6.42

Design of Experiment – Spring 2014

Project

[1]

Submitted By

Harshavardhan D. Gorakh

Table 1

FactorsLevel Factor 1 Factor 2 Factor 3

Apatite

(a) pH (b) Pb (c)abc 60 (+) 7 (+) 2.41 (+)ab 60 (+) 7 (+) 0.483 (-)ac 60 (+) 4 (-) 2.41 (+)a 60 (+) 4 (-) 0.483 (-)

bc 30 (-) 7 (+) 2.41 (+)b 30 (-) 7 (+) 0.483 (-)c 30 (-) 4 (-) 2.41 (+)

(1) 30 (-) 4 (-) 0.483 (-)

Table 2

FishBone FishBone Hydroxyapatite HydroxyapatitePb milli Mole pH Pb milli Mole pH

Replicate I

Replicate II

Replicate I

Replicate II

Replicate I

Replicate II

Replicate I

Replicate II

1.82 1.81 5.22 5.12 0.11 0.12 3.49 3.460.01 0 6.84 6.61 0 0 5.84 5.91.11 1.04 3.35 3.34 0.8 0.76 2.7 2.74

0 0.01 5.77 6.25 0.03 0.05 3.36 3.242.11 2.18 5.29 5.06 1.03 1.05 3.22 3.220.03 0.05 5.93 6.02 0 0 5.53 5.431.7 1.69 3.39 3.34 1.34 1.26 2.82 2.79

0.05 0.05 4.5 4.74 0.06 0.07 3.28 3.28

FISHBONE PbGeneral Linear Model: Fishbone Pb mM versus Apetite, pH, Pb

Factor Type Levels ValuesApetite fixed 2 -1, 1pH fixed 2 -1, 1Pb fixed 2 -1, 1

Analysis of Variance for Fishbone Pb mM, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PApetite 1 0.2652 0.2652 0.2652 400.34 0.000pH 1 0.3481 0.3481 0.3481 525.43 0.000Pb 1 10.9892 10.9892 10.9892 16587.51 0.000Apetite*pH 1 0.0225 0.0225 0.0225 33.96 0.000Apetite*Pb 1 0.1892 0.1892 0.1892 285.62 0.000pH*Pb 1 0.3600 0.3600 0.3600 543.40 0.000Apetite*pH*Pb 1 0.0196 0.0196 0.0196 29.58 0.001Error 8 0.0053 0.0053 0.0007Total 15 12.1992

S = 0.0257391 R-Sq = 99.96% R-Sq(adj) = 99.92%

General Linear Model: Fishbone Pb mM versus Apetite, pH, Pb



Source DF Seq SS Adj SS Adj MS F PApetite 1 0.2652 0.2652 0.2652 95.86 0.000pH 1 0.3481 0.3481 0.3481 125.82 0.000Pb 1 10.9892 10.9892 10.9892 3972.01 0.000Apetite*pH 1 0.0225 0.0225 0.0225 8.13 0.019Apetite*Pb 1 0.1892 0.1892 0.1892 68.39 0.000pH*Pb 1 0.3600 0.3600 0.3600 130.12 0.000Error 9 0.0249 0.0249 0.0028Total 15 12.1992

S = 0.0525991 R-Sq = 99.80% R-Sq(adj) = 99.66%




Source DF Seq SS Adj SS Adj MS F PApetite 1 0.2652 0.2652 0.2652 55.95 0.000pH 1 0.3481 0.3481 0.3481 73.44 0.000Pb 1 10.9892 10.9892 10.9892 2318.40 0.000Apetite*Pb 1 0.1892 0.1892 0.1892 39.92 0.000pH*Pb 1 0.3600 0.3600 0.3600 75.95 0.000Error 10 0.0474 0.0474 0.0047Total 15 12.1992

S = 0.0688477 R-Sq = 99.61% R-Sq(adj) = 99.42%

Figure 1

Figure 2

Figure 3

Figure 4



Final ANOVA tableAnalysis of Variance for Fishbone Pb mM, using Adjusted SS for Tests


S = 0.0688477 R-Sq = 99.61% R-Sq(adj) = 99.42%

Grouping Information Using Tukey Method and 95.0% Confidence

Apetite N Mean Grouping-1 8 1.0 A 1 8 0.7 B

Means that do not share a letter are significantly different.

Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Apetite Lower Center Upper ---+---------+---------+---------+--- 1 -0.3342 -0.2575 -0.1808 (------*-------) ---+---------+---------+---------+--- -0.30 -0.20 -0.10 -0.00

Tukey Simultaneous TestsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Difference SE of AdjustedApetite of Means Difference T-Value P-Value 1 -0.2575 0.03442 -7.480 0.0000


pH N Mean Grouping 1 8 1.0 A-1 8 0.7 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:

pH Lower Center Upper ------+---------+---------+---------+ 1 0.2183 0.2950 0.3717 (--------------*--------------)

------+---------+---------+---------+ 0.250 0.300 0.350 0.400Tukey Simultaneous TestsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:

Difference SE of AdjustedpH of Means Difference T-Value P-Value 1 0.2950 0.03442 8.570 0.0000


Pb N Mean Grouping 1 8 1.7 A-1 8 0.0 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Pb Lower Center Upper ----+---------+---------+---------+-- 1 1.581 1.658 1.734 (---------------*--------------) ----+---------+---------+---------+-- 1.600 1.650 1.700 1.750

Tukey Simultaneous TestsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Difference SE of AdjustedPb of Means Difference T-Value P-Value 1 1.658 0.03442 48.15 0.0000


Apetite Pb N Mean Grouping-1 1 4 1.9 A 1 1 4 1.4 B-1 -1 4 0.0 C 1 -1 4 0.0 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of Apetite*PbApetite = -1Pb = -1 subtracted from:

Apetite Pb Lower Center Upper -------+---------+---------+----------1 1 1.7259 1.87500 2.0241 (-*) 1 -1 -0.1891 -0.04000 0.1091 (-*) 1 1 1.2509 1.40000 1.5491 (-*) -------+---------+---------+--------- -1.2 0.0 1.2

Apetite = -1Pb = 1 subtracted from:

Apetite Pb Lower Center Upper -------+---------+---------+--------- 1 -1 -2.064 -1.915 -1.766 (*) 1 1 -0.624 -0.475 -0.326 (*) -------+---------+---------+--------- -1.2 0.0 1.2

Apetite = 1Pb = -1 subtracted from:

Apetite Pb Lower Center Upper -------+---------+---------+--------- 1 1 1.291 1.440 1.589 (*) -------+---------+---------+--------- -1.2 0.0 1.2

Tukey Simultaneous TestsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of Apetite*PbApetite = -1Pb = -1 subtracted from:

Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value-1 1 1.87500 0.04868 38.5148 0.0000 1 -1 -0.04000 0.04868 -0.8216 0.8430 1 1 1.40000 0.04868 28.7577 0.0000


Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value 1 -1 -1.915 0.04868 -39.34 0.0000 1 1 -0.475 0.04868 -9.76 0.0000


Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value 1 1 1.440 0.04868 29.58 0.0000


pH Pb N Mean Grouping 1 1 4 2.0 A-1 1 4 1.4 B-1 -1 4 0.0 C 1 -1 4 0.0 C

Means that do not share a letter are significantly different.Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

pH Pb Lower Center Upper -----+---------+---------+---------+--1 1 1.2084 1.35750 1.5066 (-*) 1 -1 -0.1541 -0.00500 0.1441 (-*) 1 1 1.8034 1.95250 2.1016 (-*)

-----+---------+---------+---------+- -1.0 0.0 1.0 2.0

pH = -1Pb = 1 subtracted from:

pH Pb Lower Center Upper -----+---------+---------+---------+- 1 -1 -1.512 -1.363 -1.213 (*-) 1 1 0.446 0.595 0.744 (-*) -----+---------+---------+---------+- -1.0 0.0 1.0 2.0

pH = 1Pb = -1 subtracted from:

pH Pb Lower Center Upper -----+---------+---------+---------+- 1 1 1.808 1.958 2.107 (-*) -----+---------+---------+---------+- -1.0 0.0 1.0 2.0

Tukey Simultaneous TestsResponse Variable Fishbone Pb mMAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value-1 1 1.35750 0.04868 27.8847 0.0000 1 -1 -0.00500 0.04868 -0.1027 0.9996 1 1 1.95250 0.04868 40.1067 0.0000


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 -1 -1.363 0.04868 -27.99 0.0000 1 1 0.595 0.04868 12.22 0.0000


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 1 1.958 0.04868 40.21 0.0000

