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This spreadsheet was designed specifically for use with the Marple Personal Cascade Impactor (Anderson Series 290).

BACKGROUND

Two data reduction spreadsheets are provided:1The "Probit Method" involves the application of the well-known method for determining the MMAD and GSD by plotting on log-probability pa

Because Excel cannot create a probability axis, probability, in terms of cumulative percent, is transformed into the associated standavalue and plotted on a linear scale. Both an "uncorrected" and "corrected" mass percent is computed, where the "correction" involvefor sampling "effectiveness" of impactor that results in the losses on each stage (1).These corrected percentages are applied to the Probit Method to determine an MMAD and GSD (for comparison only).

2The uncorrected percent is used in the "Inversion Method" in the second spreadsheet.

This method determines the MMAD and GSD that minimizes the differences between the measured mass fractionsand those computed under the assumption the aerosol is perfectly UNIMODAL and LOGNORMALLY distributed.(This version of the method does not have an option to analyze multimodal distributions).

The original paper describing this method was given by Raabe (2). A paper by O'Shaughnessy and Raabe (3)describes the application of a spreadsheet to this method where the primary utility of the spreadsheet is to make the method reand to take advantage of the powerful root-solving function, "Solver", incorporated in Excel. This is the spreadsheet resulting fr

Corrections for both inlet efficiency and inner losses are incorporated in the Inversion spreadsheet and, therefore, should be compareuncorrected percentages developed in the Probit Method data table. To explain further:

The percentages calculated in the inversion spreadsheet are manipulated to compensate for the losses etc. thatwould therefore result in the mass percentages resulting directly from an analysis of the net weights.Therefore, one should not compare "corrected" percentages to those compensated for in the Inversion method.

Another point of explanation:The Inversion method utilizes the actual stage efficiency curves in its determination. These curves were first developed byRubow et al. (1) and later reanalyzed and given numerical approximations by Rader et al. (4), which are used here.The curve functions are based on what Rader calls the "slip-corrected aerodynamic diameter", Dpc,and Raabe (5) calls the "aerodynamic resistance diameter", Dar.

Therefore, a column is included to compute Dar, given the aerodynamic diameter, Dae.To directly compare the two methods, the "stage effectiveness" values and cut-diameters given in theProbit Method sheet are those given by Rader et al. (4).

This spreadsheet could be adapted to apply to a different impactor by incorporating either functions or interpolated values to indicatestage efficiencies of the impactor used. For example, Rader (4) also gives curve functions for the Anderson Mark III impactor.

INSTRUCTIONS

1Use the Probit Method spreadsheet to record pre- and post-weights.All other values and the resulting linear regression will be automatically computed.Note the computed values of the MMAD and GSD for this method are given below the graph.The page has been set up to print all pertinent information on one sheet.The uncorrected mass fractions are automatically transferred to the "Inversion Method" spreadsheet.

2Copy and paste the MMAD and GSD as VALUEScomputed in the "Probit Method" sheet (cells E50 & E51)

to cells B17 & B18 in the "Inversion Method" sheet.3In the "Inversion Method" spreadsheet:

Use the "Solver" to minimize the sum of the weighted squared error value in F5.Go to "Tools", "Solver", then in the Solver toolbox:

"Set Target Cell:" to F5"Equal to:" check on "min""By Changing Cell::" highlight B17 and B18"Subject to Constraints:" (must be added in using "Add")

$B$17 >= 0.01$B$18 >= 1.01

Click "OK" to solveResulting MMAD and GSD will appear in B17 and B18

4To determine the Standard Error of estimates for MMAD and GSD additional "inversion" spreadsheets have been createdThese spreadsheets take the results from the Inversion Method sheet and add a small amount to the computed MMAD and GSD.SE Calc 1 adds to the MMAD and SE Calc 2 adds to the GSD. The fractions that result are then used to determine the derivativesrequired to compute the standard errors for the MMAD and GSD.

A final sheet, SE Calculator, is set up to automatically compute the matrix manipulations needed to determine the standard errors

(which, as you will see is a rather awkward process in Excel).All of this is "automatic" and therefore, results from these calculations will appear as soon as the Solver routine is finished.

5Results from the Inversion method are summarized in the sheet, "Inversion Results" for printing a hardcopy.All changes made to "Probit Method" sheet are automatically transferred to this sheet.A visual check of the linearity of the line plotted in the Probit Method sheet and the "normality" of the histogram in Inversion Resultscan be used to determine whether the aerosol is unimodal and justify use of this method.

