BooksBox, Hunter and Hunter · 1978
Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building
- Matches
- Very close
- Close
- Differs
Factorial gives the book's answers, with a few differences. Where they differ, this page says why: some are misprints in the book, and for some the reason is not known yet.
Examples
Each example, and how closely Factorial gives its answers.
Pages 1 to 99
- An industrial experiment: 10 batches by the standard method A, then 10 by the modified method BExample · pp. 22-23, 31-37, 41, 51-54, 72-86Close
- Production record of 210 consecutive batch yields by the standard process, the external reference for the plant trialExample · pp. 32-36, 51-52, 62-63, 73-75, 585-590Very close
- Cell growth rate, standard and new preparation of a specimen (Exercises 2.4, 2.13 and 3.11)Exercise · pp. 38, 53, 86Matches
- Hog-corn price ratiosExercise · p. 42Matches
- Times for 10 rats to complete a mazeExercise · p. 42Matches
- Lift of an airfoil on successive wind-tunnel trialsExercise · p. 42Misprint found
- Litres of N normal reagent to titrate Q grams of a substanceExercise · p. 42Matches
- Fuel consumption of five cars of one make and ageExercise · p. 51Matches
- A patient's temperature, three readings before and three after a drug (Exercises 2.14 and 3.12)Exercise · pp. 53, 86Misprint found
- Two methods, 4 and 5 runs (Exercises 3.6 and 3.8)Exercise · pp. 75, 78Matches
- Two methods, 5 and 3 runs (Exercises 3.7 and 3.9)Exercise · pp. 75, 78Matches
- Two methods, 5 and 4 runs (Exercise 3.10)Exercise · p. 78Close
- Tomato yields: 11 plants in a row, 5 given the standard fertilizer A and 6 the modified B, assigned at randomExample · pp. 93-97, 115-116Close
- Wear of shoe soles: 10 boys each wore one sole of material A and one of B, the foot for A chosen by a coinExample · pp. 97-101, 110-114Differs
Pages 100 to 199
Pages 200 to 299
- Penicillin yield: four process variants run in random order within each of five blends of corn steep liquorExample · pp. 209-226Close
- Pollutant levels by three methods and two technicians (Exercises 7.1 and 7.2, data set (a))Exercise · pp. 211-213Matches
- Performance of three brands in four laboratories (Exercises 7.1 and 7.2, data set (b))Exercise · pp. 211-213Matches
- Survival times of animals given three poisons and four treatments, four animals to each combination (Box and Cox 1964)Example · pp. 228-240Differs
- Reduction in oxides of nitrogen: four additives tried by four drivers in four cars, a 4 x 4 Latin squareExample · pp. 245-250Matches
- Breaking strength of synthetic yarn: three draw ratios on three spinneret heads over 12 doffs, a 3 x 3 Latin square in four replicatesExample · pp. 250-255, 266-268Not yet explained
- Weight loss of four cloths on a Martindale wear tester: a 4 x 4 hyper-Graeco-Latin square in runs, positions, emery papers and holders, replicated twiceExample · pp. 255-258Very close
- Weight loss of seven cloths in seven runs of four on a wear tester: a balanced incomplete block design that is also a Youden square in machine positionsExample · pp. 258-260, 275-279Very close
- Horizontal tension tests of a standard wire in three laboratories (Problem 6 of Part II)Exercise · pp. 282-283Matches
Pages 300 to 399
- Pilot plant: yield at two temperatures, two concentrations and two catalysts, each yield the average of two runsExample · pp. 307-324, 342-344Matches
- Yield of popcorn: brand, ratio of popcorn to oil and batch size, with four runs at the centre (Exercises 10.3, 10.6 and 10.9)Exercise · pp. 316, 321, 324Matches
- Pilot plant: the 2^3 factorial run twice, sixteen runs in random orderExample · pp. 317-321Matches
- Yield of lima beans: depth of planting, watering and type of bean, three replications (Exercises 10.4 and 10.5)Exercise · pp. 320-321, 324Matches
- Process development: conversion against catalyst charge, temperature, pressure and concentration, an unreplicated 2^4Example · pp. 324-334Matches
- Judged quality of sound: brand of tape deck, bass, treble and synthesizer (Exercise 10.11)Exercise · p. 328Matches