Figure 5

Figure 6

Figure 7

FISHBONE pHGeneral Linear Model: Fishbone pH versus Apetite, pH, Pb


Analysis of Variance for Fishbone pH, using Adjusted SS for Tests


S = 0.160954 R-Sq = 99.03% R-Sq(adj) = 98.18%

Figure 8

Figure 9

General Linear Model: Fishbone pH versus Apetite, pH, Pb


Final ANOVA tableAnalysis of Variance for Fishbone pH, using Adjusted SS for Tests


S = 0.203018 R-Sq = 98.06% R-Sq(adj) = 97.10%

Unusual Observations for Fishbone pH

Obs Fishbone pH Fit SE Fit Residual St Resid 8 6.25000 5.85000 0.12432 0.40000 2.49 R

R denotes an observation with a large standardized residual.


Apetite N Mean Grouping 1 8 5.3 A-1 8 4.8 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Apetite Lower Center Upper +---------+---------+---------+------ 1 0.3026 0.5287 0.7549 (--------------*--------------) +---------+---------+---------+------ 0.30 0.45 0.60 0.75

Tukey Simultaneous TestsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Difference SE of AdjustedApetite of Means Difference T-Value P-Value 1 0.5287 0.1015 5.209 0.0004




Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:

pH Lower Center Upper +---------+---------+---------+------ 1 1.200 1.426 1.652 (--------------*--------------) +---------+---------+---------+------ 1.20 1.35 1.50 1.65

Tukey Simultaneous TestsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:



Pb N Mean Grouping-1 8 5.8 A 1 8 4.3 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Pb Lower Center Upper ------+---------+---------+---------+ 1 -1.795 -1.569 -1.343 (----*---) ------+---------+---------+---------+ -1.50 -1.00 -0.50 0.00

Tukey Simultaneous TestsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Difference SE of AdjustedPb of Means Difference T-Value P-Value 1 -1.569 0.1015 -15.45 0.0000


Apetite Pb N Mean Grouping 1 -1 4 6.4 A-1 -1 4 5.3 B-1 1 4 4.3 C 1 1 4 4.3 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of Apetite*PbApetite = -1Pb = -1 subtracted from:

Apetite Pb Lower Center Upper -------+---------+---------+----------1 1 -1.467 -1.028 -0.5880 (--*--) 1 -1 0.630 1.070 1.5095 (--*--) 1 1 -1.480 -1.040 -0.6005 (--*--) -------+---------+---------+--------- -1.5 0.0 1.5


Apetite Pb Lower Center Upper -------+---------+---------+--------- 1 -1 1.6580 2.09750 2.5370 (--*--) 1 1 -0.4520 -0.01250 0.4270 (--*--) -------+---------+---------+--------- -1.5 0.0 1.5


Apetite Pb Lower Center Upper -------+---------+---------+--------- 1 1 -2.550 -2.110 -1.670 (--*--) -------+---------+---------+--------- -1.5 0.0 1.5

Tukey Simultaneous TestsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of Apetite*PbApetite = -1Pb = -1 subtracted from:

Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value-1 1 -1.028 0.1436 -7.158 0.0002 1 -1 1.070 0.1436 7.454 0.0001 1 1 -1.040 0.1436 -7.245 0.0001

Apetite = -1

Pb = 1 subtracted from:

Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value 1 -1 2.09750 0.1436 14.6111 0.0000 1 1 -0.01250 0.1436 -0.0871 0.9997


Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value 1 1 -2.110 0.1436 -14.70 0.0000


pH Pb N Mean Grouping 1 -1 4 6.3 A-1 -1 4 5.3 B 1 1 4 5.2 B-1 1 4 3.4 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

pH Pb Lower Center Upper -----+---------+---------+---------+--1 1 -2.400 -1.960 -1.520 (--*-) 1 -1 0.595 1.035 1.475 (-*--) 1 1 -0.582 -0.143 0.297 (--*--) -----+---------+---------+---------+- -1.6 0.0 1.6 3.2


pH Pb Lower Center Upper -----+---------+---------+---------+- 1 -1 2.555 2.995 3.435 (--*-) 1 1 1.378 1.817 2.257 (-*--) -----+---------+---------+---------+- -1.6 0.0 1.6 3.2


pH Pb Lower Center Upper -----+---------+---------+---------+- 1 1 -1.617 -1.178 -0.7380 (--*-) -----+---------+---------+---------+- -1.6 0.0 1.6 3.2