6A synopsis of the Inversion Results with a histrogram of the distribution is ready to print out in the sheet, "Inversion Results"

DISCUSSION

Note that the MMAD and GSD computed by the Inversion will always be smaller than that computed by the Probit method.The simplest explanation is (for MMAD) that for stage 1, for example, the probit method assumes that all mass is a result of particles greatethe cut-diameter of 21 microns, whereas the Inversion method "realizes" that a good portion of the mass is associated with particlesless than 21 microns. Therefore, the Inversion method attributes mass to the correct diameters and determines a more accurateMMAD than the graphical method. The implication is that an MMAD determined by the Probit method overestimates the MMAD and therefounderestimates the respirable fraction, and, consequently, the ill-health consequences associated with smaller particles.Further explanation is given by O'Shaughnessy and Raabe (3).


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REFERENCES(1) Rubow, K. L.; Marple, V. A.; Olin, J.; McCawley, M. A. 1987.

A personal cascade impactor: design, evaluation and calibration. Am. Ind. Hyg. Assoc. J. 48(6):532-538.

(2) Raabe O.G. 1978.A general method for fitting size distributions to multicomponent aerosol data using weighted least-squares. Environ. Sci. Technol. 12(10):11

(3) OShaughnessy, P. T., Raabe, O. G. 2003.

A Comparison of cascade impactor data reduction methods. Aerosol Science and Technology 37:187-200.(4) Rader DJ, Mondy LA, Brockmann JE, Lucero DA, Rubow KL. 1991.

Stage response calibration of the Mark III and Marple Personal cascade impactors. Aerosol Science and Technology 14:365-379.(5) Raabe O.G. 1976.

Aerosol aerodynamic size conventions for inertial sampler calibration. Air Pollution Control Association (APCA) Journal, 26(9):856-861

Any questions or comments please contact:Patrick T. O'ShaughnessyThe University of IowaDepartment of Occupational andEnvironmental Health100 Oakdale Campus, #137 IREHIowa City, Iowa 52242-5000

Phone: 319-335-4202FAX: 319-335-4225E-mail: [email protected]


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MARPLE IMPACTOR DATA REDUCTION Probit METHODUses Cut Diams calculated from equation given by Rader et al. rather than R

Trial Name: Small Chamber Trial 2Test Date: 11/05/00 Flow Rate: 2 lpmCalibrated: 11/05/00 Sample Time: 90 min

Uncorrected Corrected

Cut Diam. Initial Final Net Mass Stage Corrected Mass Cum. STAGE NO. mm Weight, mg Weight, mg Weight, mg Fraction, % Effect. Net Wt., mg Fraction, % % >

1 21.07 150.704 150.873 0.169 2.75 0.52 0.325 4.70 4.70 2 14.97 150.998 151.256 0.258 4.19 0.61 0.423 6.12 10.82 3 9.77 151.040 151.547 0.507 8.24 0.78 0.650 9.40 20.22 4 5.98 150.307 151.299 0.992 16.12 0.89 1.115 16.12 36.34 5 3.50 152.009 153.500 1.491 24.23 0.95 1.569 22.70 59.04 6 1.53 151.442 153.283 1.841 29.92 0.96 1.918 27.74 86.77 7 0.90 151.767 152.328 0.561 9.12 0.97 0.578 8.36 95.14 8 0.529 150.733 150.941 0.208 3.38 0.99 0.210 3.04 98.18

FILTER 12.674 12.800 0.126 2.05 1.00 0.126 1.82 100.00Sum 6.15 Sum 6.91 mg

Avg. Conc. 38.41 mg/m^3

Std. Dev. Cum %-4 0.00

-3.5 0.02-3 0.13

-2.5 0.62-2 2.28

-1.5 6.68-1 15.87

-0.5 30.850 50.00

0.5 69.151 84.13

1.5 93.322 97.72

2.5 99.383 99.87

3.5 99.984 100.00

MMAD = 4.34 mm

GSD = 2.64 mm

0.1

1.0

10.0

100.0

-3.0 -2.0 -1.0 0.0 1.0 2.0

D

iamter,microns

Standard Deviation

Marple Impactor Data Reduction


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INVERSION METHOD USING RADER ET AL. EFFICIENCY CURVES

This applies a weight equivalent to the variance of the frequency values defined as f(1-f).It also applies sampler losses and inlet efficiency corrections

Stage

MassPercentsfrom Data

Reduction

MassPercents

Computed below Variances

Weighted

Squarederror

Minimum

Error,SSE

1 2.746628 3.179175 0.026712 7.004285 55.934622 4.193077 4.458527 0.040173 1.754035

3 8.239883 8.157131 0.075609 0.090574 16.12222 15.68211 0.13523 1.4323345 24.23208 23.40541 0.183601 3.72209

