Design and Analysis of Experiments

Residual: standard order 9p. 196

Book 26.00Data -6.00

A misprint for −6.00: the run is 138 and its cell's mean 144.00, as Table 5.6 prints, and the Student residual −0.267 beside it is that of −6.00

Coefficient: material 2, Temp²p. 213

Book 0.41627Data -0.00566

The quadratic through material 2's cell means has a quadratic coefficient of -0.0056612 per °F²; the printed 0.41627 would bend the curve of Figure 5.18 far outside the data

Coefficient: material 3, Temp²p. 213

Book -0.43218Data -0.01025

The quadratic through material 3's cell means has a quadratic coefficient of -0.010248 per °F²; the printed -0.43218 would bend the curve of Figure 5.18 far outside the data

Coefficient: BC, coded equationp. 249

Book +1.06Data -1.0625

The BC coefficient is −1.06, as the table of coefficients above the equation prints it; the equation drops its sign

Ci high: A-Gapp. 250

Book 28.10Data -28.10

The upper limit is −28.10: the interval −50.81 ± 22.71 lies below zero, as the lower limit −73.52 and the coefficient's t of −4.88 say; the sign is dropped

Anova p: Cp. 260

Book <0.0001Data 0.00312441

The P-value of F = 17.38 on 1 and 8 degrees of freedom is 0.0031, not below 0.0001

Anova p: Dp. 260

Book <0.0001Data 0.000266595

The P-value of F = 38.13 on 1 and 8 degrees of freedom is 0.0003, not below 0.0001

Fitted: (1)p. 260

Book 46.22Data 46.25

The prediction is 46.25, as the next page and its table print it: 70.0625 − 10.8125 − 4.9375 − 7.3125 − 9.0625 + 8.3125

Coefficient: Intercept at x4 = 1p. 262

Book 77.3725Data 77.3750

The intercept with stirring rate at its high level is 70.0625 + 7.3125 = 77.375

Coefficient: Intercept at x1 = 1p. 262

Book 80.8725Data 80.8750

The intercept with temperature at its high level is 70.0625 + 10.8125 = 80.875

Residual std dev: B lowp. 272

Book 0.83Data 0.82

The standard deviation of the eight residuals at B − (−0.94, −0.69, −1.19, 0.56, 0.06, 0.81, −0.69, −1.44) is 0.82

Residual std dev: B −p. 273

Book 0.83Data 0.82

The standard deviation of the eight residuals at B − (−0.94, −0.69, −1.19, 0.56, 0.06, 0.81, −0.69, −1.44) is 0.82

Anova sum sq: ACp. 276

Book 451.46Data 451.56

The sum of squares is 451.56, as the mean square beside it on one degree of freedom says (Table 6.19: 451.563); a misprint

Df model: interaction onlyp. 292

Book 3Data 1

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has 1 degree of freedom for regression

Ss regression: interaction onlyp. 292

Book 71.267Data 71.244

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has a residual sum of squares of 0.1103, so 71.244 of the corrected total

Ms regression: interaction onlyp. 292

Book 23.756Data 71.244

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has one degree of freedom for regression

F regression: interaction onlyp. 292

Book 1085.95Data 4521.91

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has 1 and 7 degrees of freedom

Residual df: interaction onlyp. 292

Book 4Data 7

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has 7 residual degrees of freedom

Ss residual: interaction onlyp. 292

Book 0.088Data 0.110

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has a residual sum of squares of 0.1103, 7 × 0.1255²

Ms residual: interaction onlyp. 292

Book 0.022Data 0.016

Table 6.28 repeats the analysis of variance of Table 6.26; the one-term model through the origin has a residual mean square of 0.0158, 0.1255²

Block confounding: k = 7, 8 blocks of 16p. 316

Book ABC, DEF, AFG, ABCDEF, BCFG, ADEG, BCDEGData ABCD, ABEF, CDEF, ACEG, BDEG, BCFG, ADFG

The column prints the generalized interactions of ABC, DEF and AFG; those of the chosen ABCD, CDEF and ADFG are ABCD, CDEF, ADFG, ABEF, BCFG, ACEG and BDEG, seven four-factor interactions

Block confounding: k = 7, 8 blocks of 16p. 316

Book ABC, DEF, AFG, ABCDEF, BCFG, ADEG, BCDEGData ABCD, ABEF, ACEG, ADFG, BCFG, BDEG, CDEF

The column prints the generalized interactions of ABC, DEF and AFG; those of the chosen ABCD, CDEF and ADFG are ABCD, CDEF, ADFG, ABEF, BCFG, ACEG and BDEG, seven four-factor interactions

