a slide rule (optional)......Page 540 15H How far have we come?......Page 542 16A Reroughing......Page 543 16B Some examples......Page 546 16C If we want things still smoother......Page 551 16D Further possibilities......Page 554 16H How far have we come?......Page 562 17A Root smooth and root rough'......Page 563 17B Counts of basic counts......Page 570 17C Fitting to smoothed roots......Page 575 17D Com borers, wheat prices, and Student's simulations......Page 581 17E Bins of unequal width......Page 590 17F Double roots......Page 596 17G Cautionary examples......Page 602 17H How far have we come?......Page 607 18 PRODUCT-RATIO PLOTS......Page 608 18A Sizes and counts......Page 609 18B Product-ratio analysis......Page 614 18C Forcing the unusual to be noticed......Page 618 18D Comparisons between collections......Page 622 18E Looking at the smallest basic count......Page 624 18F When zeros are counted......Page 625 18G Under the microscope......Page 628 18H How far have we come?......Page 632 19 SHAPES OF DISTRIBUTION......Page 634 19A Looking at shapes of distribution......Page 636 19B The Gaussian reference......Page 643 19C Using letter values to look at shapes of distribution......Page 646 19D Pushback technique (optional section)......Page 657 19H How far have we come?......Page 664 20 MATHEMATICAL DISTRIBUTIONS......Page 666 20A Binnings vs. distributions......Page 668 20B Densities for distributions vs. densities for binnings......Page 671 20C Tables and pictures comparing two sets of shapes of distributions......Page 674 20H How far have we come?......Page 681 21 POSTSCRIPT......Page 682 21A Our relationship to the computer......Page 683 21B What has been omitted?......Page 684 21C How should the past chapters look different?......Page 685 21D What have we been introduced to?......Page 686 GLOSSARY......Page 687 ALPHABETICAL INDEX......Page 697 4. Pluralities, folded roots, folded logarithms......Page 709 5. Values of log_e sqrt(count + 1/6) ......Page 710 6. Values of sqrt(count + 1/6) ......Page 711 . 1 Scratching Down Numbers (stem-and-leaf), 1 Comments about the page index, 2 1A Quantitative detective work, 1 1B Pratical arithmetic, 3 1C Scratching down numbers, 6 1D Doing better with setm-and-leaf, 7 1E Using the right number of stems, 11 1F How to count by tallying, 16 1G What does it mean to "feel what the data are like"?, 19 1H How far have we come? 1K How to use stem-and-leaf to pick up additional information (optimal technique), 23 1P Additional problems, 25 . 2 Schematic Summaries (pictures and numbers), 27 2A Extremes and median, 29 2B Hinges and 5-number summaries, 32 2C Box-and-wisker plots, 39 2D Fences, and outside values, 43 2E Schematic plots, 47 2F Pros and cons; the Rayleigh example, 49 2G Eights, sisteenths, etc., 53 2H How far hve we come?, 55 . 3 Easy Re-Expression, 57 3A Logarithms = logs, 59 3B Quick logs, 61 3C Comparisons of two batches 64 3D Quick roots and quick reciprocals, 69 3E Looking quickly, 79 3F Counted data, 83 3G Relation among powers and logs (optional), 86 3H How far have we come?, 92 3K How to think about logs (background), 93 3P Additional problems, 93 . 4 Effective Comparison (including well-chosen expression), 97 4A Alternative forms of display of summaries, 99 4B Comparing several batches (continued), 102 4C A more extensive example, 105 4D The meaning of comparison, 110 4E Adjustments, rough and exact, 110 4F Residuals, 113 4H How far have we come?, 115 4P Additional problems, 116 . 5 Plots of Relationship, 125 5A How to plot y against x, 126 5B Looking at subtraction, 131 5C Subtracting straight lines, 135 5D Plotting the population of the U.S.A., 141 5E Plotting the ratio of births to deaths, 148 5F Untilting defines "tilt", 157 5H How far have we come?, 156 5P Additional problems, 157 . 6 Straight Out Plots (using three points), 169 6A Looking at three points, 171 6B Re-expressing y alone, 172 6C Re-expression x alone, 175 6D A breaking example, 181 6E The vapor pressure of H2O, 187 6F Re-expressing the second variable, 191 6G Wise change of origin as a preliminary, 193 6H How far have we come?, 197 6P Additional problems, 199 . 7 Smoothing Sequences, 205 7A Medians of 3, 210 7B Eye resmoothing, 214 7C Looking ahead, 216 7D Copyong-on- - and more, usually, 221 7E Blurring the smooth--and setting the fences, 223 7F Splitting peaks and valleys, 227 7G Hanning, 231 7H How far have we come?, 235 . 7+ Optional Sections for Chapter 7, 237 7I Breaking a smooth, 237 7J Choice of expression, 247 7K A two-section example, 259 7M How much more may we have learned?, 264 . 8 Parallel and Wandering Schematic Plots, 265 8A Parallel schematic plots, 265 8B Smoothing the cross-medians, 274 8C Smoothing broken hihges, 276 8D Dealing with the two questions, 279 8E Wandering semantic plots, 283 8F A more demanding example: Governor's salary and bank deposits, 287 8G Further questions/analysis in the example, 298 8H How far have we come?, 306 8I The need to smooth both coordinates (optional), 307 . 