6 29.92036 30.62067 0.209681 2.3389037 9.117504 9.71345 0.082862 4.2860558 3.380465 3.564796 0.032662 1.040296

F 2.047782 1.218731 0.020058 34.26605

"Solved" Valueslog values

MMAD 3.852655 0.58576

GSD 2.397895 0.37983

Sum Sum

101 99.99017 91.20127 100

a

Corrected Modified b

Cum % < "Mass" Inner Inlet "Mass" Mass Log Size Dae Dar Losses Efficiency Fraction

-0.5 0.316228 0.391042 0.212797 0.212797 0.007519 1 0.211197 0.231572

-0.475 0.334965 0.410184 0.261333 0.048536 0.007862 1 0.048154 0.0528 -0.45 0.354813 0.430422 0.319659 0.058326 0.008221 0.999999 0.057847 0.063427

-0.425 0.375837 0.451821 0.389447 0.069788 0.008597 0.999999 0.069188 0.075863 -0.4 0.398107 0.474451 0.472589 0.083142 0.008992 0.999999 0.082395 0.090344

-0.375 0.421697 0.498387 0.571212 0.098623 0.009405 0.999999 0.097696 0.107121

-0.35 0.446684 0.523707 0.687694 0.116482 0.009837 0.999999 0.115336 0.126463 -0.325 0.473151 0.550494 0.824673 0.136979 0.010289 0.999999 0.13557 0.148649

-0.3 0.501187 0.578836 0.985061 0.160387 0.010762 0.999998 0.158661 0.173968 -0.275 0.530884 0.608827 1.172045 0.186985 0.011256 0.999998 0.18488 0.202716

-0.25 0.562341 0.640565 1.389095 0.21705 0.011772 0.999998 0.214495 0.235188

-0.225 0.595662 0.674155 1.639957 0.250862 0.01231 0.999997 0.247773 0.271677 -0.2 0.630957 0.709707 1.928644 0.288687 0.012872 0.999996 0.28497 0.312463

-0.175 0.668344 0.747339 2.259425 0.33078 0.013458 0.999996 0.326327 0.35781 -0.15 0.707946 0.787176 2.636798 0.377374 0.014069 0.999995 0.372062 0.407957

-0.125 0.749894 0.829349 3.065468 0.428669 0.014705 0.999993 0.422363 0.463111

-0.1 0.794328 0.873997 3.550301 0.484834 0.015367 0.999992 0.477379 0.523435 -0.075 0.841395 0.921268 4.096288 0.545987 0.016055 0.99999 0.537216 0.589044

-0.05 0.891251 0.971318 4.708484 0.612197 0.01677 0.999988 0.601923 0.659994 -0.025 0.944061 1.024314 5.391953 0.683469 0.017513 0.999985 0.671489 0.736272

0 1 1.08043 6.151695 0.759742 0.018283 0.999981 0.745837 0.817793

0.025 1.059254 1.139851 6.992573 0.840877 0.019082 0.999977 0.824812 0.904387 0.05 1.122018 1.202776 7.919228 0.926656 0.01991 0.999971 0.90818 0.995797

0.075 1.188502 1.269412 8.936 1.016771 0.020767 0.999964 0.99562 1.091674 0.1 1.258925 1.33998 10.04683 1.11083 0.021654 0.999956 1.086728 1.191571

0.125 1.333521 1.414714 11.25518 1.208346 0.022571 0.999945 1.181008 1.294947

0.15 1.412538 1.493861 12.56392 1.308742 0.023517 0.999932 1.277877 1.401161 0.175 1.496236 1.577683 13.97527 1.411354 0.024495 0.999915 1.376667 1.509482


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0.05 1.122018 1.202776 7.9192281 0.926656 0.01991 0.999971 0.90818 0.9957970.075 1.188502 1.269412 8.9359995 1.016771 0.020767 0.999964 0.99562 1.091674

0.1 1.258925 1.33998 10.04683 1.11083 0.021654 0.999956 1.086728 1.191571

0.125 1.333521 1.414714 11.255175 1.208346 0.022571 0.999945 1.181008 1.2949470.15 1.412538 1.493861 12.563917 1.308742 0.023517 0.999932 1.277877 1.401161

0.175 1.496236 1.577683 13.975271 1.411354 0.024495 0.999915 1.376667 1.509482

0.2 1.584893 1.666458 15.490706 1.515435 0.025503 0.999895 1.476632 1.6190910.225 1.678804 1.760481 17.110866 1.62016 0.026542 0.999869 1.576951 1.729089

0.25 1.778279 1.860063 18.835503 1.724637 0.027612 0.999836 1.676742 1.8385070.275 1.883649 1.965533 20.663422 1.827919 0.028714 0.999796 1.77507 1.946321