Anova f: Ap. 318

Book 16.20Data 16.19

The F ratio on the error mean square 2550.9625 is a little smaller; the table divides by its own 2550.4625, which inherits the slips in C and AC

Anova sum sq: Cp. 318

Book 374,850.5625Data 374850.0000

The sum of squares of C is 374,850.0625, as Tables 6.5 and 6.6 print it for the same sixteen runs; the table carries its 374,850.5625 into its error sum of squares

Anova mean sq: Cp. 318

Book 374,850.5625Data 374850.0000

The mean square of C is 374,850.0625; the slip of its sum of squares

Anova f: Cp. 318

Book 146.97Data 146.94

The F ratio on the error mean square 2550.9625 is a little smaller; the table divides by its own 2550.4625, which inherits the slips in C and AC

Anova sum sq: ACp. 318

Book 94,404.5625Data 94402.6000

The sum of squares of AC is 94,402.5625, as Tables 6.5 and 6.6 print it for the same sixteen runs; the table carries its 94,404.5625 into its error sum of squares

Anova mean sq: ACp. 318

Book 94,404.5625Data 94402.6000

The mean square of AC is 94,402.5625; the slip of its sum of squares

Anova p: ACp. 318

Book <0.001Data 0.00173551

The P-value of F = 37.01 on 1 and 5 degrees of freedom is 0.0017, not below 0.001

Ss residualp. 318

Book 12,752.3125Data 12754.8000

The error sum of squares is 12,754.8125; the table takes the total less its rows, and its rows for C and AC are 0.5 and 2 too large

Ms residualp. 318

Book 2550.4625Data 2550.9600

The error mean square is 2550.9625, 12,754.8125/5; the table's error sum of squares is 2.5 too small

Column: BD = CEp. 339

Book BD = CEData not in runs 2, 4, 6, 8, 9, 11, 13, 15

The column holds the signs of BD and of CF, its aliases in Table 8.8; CE is aliased with AB, the third column

Alias matrix: A, BDp. 358

Book -1 / 3Data 0.333333

In the design of Table 8.24 the weights of BD and BE in A's alias chain are +1/3 and that of BF −1/3, the sum over the runs of A times the interaction's column over 12; the text prints the opposite signs for these three, and agrees with the table for BC and KL

Alias matrix: A, BEp. 358

Book -1 / 3Data 0.333333

In the design of Table 8.24 the weights of BD and BE in A's alias chain are +1/3 and that of BF −1/3, the sum over the runs of A times the interaction's column over 12; the text prints the opposite signs for these three, and agrees with the table for BC and KL

Alias matrix: A, BFp. 358

Book 1 / 3Data -0.333333

In the design of Table 8.24 the weights of BD and BE in A's alias chain are +1/3 and that of BF −1/3, the sum over the runs of A times the interaction's column over 12; the text prints the opposite signs for these three, and agrees with the table for BC and KL

Alias matrix: X5 row, X3X4 columnp. 361

Book 0Data 0.2

The entry is the J-characteristic of X3, X4 and X5 over 20, which in this design can only be ±4/20 or ±12/20; it is 4/20 = 0.2, as X3's row prints for X4X5 and X4's for X3X5, which are the same product of columns

Largest effect: initial runs, Ap. 369

Book 152.81Data 158.12

The axis ends at the largest effect, as those of Figures 8.26 and 8.27 do; the largest of the sixteen runs of Table 8.31 is A's, 158.125, as Figure 8.27's axis has it for the partial fold over. 152.81 is the largest effect of the 32 runs of Table 8.32 (Figure 8.26)

Coefficient: nozzle 2, intercept, codedp. 400

Book 25.6Data -17.8

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, x1, codedp. 400

Book −22.8Data -5.08333

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, x1², codedp. 400

Book 14.1Data 84.2

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, x2², codedp. 400

Book −56.9Data -60.25

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, intercept, naturalp. 400

Book 180.1Data 2526.7

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, S, naturalp. 400

Book −9.475Data -50.6917

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, P, naturalp. 400

Book 66.75Data 70.75

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, S², naturalp. 400

Book 0.035Data 0.211

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Coefficient: nozzle 2, P², naturalp. 400

Book −2.2767Data -2.41

The least squares fit to nozzle 2's eighteen runs of Table 9.1 is ŷ = −17.8 − 5.1x1 − 12.3x2 + 84.3x1² − 60.3x2² − 0.8x1x2, and in the natural units ŷ = 2526.7 − 50.692S + 70.75P + 0.21063S² − 2.41P² − 0.0075SP; the printed models agree with it in x2, x1x2 and SP only. They agree in every term with a fit in which the means of the middle pressure, at the three speeds, are about 67, 87.5 and −49.6 in place of the table's 87.5, −49.5 and 77: two of the three means one speed to the right, as if a row of nozzle 2's data were shifted by a column in the fit