9 Delineations of Batches of Points, 309 9A E-traces and D-traces, 309 9B Simple dileneation - - Twin Riyers again, 311 9C Reduced and schematic delineations, 313 9D What our schematic plots and delineations have missed, 319 9E Threee variables at once - - or more, 321 9H How far have we come?, 329 . 10 Using Two-Way Analysis, 331 10A Two-way risiduals; row-PLUS-column analysis, 332 10B The row-PLUS-column fit, 337 10C Some points of technique, 343 10D Row-TIMES-column analysis, 344 10E Looking at row-PLUS-column fits and their residuals, 349 10F Fitting one more constant, 352 10G Converting PLUS to TIMES; re-expression, 358 10H How far have we come?, 360 . 11 Making Two-Way Analyses, 362 11A Taking medians out, 363 11B Alternative organizations of the arithmetic, 372 11C Making the core of a two-way plot, 374 11D Going on with the residuals, 378 11E Coding risiduals; condensing fits and residuals, 382 11F We can combine!, 390 11G Guidance for expression, 396 11H How far have we come?, 399 . 11+ Optional Sections for Chapters 10 and 11, 401 11I Exploring beyond PLUS-one (extends Chapter 10), 401 11J Taking out any summary, 404 11K An example of re-expresssion - - city killings, 408 11L An unusual fit, 415 11M How much more may we have learned?, 419 . 12 Advanced Fits, 420 12A PLUS-one fits, 421 12B Picutres for "-Plus-one" fits, 424 12C Making those pictures, 428 12D Sometimes we can have parallel-line plots, still, 431 12E More extended fits, 438 12F Simplification is sometimes possible, 438 12H How far have we come?, 441 . 13 Three-Way Fits, 443 13A Three- and more-way analyses: Arrangement and tagging, 443 13B An analysis of the psychological example, 448 13C Making three-way analysis, 452 13D Three-way re-expression, 458 13E More about the example, 462 13H How far have we come?, 465 . 14 Looking in Two or More Ways at Batches of Points, 466 14A Coordinates and level traces, 467 14B Different middle traces for the same slices, 470 14C An explanation, 475 14D Changing the slicing coordinate, 476 14E What matters? 14F Rematching and strength of relationship, 482 14H How far have we come?, 491 14I The ubiquity of medians (optional section), 492 . 15 Counted Fractions, 494 15A Started counts and counted fractions, 496 15B Three matched scales for counted fractions, 498 15C Quicker calculations, 502 15D Examples where careful expression clearly pays off, 508 15E Double Folding — — the 2 x 2 case, 513 15F Double folding — — larger cases, 516 15G Easy froots and flogs with a slide rule (optional), 520 15H How far have we come?, 522 . 16 Better Smoothing, 523 16A Reroughing, 523 16B Some examples, 526 16C If w want things still smother, 531 16D Further possibilities, 534 16H How far have we come?, 542 . 17 COUNTS in BIN after BIN, 543 17A Root smooth and root rough, 453 17B Counts of basic counts, 550 17C Fitting to smoothed roots, 555 17D Corn borers, wheat prices, and Student's simulations, 561 17E Bins of unequal width, 570 17F Double roots, 576 17G Cautionary examples, 582 17H How far have we come?, 587 . 18 Product-Ratio Plots, 588 18A Sizes and counts, 589 18B Product-ratio analysis, 594 18C Forcing the unusual to be noticed, 598 18D Comparisons between collections, 602 18E Looking at the smallest basic count, 604 18F When zeros are counted, 605 18G Under the microscope, 608 18H How far have we come?, 612 . 19 Shapes of Distributions, 614 19A Looking at shapes of distribution, 616 19B The Gaussian reference, 623 19C Using letter values to look at shapes of distribution, 626 19D Pushback technique (optinal section), 637 19H How far have we come?, 644 . 20 Mathematical Distributions, 646 20A Binnings vs. distributions, 648 20B Densities for distributions vs. densities for binnings, 651 20C Tables and pictures comparing two sets of shapes of distributions, 654 20H How far have we come?, 661 . 21 Postscript, 662 21A Our relationship to the computer, 663 21B What as been omitted?, 664 21C How should the past chapters look different?, 665 21D What have we been introduced to?, 666 Glossary, 667 Index to Reference Tables, 677 Frontpapers 1 Break table for two-decimal logs 2 Break table for (square) roots 3 Main break table— —digits of negative reciprocals Rearpapers 4 Pluralities, folded roots, folded logarithms 5 Value of loge √(count + 1/6) 6 Values of √(count + 1/6) Scratching Down Numbers (stem-and-leaf) -- Schematic Summaries (pictures And Numbers) -- Easy Re-expression -- Effective Comparison (including Well-chosen Expression) -- Plots Of Relationship -- Straightening Out Plots (using Three Points) -- Smoothing Sequences -- Optional Sections For Chapter 7 -- Parallel And Wandering Schematic Plots -- Delineations Of Batches Of Points -- Using Two-way Analyses -- Making Two-way Analyses -- Optional Sections For Chapters 10 And 11 -- Advanced Fits -- Three-way Fits -- Looking In Two Or More Ways At Batches Of Points -- Counted Fractions -- Better Smoothing -- Counts In Bin After Bin -- Product-ration Plots -- Shapes Of Distribution -- Mathematical Distributions -- Postscript. John W. Tukey. On Spine: Eda. Includes Index. Includes Bibliographical References (page 666) And Index.