- Rate of advance of a stone drill: load, flow, speed and type of mud (Daniel 1976), with a Box-Cox transformationExample · pp. 334-336Differs
- Blocking arrangements for 2^k factorial designs, k = 3 to 7, in blocks of 2 to 64 runspp. 336-350Differs
- Screening storm water overflows, phase (a): collar and horizontal screen mesh and flow rate against solids removedCase study · pp. 354-360Matches
- Evolutionary operation on a petrochemical plant, phase I: reflux ratio and recycle/purge ratio against cost per tonCase study · pp. 362-365Differs
- Evolutionary operation on a petrochemical plant, phase IICase study · pp. 362-365Matches
- Evolutionary operation on a petrochemical plant, phase IIICase study · pp. 362-365Matches
- Evolutionary operation on a polymer latex unit, phase I: addition time and stirring rate against optical densityCase study · pp. 365-368Misprint found
- Evolutionary operation on a polymer latex unit, phase IICase study · pp. 365-368Matches
- Evolutionary operation on a polymer latex unit, phase IIICase study · pp. 365-368Matches
- Evolutionary operation on a polymer latex unit, phase IVCase study · pp. 365-368Matches
- Evolutionary operation on a polymer latex unit, phase VCase study · pp. 365-368Matches
- Time to ride a bicycle up a hill: seat height, generator and tire pressure, each setup run twice (a student's experiment)Case study · pp. 368-372Matches
- Reactor: percent reacted against feed rate, catalyst, agitation, temperature and concentration, a 2^5 factorial and its two half fractionsExample · pp. 376-389Misprint found
- Time to cycle up a hill against seven variables: two 2^(7-4) fractions of eight runs each (hypothetical data)Example · pp. 390-397, 409-411Differs
- Injection molding: shrinkage against eight variables, a 2^(8-4) resolution IV fraction, then four runs to separate an interaction stringExample · pp. 398-416Matches
- Plackett and Burman design for 11 factors in 12 runsp. 398Matches
Pages 400 to 499
- Two-level fractional factorial designs for 3 to 11 variables in 4 to 128 runs, with their generators and resolutionspp. 408-410Matches
- Cast films: a 2^(5-2) fraction (4 = 23, 5 = 123) whose six responses are yes-or-no judgementspp. 419-421Matches
- Stability of a new household product: acid, catalyst, temperature and monomer in a 2^(4-1) fractionExample · pp. 422-424Matches
- Filtration time at a new plant: seven suspected causes in a 2^(7-4) fraction, then its fold-overCase study · pp. 424-429Misprint found
- Sensitivity analysis of an air traffic control simulation: eight factors in a 2^(8-4) fractionCase study · pp. 429-431Misprint found
- Decay of an aerosol: dispersion against age, a straight line through the originExample · pp. 453-461Very close
- Rate of formation of an impurity against monomer and dimer concentration, a plane through the originExample · pp. 462-472Differs
- Inertia welding: breaking strength against velocity, a straight lineExample · pp. 473-478Not yet explained
- Growth rate of rats against the amount of a dietary supplement: a straight line, then a quadraticExample · pp. 480-483, 500-502Misprint found
Pages 500 to 599
- Resiliency: a 2^3 factorial in temperature, pH and water, as executed with settings off planExample · pp. 503-504Matches
- Resiliency: the same eight results credited to the 2^3 as plannedExample · pp. 503-504Matches
- Yield against time and temperature: a 2^2 factorial with three centre points, then three runs along the path of steepest ascentExample · pp. 513-519Misprint found
- Exercise 15.4: the first-order design with two yields changedExercise · p. 518Matches
- Yield against time and temperature near the maximum: a 2^2 with centre points, completed by a star to a composite design in two orthogonal blocksExample · pp. 519-532Misprint found
- Four fitted second-degree equations and their canonical forms: maximum, minimax, stationary ridge and rising ridgepp. 526-532Matches
- Moisture of pigment paste: duplicate tests on duplicate samples of 15 batches, a hierarchical design for components of varianceExample · pp. 571-582Not yet explained
Misprints
Misprints found in the book, by page. Each shows what the book prints and what its own data give.