0.3 1.995262 2.077242 22.592435 1.929013 0.029848 0.999745 1.87096 2.0514630.325 2.113489 2.19556 24.619337 2.026902 0.031013 0.999682 1.963417 2.152839

0.35 2.238721 2.320878 26.739893 2.120556 0.032212 0.999603 2.051434 2.2493480.375 2.371374 2.453612 28.948842 2.20895 0.033444 0.999505 2.134017 2.339898

0.4 2.511886 2.594202 31.239928 2.291085 0.034709 0.999382 2.210196 2.4234270.425 2.660725 2.743113 33.605934 2.366006 0.03601 0.999229 2.279048 2.498921

0.45 2.818383 2.900841 36.038753 2.432819 0.037346 0.999038 2.339711 2.5654370.475 2.985383 3.067906 38.529461 2.490709 0.038719 0.998802 2.391402 2.622115

0.5 3.162278 3.244863 41.068419 2.538957 0.040131 0.998508 2.433432 2.6681990.525 3.349654 3.432299 43.645375 2.576957 0.041583 0.998145 2.465218 2.7030520.55 3.548134 3.630834 46.249598 2.604222 0.043079 0.997697 2.486298 2.726166

0.575 3.758374 3.841127 48.870002 2.620404 0.04462 0.997146 2.496338 2.7371740.6 3.981072 4.063875 51.495294 2.625293 0.046211 0.996471 2.495138 2.735859

0.625 4.216965 4.299815 54.114119 2.618825 0.047855 0.995645 2.482642 2.722157

0.65 4.466836 4.549731 56.715204 2.601085 0.049558 0.994641 2.458932 2.6961590.675 4.731513 4.81445 59.287505 2.572301 0.051326 0.993426 2.424233 2.658113

0.7 5.011872 5.094849 61.820347 2.532843 0.053166 0.991964 2.37891 2.6084180.725 5.308844 5.391859 64.303561 2.483213 0.055086 0.990214 2.323461 2.547619

0.75 5.623413 5.706464 66.727597 2.424036 0.057096 0.988134 2.258511 2.4764030.775 5.956621 6.039706 69.08364 2.356044 0.059208 0.985679 2.184803 2.395584

0.8 6.309573 6.39269 71.363704 2.280063 0.061436 0.982805 2.103187 2.306095

0.825 6.683439 6.766586 73.560702 2.196998 0.063796 0.979469 2.014609 2.2089710.85 7.079458 7.162633 75.668514 2.107812 0.066307 0.975632 1.920093 2.105336

0.875 7.498942 7.582145 77.682021 2.013507 0.068991 0.971264 1.820725 1.9963810.9 7.943282 8.02651 79.597131 1.91511 0.071874 0.966341 1.717636 1.883346

0.925 8.413951 8.497204 81.410781 1.81365 0.074988 0.960856 1.611977 1.7674940.95 8.912509 8.995784 83.120925 1.710144 0.078369 0.954812 1.504899 1.650086

0.975 9.440609 9.523905 84.726502 1.605577 0.08206 0.94823 1.397523 1.532351 10 10.08332 86.227392 1.500889 0.086112 0.941146 1.290918 1.41546

1.025 10.59254 10.67587 87.624357 1.396965 0.090585 0.933606 1.186073 1.3005011.05 11.22018 11.30354 88.918975 1.294618 0.095551 0.925665 1.083877 1.188445

1.075 11.88502 11.96839 90.113561 1.194585 0.101096 0.917378 0.985097 1.0801351.1 12.58925 12.67264 91.211079 1.097519 0.107322 0.908787 0.890367 0.976266

1.125 13.33521 13.41862 92.215061 1.003982 0.114352 0.899913 0.80018 0.8773781.15 14.12538 14.20879 93.129509 0.914448 0.122335 0.890738 0.714887 0.783857

1.175 14.96236 15.04579 93.958808 0.8293 0.131448 0.881184 0.634708 0.6959421.2 15.84893 15.93238 94.707638 0.74883 0.141905 0.871093 0.559736 0.613737

1.225 16.78804 16.8715 95.380885 0.673247 0.153964 0.860199 0.489962 0.5372311.25 17.78279 17.86626 95.983561 0.602677 0.167935 0.848086 0.425286 0.466316

1.275 18.83649 18.91997 96.520734 0.537173 0.18419 0.834138 0.365545 0.4008121.3 19.95262 20.03611 96.997453 0.476719 0.203165 0.817459 0.310525 0.340484