Component ss: ABC² = Y(ABC)p. 402

Book 18.77Data 584.11

By the book's rule ABC² groups the runs by x1 + x2 + 2x3 (mod 3), whose totals are 138, 4 and 23 and whose sum of squares is 584.11; the totals 63, 62 and 40, and 18.778 from them (which the book cuts to 18.77), are ABC's: the book lists the J(AB) totals in the reverse order of the I(AB) totals (u = 2, 1, 0), which exchanges the I and J diagonals of its display of J(AB) with C

Component ss: ABC = Z(ABC)p. 402

Book 584.11Data 18.78

ABC groups the runs by x1 + x2 + x3 (mod 3), whose totals are 40, 62 and 63 and whose sum of squares is 18.78; 584.11 is ABC²'s: the book lists the J(AB) totals in the reverse order of the I(AB) totals (u = 2, 1, 0), which exchanges the I and J diagonals of its display of J(AB) with C

Contrast values: block 6p. 407

Book (1,6)Data (1, 0)

Every run of block 6 has L1 = 1 and L2 = 0; a value modulo 3 is 0, 1 or 2, so (1,6) misprints (1,0), the one pair no other block has

Orthogonal: the fifteen columnsp. 418

Book 1Data 1.3

Run 6 prints 1 in column G; with −1 there, and run 12 restored as the row that completes the design, each column is balanced and every pair of the fifteen columns is orthogonal. The columns D, E, H, K, M and Q that Table 9.20 takes do not change, and Table 9.20's run 12 is the restored run's

Orthogonal: the fifteen columnsp. 419

Book 1Data 1.3

Run 16 prints 1 in column N; with −1 there each column is balanced and every pair of the fifteen columns is orthogonal

Orthogonal: the fifteen columnsp. 419

Book 1Data 1.3

Run 11 prints 1 in column H; with −1 there each column is balanced and every pair of the fifteen columns is orthogonal, and Table 9.22, whose column E is Hall IV's H, has −1 in run 11

Projection: columns of Hall IIIp. 420

Book A, B, D, H, J, M, and QData not in runs 5, 6, 7, 8, 9, 10, 15, 16

The fifth column of Table 9.21 is Hall III's K: its J differs in eight runs

Projection: columns of Hall IVp. 420

Book A, B, D, F, H, J, M, and OData not in runs 5, 6, 7, 8, 9, 11, 13, 15

Table 9.22's sixth column is Hall IV's K, not J, and its eighth is P: Hall's designs have no column O

Count: L1 in X2p. 434

Book 3Data 4

Table 9.35's column X2 holds L1 four times (runs 3, 4, 5 and 11) and L3 three times (runs 1, 7 and 9); the text exchanges the two counts

Count: L3 in X2p. 434

Book 4Data 3

Table 9.35's column X2 holds L1 four times (runs 3, 4, 5 and 11) and L3 three times (runs 1, 7 and 9); the text exchanges the two counts

Coefficient: least squares estimate, run 8 missing, Interceptp. 459

Book 51.25Data 51.06

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: least squares estimate, run 8 missing, temperaturep. 459

Book 5.75Data 5.71

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: least squares estimate, run 8 missing, pressurep. 459

Book 10.75Data 10.71

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: least squares estimate, run 8 missing, concentrationp. 459

Book 1.25Data 1.21

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: fitted model, run 8 missing, Interceptp. 459

Book 51.25Data 51.06

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: fitted model, run 8 missing, temperaturep. 459

Book 5.75Data 5.71

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: fitted model, run 8 missing, pressurep. 459

Book 10.75Data 10.71

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

Coefficient: fitted model, run 8 missing, concentrationp. 459

Book 1.25Data 1.21

The product of the printed (X'X)^-1 and X'y, and the least squares fit to the eleven runs, is β̂ = (51.058, 5.712, 10.712, 1.212): 51.058 = (5/52)(544) + (1/52)(−23 + 17 − 59). The printed estimates are each 1/8 to 1/4 above the fit

(X'X)^-1: (X'X)^-1 [3, 4]p. 461

Book 4.37851e-3Data 0.0043729

The book inverts X'X as printed, its entries rounded to four decimals, which gives 4.37351 × 10^−3, and prints it as 4.37851; the X'X of the coded levels gives 4.37290 × 10^−3