Tukey Simultaneous TestsResponse Variable Fishbone pHAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value-1 1 -1.960 0.1436 -13.65 0.0000 1 -1 1.035 0.1436 7.21 0.0001

1 1 -0.143 0.1436 -0.99 0.7569


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 -1 2.995 0.1436 20.86 0.0000 1 1 1.817 0.1436 12.66 0.0000


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 1 -1.178 0.1436 -8.202 0.0001

Figure 10

Figure 11

Figure 12

Hydroxyapatite PbGeneral Linear Model: Hydroxyapatite Pb mM versus Apetite, pH, Pb


Analysis of Variance for Hydroxyapatite Pb mM, using Adjusted SS for Tests


S = 0.0237171 R-Sq = 99.89% R-Sq(adj) = 99.79%

Figure 13

Figure 14

General Linear Model: Hydroxyapatite Pb mM versus Apetite, pH, Pb


Final ANOVA tableAnalysis of Variance for Hydroxyapatite Pb mM, using Adjusted SS for Tests


S = 0.0931799 R-Sq = 97.84% R-Sq(adj) = 96.76%


Apetite N Mean Grouping-1 8 0.6 A 1 8 0.2 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Apetite Lower Center Upper -+---------+---------+---------+----- 1 -0.4713 -0.3675 -0.2637 (------*-----) -+---------+---------+---------+----- -0.45 -0.30 -0.15 0.00

Tukey Simultaneous TestsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Difference SE of AdjustedApetite of Means Difference T-Value P-Value 1 -0.3675 0.04659 -7.888 0.0000


pH N Mean Grouping-1 8 0.5 A 1 8 0.3 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:

pH Lower Center Upper ------+---------+---------+---------+ 1 -0.3613 -0.2575 -0.1537 (---------*----------) ------+---------+---------+---------+ -0.30 -0.20 -0.10 -0.00

Tukey Simultaneous TestsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:

Difference SE of AdjustedpH of Means Difference T-Value P-Value 1 -0.2575 0.04659 -5.527 0.0003


Pb N Mean Grouping 1 8 0.8 A-1 8 0.0 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Pb Lower Center Upper -------+---------+---------+--------- 1 0.6787 0.7825 0.8863 (----------------*-----------------) -------+---------+---------+--------- 0.720 0.780 0.840

Tukey Simultaneous TestsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Difference SE of AdjustedPb of Means Difference T-Value P-Value 1 0.7825 0.04659 16.80 0.0000


Apetite Pb N Mean Grouping-1 1 4 1.2 A 1 1 4 0.4 B-1 -1 4 0.0 C 1 -1 4 0.0 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of Apetite*PbApetite = -1Pb = -1 subtracted from:

Apetite Pb Lower Center Upper -------+---------+---------+----------1 1 0.9358 1.13750 1.3392 (-*--) 1 -1 -0.2142 -0.01250 0.1892 (--*-) 1 1 0.2133 0.41500 0.6167 (-*--) -------+---------+---------+--------- -0.80 0.00 0.80


Apetite Pb Lower Center Upper -------+---------+---------+--------- 1 -1 -1.352 -1.150 -0.9483 (--*-) 1 1 -0.924 -0.723 -0.5208 (--*-) -------+---------+---------+--------- -0.80 0.00 0.80


Apetite Pb Lower Center Upper -------+---------+---------+--------- 1 1 0.2258 0.4275 0.6292 (-*--) -------+---------+---------+--------- -0.80 0.00 0.80

Tukey Simultaneous TestsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of Apetite*PbApetite = -1Pb = -1 subtracted from:

Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value-1 1 1.13750 0.06589 17.2641 0.0000 1 -1 -0.01250 0.06589 -0.1897 0.9974 1 1 0.41500 0.06589 6.2986 0.0004


Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value 1 -1 -1.150 0.06589 -17.45 0.0000 1 1 -0.723 0.06589 -10.97 0.0000