Variancep. 42
Book 667.50Data 667.90
The variance of these seven values is 667.90; the book prints 667.50, though its s = 25.84 is the root of 667.90
P value: five techniques (d)p. 86
Book 0.15Data 0.06
The t-test on these six readings (t = 2.00 on 4 df) gives 0.058; the book prints 0.15, which does not follow from the data
P value: randomization at the 95% limitsp. 113
Book 25/1024Data 0.0283203
Less 0.14, 29 of the 1024 averages are at least the observed 0.27 (2.8%): 28 above it, and the observed pattern itself; the book counts 25
P value: randomization at the 95% limitsp. 113
Book 19/1024Data 0.0263672
Less 0.68, 27 of the 1024 averages are at most the observed -0.27 (2.6%): 26 below it, and the observed pattern itself; the book counts 19
Ss regressionp. 229
Book 2.2055Data 2.2044
The between-groups sum of squares is 2204.4 (x 1000); the book's 2205.5 carries its treatments sum of squares 922.4, which the data do not give (921.2)
Show the rest
Ms regressionp. 229
Book 0.2005Data 0.2004
The between-groups mean square is 200.4 (x 1000), from 2204.4/11
Ss totalp. 229
Book 3.0062Data 3.0051
The total corrected sum of squares is 3005.1 (x 1000); the book's 3006.2 carries the same 1.1 as its treatments sum of squares
Anova sum sq: treatmentp. 230
Book 0.9224Data 0.9212
The treatments sum of squares is 921.2 (x 1000); the book prints 922.4, though all twelve cell averages it prints in Table 7.14 reproduce from the data
Anova mean sq: treatmentp. 230
Book 0.3075Data 0.3071
The treatments mean square is 307.1 (x 1000), from 921.2/3
Mean: replicate Ip. 256
Book 275.8125Data 267.1250
The replicate averages are swapped: runs R1 to R4 (replicate I) average 267.1250 and R5 to R8 (replicate II) 275.8125, as the book's own run averages give
Mean: replicate IIp. 256
Book 267.1250Data 275.8120
The replicate averages are swapped: runs R1 to R4 (replicate I) average 267.1250 and R5 to R8 (replicate II) 275.8125, as the book's own run averages give
Anova mean sq: runp. 278
Book 16,232.33Data 16232.50
97,394.72/6 is 16,232.45; the book prints 16,232.33 in Table 8D.4 and 16,232.45 in Table 8D.5
Effect: timep. 366
Book 0.2Data -0.1
The four corner averages printed give -0.1 for addition time, -0.1 for stirring rate and 0.9 for the interaction; no arrangement of the four values gives the printed effects, so one of the printed averages or effects is wrong
Effect: stirringp. 366
Book -0.4Data -0.1
The four corner averages printed give -0.1 for addition time, -0.1 for stirring rate and 0.9 for the interaction; no arrangement of the four values gives the printed effects, so one of the printed averages or effects is wrong
Effect: time x stirringp. 366
Book 0.6Data 0.9
The four corner averages printed give -0.1 for addition time, -0.1 for stirring rate and 0.9 for the interaction; no arrangement of the four values gives the printed effects, so one of the printed averages or effects is wrong
Effect: 14p. 378
Book 0.875Data -0.875
The data give -0.875, as the book's own half fraction requires: l14 = 14 + 235 = -0.75 there, and 235 = 0.125; the sign is lost
Effect: 12345p. 378
Book -0.25Data -0.50
The data give -0.5, as the book's own half fraction requires: its average 65.25 is the average 65.5 plus half of 12345
Effect: 6, second fractionp. 395
Book 2.2Data -2.2