1.325 21.13489 21.21839 97.418694 0.421241 0.225373 0.796763 0.259988 0.28507


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1.35 22.38721 22.47072 97.789305 0.370611 0.251395 0.77021 0.213688 0.2343041.375 23.71374 23.79725 98.113962 0.324657 0.281872 0.735203 0.171409 0.187946

1.4 25.11886 25.20239 98.397134 0.283172 0.317462 0.688181 0.133009 0.145841

1.425 26.60725 26.69078 98.643054 0.245921 0.358776 0.624654 0.098502 0.1080051.45 28.18383 28.26737 98.855701 0.212647 0.406259 0.540075 0.068188 0.074767

1.475 29.85383 29.93737 99.038782 0.183081 0.460021 0.432727 0.042779 0.046906

1.5 31.62278 31.70633 99.195727 0.156944 0.519624 0.309164 0.023309 0.0255571.525 33.49654 33.5801 99.329685 0.133958 0.583876 0.18817 0.010489 0.011501

1.55 35.48134 35.5649 99.443528 0.113844 0.65071 0.093537 0.003719 0.0040781.575 37.58374 37.66731 99.53986 0.096332 0.717271 0.036857 0.001004 0.001101

1.6 39.81072 39.89429 99.621022 0.081161 0.780288 0.011267 0.000201 0.000221.625 42.16965 42.25323 99.689106 0.068085 0.836676 0.002603 2.89E-05 3.17E-05

1.65 44.66836 44.75195 99.745974 0.056868 0.88418 0.000437 2.88E-06 3.16E-061.675 47.31513 47.39872 99.793268 0.047294 0.921788 5.06E-05 1.87E-07 2.05E-07

1.7 50.11872 50.20232 99.83243 0.039162 0.949766 3.77E-06 7.41E-09 8.13E-091.725 53.08844 53.17204 99.864718 0.032288 0.969343 1.67E-07 1.66E-10 1.81E-10

1.75 56.23413 56.31773 99.891223 0.026505 0.982243 4.03E-09 1.9E-12 2.08E-121.775 59.56621 59.64982 99.912888 0.021664 0.990255 4.75E-11 1E-14 1.1E-14

1.8 63.09573 63.17934 99.930519 0.017631 0.994945 2.42E-13 2.16E-17 2.36E-171.825 66.83439 66.918 99.944806 0.014287 0.997529 4.61E-16 1.63E-20 1.78E-201.85 70.79458 70.87819 99.956332 0.011527 0.998866 2.79E-19 3.65E-24 4E-24

1.875 74.98942 75.07304 99.965592 0.00926 0.999514 4.45E-23 2E-28 2.2E-281.9 79.43282 79.51644 99.972999 0.007406 0.999806 1.5E-27 2.15E-33 2.36E-33

1.925 84.13951 84.22314 99.978897 0.005898 0.999928 8.25E-33 3.48E-39 3.82E-39

1.95 89.12509 89.20872 99.983574 0.004677 0.999976 5.58E-39 6.33E-46 6.94E-461.975 94.40609 94.48971 99.987267 0.003693 0.999993 3.31E-46 9.18E-54 1.01E-53

2 100 100.0836 99.99017 0.002903 0.999998 1.18E-54 7.18E-63 7.87E-63


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to do multiple steps for this in the "Inversion Method" page, e SE. Final results are given in the "Inversion Results" page. changing the MMAD value by 1E-9.

Total Frequency/Stage

3.17917548 4.458527325

a = 26.06 17.77 11.22b = 2.871 3.616 4.62

Stage 1 Mass Mass Stage 2 Mass Mass Stage 3Percent Penetratin Deposited Percent Penetratin Deposited Percent

0.000581 0.231571 1.3449E-06 0.000102 0.231571 2.35122E-07 1.84122E-05

0.000666 0.0528 3.5175E-07 0.000121 0.052799 6.37223E-08 2.29612E-050.000765 0.063427 4.852E-07 0.000144 0.063427 9.11096E-08 2.86829E-050.000879 0.075863 6.6708E-07 0.000171 0.075862 1.29872E-07 3.58902E-050.001012 0.090343 9.1407E-07 0.000204 0.090343 1.84557E-07 4.49818E-05

0.001165 0.10712 1.2483E-06 0.000244 0.10712 2.61457E-07 5.64665E-050.001344 0.126461 1.699E-06 0.000292 0.126461 3.69241E-07 7.09939E-050.00155 0.148646 2.3046E-06 0.00035 0.148646 5.19811E-07 8.93943E-05

0.001791 0.173965 3.1153E-06 0.000419 0.173964 7.29446E-07 0.000112730.00207 0.202712 4.1967E-06 0.000503 0.202711 1.02033E-06 0.000142362