(X'X)^-1: (X'X)^-1 [4, 3]p. 461

Book 4.37851e-3Data 0.0043729

The book inverts X'X as printed, its entries rounded to four decimals, which gives 4.37351 × 10^−3, and prints it as 4.37851; the X'X of the coded levels gives 4.37290 × 10^−3

Path ξ2: step 11p. 484

Book 179Data 178

The book adds 2°F a step, the step of 2.10°F rounded; on the path the temperature after 11 steps is 178.06°F; 2°F a step would give 177°F, so 179 is a misprint as well

Path ξ2: step 12p. 484

Book 181Data 180

The book adds 2°F a step, the step of 2.10°F rounded; on the path the temperature after 12 steps is 180.16°F; 2°F a step would give 179°F, so 181 is a misprint as well

M': w2 on x1p. 494

Book 0.9574Data 0.9571

−0.9571, M12 as the book prints it above; −0.9574 is a misprint

W equation: w1 on x1p. 495

Book 0.2897Data 0.2898

0.2898 to four decimals (0.28978), as M prints it; the equation's 0.2897 is a misprint

W equation: w2 on x2p. 495

Book 0.2888Data 0.2898

0.2898 to four decimals, as M prints it; 0.2888 is a misprint

N: k = 7, ½ Rep.p. 511

Book 80Data 90

The blocks hold 8 × 9 + 18 = 90 runs, as the library's design with 12 centre runs has; 80 is a misprint

Conference matrix: m = 12p. 522

Book constructed from a conference matrixData no relabelling of the library's columns gives the printed runs

The printed design is not the library's, made from a conference matrix of order 12, in any order or sign of its columns: its main effects are not orthogonal, ten pairs of columns having x_i'x_j = ±4

Linear mixture ms: Linear Mixturep. 538

Book 1465.66Data 1465.55

2931.09/2 = 1465.55; the table's 1465.66 is a misprint

Effect: cycle 1, change in meanp. 541

Book 0.02Data -0.02

(84.2 + 84.9 + 84.5 + 84.3 − 4 × 84.5)/5 = −0.02; the sheet prints it without its minus sign

Effect: information board, Change in meanp. 543

Book 0.07Data -0.07

The change in mean is −0.07, as Table 11.25 prints it; the board drops its sign

New centre: point (3), temperaturep. 543

Book 3Data 0

Point (3) is run at 255°F and 150 psi in each cycle (Figure 11.49); no run is at 225°F, a misprint for 255°F

Distinct runs: Table 12.2's outer arrayp. 557

Book 8Data 7

The sixth column prints G as −, the fifth's setting; a 2^3 needs + there, as the pattern − + − + of the other columns has it

Mean: C, D run 1p. 570

Book 57.75Data 57.25

The four readings 45, 48, 71 and 65 (Example 6.2's runs (1), b, a and ab) average 57.25

Alias weight: β11 on β34p. 572

Book 0Data 1

The alias matrix gives β11's estimate the weight +1 on β34 as well: E(β̂11) = β11 − (β23 − β24)/2 + β34, as β33's and β44's carry β14 and β13

P: ABp. 594

Book 0.01Data 0.00

The P-value of F = 14.59 on 6 and 12 degrees of freedom is 0.00007, which Table 13.11 prints as 0.000; Table 13.10 prints it as 0.01

Anova sum sq: Fixtures (F)p. 617

Book 82.80Data 82.79

The fixtures' sum of squares is 82.792 (Σy²i.../16 − y²..../48 = 32739.125 − 32656.333), as Minitab prints it in Table 14.13; 82.80 is not its rounding

Anova mean sq: Layouts (L)p. 617

Book 4.09Data 4.08

The layouts' mean square is their sum of squares on one degree of freedom, 4.083, as Table 14.13 prints it; the 4.08 beside it is that rounded, 4.09 is not

P: Operators (within layouts), O(L)p. 617

Book 0.01Data 0.00

The P-value of F = 5.137 on 6 and 24 degrees of freedom is 0.0016, as Minitab's 0.002 in Table 14.13; the table prints 0.01

P: Temperature (B)p. 623

Book 0.01Data 0.00

The P-value of F = 42.01 on 3 and 6 degrees of freedom is 0.0002; the table prints 0.01