The times of Table 12.7 give -2.25 (the breakfast column is +, +, -, -, -, -, +, +); the sign is lost, and Table 12.9 carries the slip
Effect: 6, both fractionsp. 396
Book 1.8Data -0.6
The data give -0.625 (1/2(1.0 - 2.25)); the book uses l'6 = 2.2 with its sign lost, and 1/2(1.0 + 2.2) is 1.6, not the 1.8 printed
Effect: 45, both fractionsp. 396
Book -0.6Data 1.6
The data give 1.625 (1/2(1.0 + 2.25)); the book uses l'6 = 2.2 with its sign lost
Effect: 4, sixteen runsp. 428
Book 2.8Data 2.7
The sixteen runs give 2.71 (1/2(3.175 + 2.25)), and 12, from the same two contrasts, reproduces; 2.8 is a slip
Effect: 6, sixteen runsp. 428
Book 0.1Data -0.1
The sixteen runs give -0.06 (1/2(-3.425 + 3.3)), and 17, from the same two contrasts, reproduces; 0.1 is a slip
Effect: 7, sixteen runsp. 428
Book -4.4Data -4.3
The sixteen runs give -4.31 (1/2(0.525 - 9.15)); the book's -4.4 and its 4.9 for 16 both follow from a second-fraction contrast of -9.3 for -9.15
Effect: 16, sixteen runsp. 428
Book 4.9Data 4.8
The sixteen runs give 4.84 (1/2(0.525 + 9.15)); see 7
Aliases: 13, sorted listp. 431
Book BE, CG, FHData ABCDEG, ABCEFH, ABDH, ABFG, ACDFGH, ADEF, AEGH, BCDF, BCGH, BDEFGH, BE, CDEH, CEFG, DG, FH
37 is not an alias of 13 under the generators 1235, 1246, 1347 and 2348 (47 is, as Table 13.8 prints it); the sorted list misprints 47 as 37
Ms residualp. 467
Book 0.3309Data 0.3327
1.3308/4 is 0.3327; the book prints 0.3309, and its s and standard errors follow from that
Residual std errorp. 467
Book 0.5752Data 0.5768
1.3308/4 is 0.3327; the book prints 0.3309, and its s and standard errors follow from that
Std error: x1p. 468
Book 0.383Data 0.384
1.3308/4 is 0.3327; the book prints 0.3309, and its s and standard errors follow from that
Std error: x2p. 468
Book 0.534Data 0.535
1.3308/4 is 0.3327; the book prints 0.3309, and its s and standard errors follow from that
Anova sum sq: x²p. 483
Book 643.2Data 641.2
The data give 641.2: the book's 643.2 is 2.0 away, and so are its model and lack-of-fit sums; its coefficients and normal equations reproduce, so the slip is in the sums of squares
Ss residualp. 483
Book 43.2Data 45.2
The data give 45.2: the book's 43.2 is 2.0 away, and so are its model and lack-of-fit sums; its coefficients and normal equations reproduce, so the slip is in the sums of squares
Lack of fit fp. 483
Book 0.80Data 0.90
The ratio is 0.90 (6.06/6.75); the book's 0.80 carries the 2.0 by which its residual sum of squares is short
Prediction: t = 100, T = 152p. 522
Book 71.20Data 71.40
The fitted equation gives 71.40 at x1 = 1, x2 = 1.4, and so does the printed equation (15.19) with its rounded coefficients (71.39); the answer prints 71.20
Prediction: largest, Exercise 15.8p. 524
Book 66.86Data 68.86
The largest fitted value, at (+1, +1), is 62.01 + 2.35 + 4.50 = 68.86; the answer misprints it as 66.86
Canonical: origin and linear termp. 532
Book 88.2Data 87.4
The ridge form (Box and Draper's Eq. 11.1.2) of the fit of equation 15.19 has its origin nearest the centre at y0 = 87.37 (87.38 from the rounded coefficients 15.19 prints), a linear term of size 1.31 along the ridge and the ridge 0.63x1 + 0.77x2 + 0.06 = 0, as the library finds; the book's 88.2 does not follow from 15.19, since the offset is fixed by b and the larger eigenvalue wherever the origin sits along the ridge