0.002395 0.235183 5.6337E-06 0.000605 0.235181 1.42255E-06 0.0001800340.002774 0.271669 7.5363E-06 0.000728 0.271667 1.97681E-06 0.0002279830.003215 0.312453 1.0046E-05 0.000876 0.31245 2.73789E-06 0.00028908

0.003729 0.357797 1.3343E-05 0.001056 0.357793 3.77926E-06 0.0003670170.004329 0.40794 1.7659E-05 0.001274 0.407935 5.19903E-06 0.0004665360.005028 0.463088 2.3287E-05 0.001539 0.46308 7.12767E-06 0.0005937440.005845 0.523404 3.0597E-05 0.001861 0.523395 9.73795E-06 0.0007565

0.0068 0.589004 4.0053E-05 0.002251 0.588991 1.32577E-05 0.0009649310.007915 0.659941 5.2239E-05 0.002725 0.659923 1.7986E-05 0.0012320940.009219 0.736204 6.7878E-05 0.003303 0.73618 2.43139E-05 0.001574830.010745 0.817705 8.7869E-05 0.004005 0.817672 3.275E-05 0.0020148770.01253 0.904273 0.00011332 0.004861 0.904229 4.39535E-05 0.00258031


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0.01462 0.995651 0.00014559 0.005903 0.995593 5.87741E-05 0.0033074010.017068 1.091488 0.00018633 0.007174 1.091409 7.83026E-05 0.0042430410.019936 1.191334 0.00023755 0.008724 1.19123 0.000103932 0.005447878

0.023297 1.294645 0.00030169 0.010616 1.294508 0.000137435 0.0070003820.027238 1.400779 0.00038165 0.012925 1.400598 0.000181053 0.0090021340.03186 1.509001 0.00048093 0.015746 1.508764 0.000237607 0.011584681

0.037283 1.618488 0.00060364 0.019193 1.618177 0.000310634 0.014918440.043646 1.728334 0.00075468 0.023406 1.72793 0.00040454 0.0192242740.051115 1.837568 0.00093976 0.028559 1.837043 0.00052479 0.0247885160.059885 1.945156 0.00116556 0.034862 1.944478 0.000678125 0.0319825030.070185 2.050023 0.00143981 0.042576 2.04915 0.000872816 0.0412879670.082284 2.151068 0.00177144 0.052018 2.149949 0.001118953 0.0533300380.096499 2.247178 0.00217061 0.063581 2.245749 0.001428783 0.0689201650.113206 2.337249 0.00264891 0.077744 2.335432 0.001817076 0.089111931

0.132844 2.420207 0.00321938 0.095097 2.417906 0.002301549 0.1152736580.155932 2.495025 0.00389662 0.116364 2.492121 0.002903317 0.1491828590.183081 2.56074 0.00469682 0.142435 2.557093 0.003647387 0.1931491420.215011 2.616477 0.00563783 0.174402 2.611914 0.00456318 0.250174124

0.25257 2.66146 0.00673907 0.213607 2.655775 0.005685069 0.3241595720.296757 2.695031 0.0080215 0.261701 2.687978 0.007052915 0.4201782740.34875 2.716658 0.0095075 0.32071 2.707946 0.008712584 0.544826594

0.409936 2.725954 0.01122066 0.393125 2.715237 0.010716402 0.7066832750.48195 2.722674 0.01318547 0.482009 2.70955 0.013123529 0.916906399

0.566718 2.70673 0.01542696 0.591125 2.69073 0.016000171 1.190009735

0.666512 2.678189 0.01797023 0.725102 2.65877 0.019419596 1.5448715040.784007 2.637273 0.0208398 0.889626 2.613811 0.023461871 2.0060431710.922357 2.584359 0.02405893 1.091692 2.556145 0.028213227 2.6054429111.08528 2.51997 0.0276488 1.339895 2.486205 0.033764964 3.384536686

1.277155 2.444775 0.03162751 1.644805 2.404564 0.04021179 4.3971246451.503146 2.359575 0.03600912 2.019409 2.311925 0.047649472 5.7128504391.769334 2.265292 0.04080252 2.479667 2.20912 0.05617169 7.421508365

2.082887 2.16296 0.04601037 3.045176 2.097094 0.065865959 9.638076542.452247 2.053708 0.05162802 3.739991 1.976899 0.076808484 12.508020392.887352 1.938738 0.05764255 4.593594 1.849681 0.089057772 16.211517023.399902 1.819314 0.06403193 5.642059 1.716668 0.102646782 20.96333139

4.003656 1.69673 0.07076439 6.929403 1.579157 0.117573248 27.00130094.71478 1.572288 0.07779791 8.509106 1.4385 0.133787632 34.54995026