Coefficient: Interceptp. 630

Book 49.73875Data 49.74190

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: Gap (A)p. 630

Book 10.0625Data 10.0656

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: Gas flow (B)p. 630

Book 5.6275Data 5.6244

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: Pressure (C)p. 630

Book 1.325Data 1.328

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: Time (D)p. 630

Book −2.0725Data -2.06938

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: RF power (E)p. 630

Book 5.12625Data 5.12313

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: ABp. 630

Book 7.34625Data 7.34313

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: ACp. 630

Book 1.83125Data 1.83438

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: ADp. 630

Book −3.00875Data -3.00562

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: AEp. 630

Book 6.505Data 6.502

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: BCp. 630

Book −0.60125Data -0.604375

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: BDp. 630

Book −1.35875Data -1.36188

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: BEp. 630

Book −0.2125Data -0.209375

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: CDp. 630

Book 1.86625Data 1.86938

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Coefficient: CEp. 630

Book −1.485Data -1.48813

Every coefficient of Table 14.23 differs from the fit to Table 14.22 by 0.05/16 = 0.003125, with the signs of run 12 (whole plot 6, A+ B− C+ D+ E−): they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Largest effect: subplot effects, AEp. 631

Book 13.01Data 13.00

2 × 6.50187 = 13.0037 from the fit to Table 14.22; the axis ends at twice Table 14.23's 6.505, they are the coefficients of the runs with 38.03 there, where Table 14.22 prints 38.08

Total: y3., in Txyp. 660

Book 184Data 180

Machine 3's strengths total 180, as Table 15.10 prints; the formula for Txy writes (106)(184), though its 96.00 is worked with 180

MSE: without the covariatep. 668

Book 470.82Data 470.86

The residual mean square of this model is 4708.56/10 = 470.86

Selected: different samples starredp. 676

Book 20Data 15

The starred samples hold only 15 different pairs of viscosity and molecular weight: samples 2 and 22, 4 and 24, 5 and 25, 9 and 29, and 18 and 38 are the same, and no sample with (44, 1260), (58, 1359), (33, 1275), (58.3, 1330) or (31.9, 1250) is starred; Table 15.22 holds each of the 20 different pairs once

Alias matrix: X3X4 row, 14 columnp. 677

Book −0.04Data 0.0399675

The runs of Table 15.22 give +0.040; the table prints its sign as minus

Alias matrix: X3X4 row, 24 columnp. 677

Book −0.042Data 0.0418117

The runs of Table 15.22 give +0.042; the table prints its sign as minus

Defining relation: 2^(10-6)p. 712

Book I = ABCE = BCDF = ADEF = ACDG = BDEG = ABFG = CEFG = ABDH = CDEH = ACFH = BEFH = BCGH = AEGH = DFGH = ABCDEFGH = ABCDJ = DEJ = AFJ = BCEFJ = BGJ = ACEGJ = CDFGI = ABDEFGJ = CHJ = ABEHJ = BDFHJ = ACDEFHJ = ADGHJ = BCDEGHJ = ABCFGHJ = EFGHJ = ABK = CEK = ACDFK = BDEFK = BCDGK = ADEGK = FGK = ABCEFGK = DHK = ABCDEHK = BCFHK = AEFHK = ACGHK = BEGHK = ABDFGHK = CDEFGHK = CDJK = ABDEJK = BFJK = ACEFJK = AGJK = BCEGJK = ABCDFGJK = DEFGJK = ABCHJK = EHJK = ADFHJK = BCDEFHJK = BDGHJK = ACDEGHJK = CFGHJK = ABEFGHJKData ABCDEFGH, ABCDEHK, ABCDFGJK, ABCDJ, ABCE, ABCEFGK, ABCFGHJ, ABCHJK, ABDEFGJ, ABDEJK, ABDFGHK, ABDH, ABEFGHJK, ABEHJ, ABFG, ABK, ACDEFHJ, ACDEGHJK, ACDFK, ACDG, ACEFJK, ACEGJ, ACFH, ACGHK, ADEF, ADEGK, ADFHJK, ADGHJ, AEFHK, AEGH, AFJ, AGJK, BCDEFHJK, BCDEGHJ, BCDF, BCDGK, BCEFJ, BCEGJK, BCFHK, BCGH, BDEFK, BDEG, BDFHJ, BDGHJK, BEFH, BEGHK, BFJK, BGJ, CDEFGHK, CDEH, CDFGJ, CDJK, CEFG, CEK, CFGHJK, CHJ, DEFGJK, DEJ, DFGH, DHK, EFGHJ, EHJK, FGK

The relation prints CDFGI, with I, the identity, for the factor J: the word is CDFGJ, the product of the generators' words BCDF, ACDG and ABCDJ, printed so in the relations of designs (o) and (u)

Factors: 2^(15-11)p. 717

Book 5Data 15

The heading prints 5 factors in 16 runs for 15: the label 2^(15−11) and the generators, which name the factors A to P without I, make fifteen, as Table 8.14 lists this design