Difference SE of AdjustedApetite Pb of Means Difference T-Value P-Value 1 1 0.4275 0.06589 6.488 0.0003


pH Pb N Mean Grouping-1 1 4 1.0 A 1 1 4 0.6 B-1 -1 4 0.1 C 1 -1 4 -0.0 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

pH Pb Lower Center Upper --------+---------+---------+---------1 1 0.7858 0.98750 1.1892 (--*--) 1 -1 -0.2542 -0.05250 0.1492 (--*--) 1 1 0.3233 0.52500 0.7267 (--*-) --------+---------+---------+-------- -0.70 0.00 0.70


pH Pb Lower Center Upper --------+---------+---------+-------- 1 -1 -1.242 -1.040 -0.8383 (--*--) 1 1 -0.664 -0.463 -0.2608 (-*--) --------+---------+---------+-------- -0.70 0.00 0.70pH = 1Pb = -1 subtracted from:

pH Pb Lower Center Upper --------+---------+---------+-------- 1 1 0.3758 0.5775 0.7792 (--*--) --------+---------+---------+-------- -0.70 0.00 0.70Tukey Simultaneous TestsResponse Variable Hydroxyapatite Pb mMAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value-1 1 0.98750 0.06589 14.9875 0.0000 1 -1 -0.05250 0.06589 -0.7968 0.8544 1 1 0.52500 0.06589 7.9680 0.0001pH = -1Pb = 1 subtracted from: Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 -1 -1.040 0.06589 -15.78 0.0000 1 1 -0.463 0.06589 -7.02 0.0002


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 1 0.5775 0.06589 8.765 0.0000

Figure 15

Figure 16

Hydroxyapatite pHGeneral Linear Model: Hydroxyapatite pH versus Apatite, pH, Pb


Analysis of Variance for Hydroxyapatite pH, using Adjusted SS for Tests


S = 0.0443001 R-Sq = 99.92% R-Sq(adj) = 99.86%

Figure 17

Figure 18

General Linear Model: Hydroxyapatite pH versus Apetite, pH, Pb


Analysis of Variance for Hydroxyapatite pH, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PApetite 1 0.0841 0.0841 0.0841 47.53 0.000pH 1 8.8209 8.8209 8.8209 4985.12 0.000Pb 1 8.1510 8.1510 8.1510 4606.54 0.000Apetite*pH 1 0.1260 0.1260 0.1260 71.22 0.000Apetite*Pb 1 0.0144 0.0144 0.0144 8.14 0.019pH*Pb 1 3.2400 3.2400 3.2400 1831.08 0.000Error 9 0.0159 0.0159 0.0018Total 15 20.4524

S = 0.0420648 R-Sq = 99.92% R-Sq(adj) = 99.87%

Figure 19

Figure 20

General Linear Model: Hydroxyapatite pH versus Apetite, pH, Pb


Final ANOVA tableAnalysis of Variance for Hydroxyapatite pH, using Adjusted SS for Tests

Source DF Seq SS Adj SS Adj MS F PApetite 1 0.0841 0.0841 0.0841 27.73 0.000pH 1 8.8209 8.8209 8.8209 2908.79 0.000Pb 1 8.1510 8.1510 8.1510 2687.89 0.000Apetite*pH 1 0.1260 0.1260 0.1260 41.56 0.000pH*Pb 1 3.2400 3.2400 3.2400 1068.43 0.000Error 10 0.0303 0.0303 0.0030Total 15 20.4524

S = 0.0550681 R-Sq = 99.85% R-Sq(adj) = 99.78%


Apetite N Mean Grouping 1 8 3.841 A-1 8 3.696 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Apetite Lower Center Upper ------+---------+---------+---------+ 1 0.08365 0.1450 0.2063 (----------------*-----------------) ------+---------+---------+---------+ 0.105 0.140 0.175 0.210

Tukey Simultaneous TestsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of ApetiteApetite = -1 subtracted from:

Difference SE of AdjustedApetite of Means Difference T-Value P-Value 1 0.1450 0.02753 5.266 0.0004




Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:

pH Lower Center Upper ---+---------+---------+---------+--- 1 1.424 1.485 1.546 (----------------*-----------------) ---+---------+---------+---------+---

1.435 1.470 1.505 1.540

Tukey Simultaneous TestsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of pHpH = -1 subtracted from:



Pb N Mean Grouping-1 8 4.483 A 1 8 3.055 B


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Pb Lower Center Upper +---------+---------+---------+------ 1 -1.489 -1.428 -1.366 (*-) +---------+---------+---------+------ -1.50 -1.00 -0.50 0.00

Tukey Simultaneous TestsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of PbPb = -1 subtracted from:

Difference SE of AdjustedPb of Means Difference T-Value P-Value 1 -1.428 0.02753 -51.84 0.0000