Canonical: origin and linear termp. 532
Book 2.4Data 1.3
The ridge form (Box and Draper's Eq. 11.1.2) of the fit of equation 15.19 has its origin nearest the centre at y0 = 87.37 (87.38 from the rounded coefficients 15.19 prints), a linear term of size 1.31 along the ridge and the ridge 0.63x1 + 0.77x2 + 0.06 = 0, as the library finds; the book's 2.4 does not follow from 15.19, since the offset is fixed by b and the larger eigenvalue wherever the origin sits along the ridge
Canonical: ridge offsetp. 532
Book 0.33Data 0.06
The ridge form (Box and Draper's Eq. 11.1.2) of the fit of equation 15.19 has its origin nearest the centre at y0 = 87.37 (87.38 from the rounded coefficients 15.19 prints), a linear term of size 1.31 along the ridge and the ridge 0.63x1 + 0.77x2 + 0.06 = 0, as the library finds; the book's 0.33 does not follow from 15.19, since the offset is fixed by b and the larger eigenvalue wherever the origin sits along the ridge
Variance component: batchesp. 577
Book 6.9Data 7.1
The batch component is 7.1 (VB - VS/2 = 21.62 - 14.50); the book's own expression, 21.6 - 28.5/2 - 0.92/4, is 7.1 as well, so 6.9 is a slip
Residual: test 3p. 614
Book 41Data 31
The engineer's fitted equation gives a residual of 30.8; the problem asks the reader to check these calculations, and three of the twelve are wrong
Residual: test 6p. 614
Book 29Data 28
The engineer's fitted equation gives a residual of 27.6; the problem asks the reader to check these calculations, and three of the twelve are wrong
Residual: test 8p. 614
Book -29Data -19
The engineer's fitted equation gives a residual of -19.2; the problem asks the reader to check these calculations, and three of the twelve are wrong
Not yet
Answers the book prints that Factorial cannot compute yet, by what it lacks.
- The crude sum of squares and the correction for the average, which the library's sums about the mean leave outpp. 211, 248, 253 and more
- A model nonlinear in its parameters, η = β1(1 - exp(-β2 x)), which the library does not fitpp. 484, 485 and 487
- The crude sum of squares and the correction for the average, which the library's sums about the mean leave out; 228 and 112 are checkedp. 173
- The crude sum of squares, Σy², which the library's sums about the mean leave out (it reproduces)p. 283
- The crude total, Σy², which the library's sums do not reportp. 460
Show the rest
- Crude sums of squares of the fitted values and data, which the library's sums do not reportp. 465
- Crude sums of squares, about zero, which the library's sums about the mean do not reportp. 481
- The library does not fit (scipy reproduces 213.8 and 0.5473)p. 484
- The cumulative sum of the deviations from target, which no check computes (each reproduces); the library's CUSUM chart works with a reference value and decision interval insteadp. 561
- The correction for the average and the crude total, which the library's sums about the mean do not reportp. 582
- The library reports the stationary point of the fitted quadratic and its eigenvalues, not the ridge (B-canonical) form, whose origin is the point of the ridge nearest the design centre and which carries a linear term along the ridge; for this equation the library's stationary point is at (414, -758) coded with ŷ = -1197, a point of no usep. 530