5.552245 1.447271 0.08507986 10.44572 1.296093 0.15117786 43.737855456.53827 1.322914 0.09254662 12.81638 1.153364 0.169549588 54.44741395

7.698807 1.200377 0.10012302 15.71175 1.011777 0.188600303 66.111853039.064054 1.080723 0.10772128 19.23576 0.872838 0.207885335 77.5852179810.66897 0.964896 0.11523925 23.50247 0.738121 0.226774305 87.3483954312.55371 0.853708 0.12255752 28.62792 0.609309 0.244398887 94.19429217

14.76389 0.747843 0.12953508 34.71307 0.488244 0.259599111 97.9529898917.35055 0.647853 0.13600347 41.81332 0.376964 0.270889027 99.4827401720.36941 0.554183 0.14175926 49.89081 0.277696 0.276486183 99.9145290123.87915 0.467182 0.14655523 58.75204 0.192703 0.274478972 99.9918373427.93796 0.38714 0.15009141 67.99009 0.123923 0.263216678 99.9996177632.59757 0.314309 0.15200782 76.97555 0.072368 0.241940741 99.9999929337.89382 0.248929 0.15188281 84.95438 0.037453 0.211475916 99.9999999643.8327 0.191241 0.14924323 91.26954 0.016696 0.174544336 100

50.37207 0.141474 0.14359574 95.61508 0.006204 0.135270864 100


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8.157130829 15.68211 23.40541

6.752 3.9545.577 5.992

Mass Mass Stage 4 Mass Mass Stage 5 Mass MassPenetrating Deposited Percent Penetratin Deposited Percent Penetratin Deposited

0.2315706 4.26371E-08 1.259E-05 0.231571 2.92E-08 9.53143E-05 0.23157 2.21E-07

0.0527995 1.21234E-08 1.644E-05 0.052799 8.68E-09 0.000126919 0.052799 6.7E-080.0634267 1.81926E-08 2.15E-05 0.063427 1.36E-08 0.000169375 0.063427 1.07E-070.0758624 2.72272E-08 2.818E-05 0.075862 2.14E-08 0.000226523 0.075862 1.72E-070.0903425 4.06377E-08 3.701E-05 0.090342 3.34E-08 0.000303595 0.090342 2.74E-07

0.1071194 6.04867E-08 4.871E-05 0.107119 5.22E-08 0.000407733 0.107119 4.37E-070.1264606 8.97794E-08 6.421E-05 0.126461 8.12E-08 0.000548698 0.12646 6.94E-070.1486458 1.32881E-07 8.481E-05 0.148646 1.26E-07 0.000739853 0.148645 1.1E-060.1739641 1.9611E-07 0.0001122 0.173964 1.95E-07 0.000999516 0.173962 1.74E-060.2027105 2.88583E-07 0.0001487 0.20271 3.01E-07 0.00135283 0.202707 2.74E-060.2351808 4.23406E-07 0.0001975 0.23518 4.64E-07 0.001834349 0.235176 4.31E-060.2716667 6.19354E-07 0.0002626 0.271666 7.13E-07 0.002491627 0.271659 6.77E-060.3124491 9.03231E-07 0.0003497 0.312448 1.09E-06 0.003390175 0.312437 1.06E-05

0.3577915 1.31316E-06 0.0004665 0.35779 1.67E-06 0.004620358 0.357773 1.65E-050.4079326 1.90316E-06 0.0006232 0.40793 2.54E-06 0.006306951 0.407904 2.57E-050.4630777 2.74951E-06 0.0008338 0.463074 3.86E-06 0.008622438 0.463034 3.99E-050.5233907 3.95948E-06 0.001117 0.523385 5.85E-06 0.011805483 0.523323 6.18E-050.588985 5.68335E-06 0.0014984 0.588976 8.83E-06 0.016186657 0.588881 9.53E-05

0.6599152 8.13087E-06 0.0020127 0.659902 1.33E-05 0.022224252 0.659755 0.0001470.7361682 1.15936E-05 0.0027067 0.736148 1.99E-05 0.030554203 0.735923 0.0002250.8176556 1.64751E-05 0.0036444 0.817626 2.98E-05 0.042059704 0.817282 0.0003440.9042061 2.33319E-05 0.0049124 0.904162 4.44E-05 0.05796835 0.903638 0.000524


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30.62067 9.71345 3.564796

1.757 1.061 0.6917.169 7.946 4.599

Stage 6 Mass Mass Stage 7 Mass Mass Stage 8 Mass MassPercent Penetratin Deposited Percent Penetratin Deposited Percent Penetratin Deposited0.002098 0.231565 4.86E-06 0.035931 0.231482 8.32E-05 7.279582 0.214631 0.016851