Apetite pH N Mean Grouping 1 1 4 4.673 A-1 1 4 4.350 B-1 -1 4 3.043 C 1 -1 4 3.010 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of Apetite*pHApetite = -1pH = -1 subtracted from:

Apetite pH Lower Center Upper -----+---------+---------+---------+--1 1 1.1883 1.30750 1.42672 (*) 1 -1 -0.1517 -0.03250 0.08672 (-*) 1 1 1.5108 1.63000 1.74922 (*) -----+---------+---------+---------+- -1.0 0.0 1.0 2.0

Apetite = -1pH = 1 subtracted from:

Apetite pH Lower Center Upper -----+---------+---------+---------+- 1 -1 -1.459 -1.340 -1.221 (-*) 1 1 0.203 0.323 0.442 (*) -----+---------+---------+---------+- -1.0 0.0 1.0 2.0

Apetite = 1pH = -1 subtracted from:

Apetite pH Lower Center Upper -----+---------+---------+---------+- 1 1 1.543 1.662 1.782 (-*) -----+---------+---------+---------+- -1.0 0.0 1.0 2.0

Tukey Simultaneous TestsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of Apetite*pHApetite = -1pH = -1 subtracted from:

Difference SE of AdjustedApetite pH of Means Difference T-Value P-Value-1 1 1.30750 0.03894 33.5781 0.0000 1 -1 -0.03250 0.03894 -0.8346 0.8370 1 1 1.63000 0.03894 41.8603 0.0000

Apetite = -1pH = 1 subtracted from:

Difference SE of AdjustedApetite pH of Means Difference T-Value P-Value 1 -1 -1.340 0.03894 -34.41 0.0000 1 1 0.323 0.03894 8.28 0.0001

Apetite = 1pH = -1 subtracted from:

Difference SE of AdjustedApetite pH of Means Difference T-Value P-Value 1 1 1.662 0.03894 42.69 0.0000


pH Pb N Mean Grouping 1 -1 4 5.675 A 1 1 4 3.348 B-1 -1 4 3.290 B-1 1 4 2.763 C


Tukey 95.0% Simultaneous Confidence IntervalsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

pH Pb Lower Center Upper ------+---------+---------+---------+-1 1 -0.6467 -0.5275 -0.4083 *) 1 -1 2.2658 2.3850 2.5042 (*) 1 1 -0.0617 0.0575 0.1767 *) ------+---------+---------+---------+ -1.5 0.0 1.5 3.0


pH Pb Lower Center Upper ------+---------+---------+---------+ 1 -1 2.7933 2.9125 3.0317 *) 1 1 0.4658 0.5850 0.7042 (*) ------+---------+---------+---------+ -1.5 0.0 1.5 3.0


pH Pb Lower Center Upper ------+---------+---------+---------+ 1 1 -2.447 -2.328 -2.208 *) ------+---------+---------+---------+ -1.5 0.0 1.5 3.0

Tukey Simultaneous TestsResponse Variable Hydroxyapatite pHAll Pairwise Comparisons among Levels of pH*PbpH = -1Pb = -1 subtracted from:

Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value-1 1 -0.5275 0.03894 -13.55 0.0000 1 -1 2.3850 0.03894 61.25 0.0000 1 1 0.0575 0.03894 1.48 0.4849


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 -1 2.9125 0.03894 74.80 0.0000 1 1 0.5850 0.03894 15.02 0.0000


Difference SE of AdjustedpH Pb of Means Difference T-Value P-Value 1 1 -2.328 0.03894 -59.77 0.0000

Figure 21

Figure 22

Figure 23

Test for equal varianceFor Fishbone Pb concentration mM P value 0.309 implies rejecting alternative hypothesis in favor of null hypothesis

Figure 24

Test for equal variance for Fishbone pH P- value 0.324 implies rejecting alternative hypothesis in favor of null hypothesis

Figure 25

Test for equal variance for hydroxyapatite Pb mM concentration. P-value 0.452 implies rejecting alternative hypothesis in favor of null hypothesis

Figure 26

Test for equal variance for hydroxyapatite Pb mM concentration. P-value 0.782 implies rejecting alternative hypothesis in favor of null hypothesis.

Figure 27

Conclusiona) For the lead response of the Fishbone apatite concentration of Pb and apatite amount is

important factor. F-value for Pb concentration is highest. Factor effects were calculated using formula given in the book (example 6.1) The following table constructed

b) The standard residuals are generated after eliminating interaction with very small F-value compare to F-value of other factors and interactions. These standard residuals are then tested for normal distribution hypothesis. As seen from Figure 6 p-value generated is 0.055 which is greater than 0.05 (assumed). Figure 24 for equal variance check shows that data is adequate with P-value 0.309. Hence the model is adequate

c) For pH response of the Fishbone apatite, concentration of Pb and pH are more important than others. Factor effects are calculated as shown in the following table.

Factor effects

Fihbone pH

A0.5287

5

B1.4262

5 Highest

C

-1.5687

5 Lowest

AB

-0.1562

5Eliminated

AC -0.5412

Fishbone Pb

Replicate 1

Replicate 2 Total

abc 1.82 1.81 3.63ab 0.01 0 0.01ac 1.11 1.04 2.15A 0 0.01 0.01bc 2.11 2.18 4.29B 0.03 0.05 0.08C 1.7 1.69 3.39

(1) 0.05 0.05 0.1

Factor effects

Fishbone Pb

A -0.2575 LowestB 0.295C 1.6575 Highest

AB 0.075Eliminated

AC -0.2175BC 0.3

ABC 0.07Eliminated

Fishbone pHReplicate 1

Replicate 2 Total

abc 5.22 5.12 10.34ab 6.84 6.61 13.45ac 3.35 3.34 6.69a 5.77 6.25 12.02bc 5.29 5.06 10.35b 5.93 6.02 11.95c 3.39 3.34 6.73

(1) 4.5 4.74 9.24

5

BC0.3912

5

ABC0.1637

5Eliminated

d) After eliminating non influencing factors and generating standard residuals and testing them for normality assumption, P-values obtained is 0.245 which is greater than 0.05. Therefore the data is normal and model is adequate, Shown in Figure 11. Also Figure 25 shows that model has equal variance implies adequate model with P-value of 0.324.

e) For the lead response of the Hydroxyapatite apatite, concentration of Pb and amount of apatite were important factor. Factor effects also suggest the same conclusion as shown in table below.

Factor effects

Hydroxyapatite Pb

A -0.3675 LowestB -0.2575C 0.7825 HighestAB -0.095 EliminatedAC -0.355BC -0.205ABC -0.1075 Eliminated

f) After eliminating interactions with very small F-value as compare to others the standard residuals are tested for normality. P-value of 0.171 in Figure 15 suggests that model is adequate. Also test for equal variance as shown in Figure 26 also suggests that model is adequate with P-value of 0.452.

g) For the pH response of the Hydroxyapatite apatite, pH factor is most important among all factor. Factor effects are shown in below mentioned table.

Factor effects

Hydroxyapatite Pb

A 0.145B 1.485 HighestC -1.4275 LowestAB 0.1775

AC -0.06Eliminated

Hydroxyapatite Pb

Replicate 1

Replicate 2 Total

abc 0.11 0.12 0.23ab 0 0 0ac 0.8 0.76 1.56a 0.03 0.05 0.08bc 1.03 1.05 2.08b 0 0 0c 1.34 1.26 2.6(1) 0.06 0.07 0.13

Hydroxyapatite pH

Replicate 1

Replicate 2 Total

abc 3.49 3.46 6.95ab 5.84 5.9 11.74ac 2.7 2.74 5.44a 3.36 3.24 6.6bc 3.22 3.22 6.44b 5.53 5.43 10.96c 2.82 2.79 5.61(1) 3.28 3.28 6.56

BC -0.9

ABC -0.0075Eliminated

h) After eliminating interactions with very small F-value as compare to others the standard residuals are tested for normality. P-value of 0.966 shown in Figure 22 suggests that model is adequate. Also test for equal variance as shown in Figure 27 suggests that model is adequate with P-value of 0.782.

i) From above 23 designs it is observed that for given amount of apatite the fishbone and hydroxyapatite has similar response. Also the pattern of effects of Factor in case of fishbone and hydroxyapatite are similar. I second the author’s conclusion that fishbone apatite can replace the hydroxyapatite apatite because it is cheaper and has almost similar effects as that of hydroxyapatite.

References:

[1]

W. B. Brentlinger, W. B. Leonard and M. Lee, Artists, New Lamar Universtiy Logo 2013. [Art]. Lamar University, 1982.

[2]

D. C. Montgomery, Design and Analysis of Experiments, Arizona: John Wiley & Sons, INC, 2013.

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