0.002956 0.052798 1.56E-06 0.052528 0.05277 2.77E-05 9.060187 0.047989 0.0047810.004175 0.063424 2.65E-06 0.077017 0.063375 4.88E-05 11.28922 0.056221 0.0071550.005911 0.075858 4.48E-06 0.113247 0.075772 8.59E-05 14.07782 0.065105 0.0106670.008392 0.090335 7.58E-06 0.166987 0.090184 0.000151 17.55982 0.074348 0.015836

0.011942 0.107106 1.28E-05 0.246905 0.106842 0.000264 21.89091 0.083453 0.0233890.017036 0.126438 2.15E-05 0.366049 0.125975 0.000463 27.24099 0.091659 0.034317

0.02436 0.148608 3.62E-05 0.544103 0.1478 0.000809 33.7731 0.097883 0.0499170.034913 0.173901 6.07E-05 0.810818 0.172491 0.00141 41.59848 0.100738 0.071754

0.05015 0.202606 0.000102 1.211245 0.200152 0.002454 50.69633 0.098682 0.101470.072191 0.235006 0.00017 1.81371 0.230744 0.004262 60.79772 0.090457 0.1402870.104138 0.271376 0.000283 2.721955 0.26399 0.007387 71.27244 0.075838 0.1881520.150528 0.311967 0.00047 4.093522 0.299197 0.01277 81.12638 0.056469 0.242727

0.218012 0.356993 0.00078 6.16719 0.334977 0.022016 89.24835 0.036016 0.2989610.316351 0.406614 0.00129 9.302419 0.368789 0.037825 94.89236 0.018836 0.3499530.459892 0.460904 0.002129 14.03064 0.396237 0.064668 98.06712 0.007659 0.3885780.669745 0.519818 0.003505 21.10226 0.410125 0.109693 99.44932 0.002258 0.4078660.977014 0.583127 0.005753 31.45564 0.399701 0.183426 99.89024 0.000439 0.3992621.427569 0.650337 0.009418 45.87486 0.351996 0.298341 99.98611 4.89E-05 0.3519472.089115 0.720549 0.015374 63.87608 0.260291 0.460258 99.99902 2.55E-06 0.260288

3.0616 0.79226 0.025022 81.94395 0.143051 0.649209 99.99997 4.69E-08 0.1430514.492457 0.863042 0.040596 94.33448 0.048896 0.814146 100 2.05E-10 0.048896


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6.598492 0.929062 0.065635 99.11677 0.008206 0.920857 100 1.27E-13 0.0082069.69599 0.984367 0.105692 99.9511 0.000481 0.983886 100 5.54E-18 0.000481

14.23766 1.019886 0.169314 99.99944 5.73E-06 1.019881 100 0 5.73E-06

20.84315 1.022285 0.269182 100 5.83E-09 1.022285 100 0 5.83E-0930.27163 0.973448 0.422609 100 1.32E-13 0.973448 100 0 1.32E-1343.18796 0.853319 0.648685 100 0 0.853319 100 0 0

59.43375 0.652365 0.955783 100 0 0.652365 100 0 076.7531 0.398243 1.314858 100 0 0.398243 100 0 0

90.60093 0.170611 1.644582 100 0 0.170611 100 0 097.73448 0.043326 1.869073 100 0 0.043326 100 0 099.73957 0.005214 1.997013 100 0 0.005214 100 0 099.98977 0.000213 2.081359 100 0 0.000213 100 0 099.99992 1.75E-06 2.146501 100 0 1.75E-06 100 0 0

100 1.33E-09 2.191987 100 0 1.33E-09 100 0 0

100 2.86E-14 2.211528 100 0 2.86E-14 100 0 0100 0 2.196754 100 0 0 100 0 0100 0 2.137047 100 0 0 100 0 0100 0 2.019548 100 0 0 100 0 0

100 0 1.830369 100 0 0 100 0 0100 0 1.55885 100 0 0 100 0 0100 0 1.207728 100 0 0 100 0 0100 0 0.809712 100 0 0 100 0 0100 0 0.437179 100 0 0 100 0 0100 0 0.173016 100 0 0 100 0 0

100 0 0.044694 100 0 0 100 0 0100 0 0.006485 100 0 0 100 0 0100 0 0.000427 100 0 0 100 0 0100 0 9.31E-06 100 0 0 100 0 0100 0 4.31E-08 100 0 0 100 0 0100 0 2.24E-11 100 0 0 100 0 0100 0 6.5E-16 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0


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100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0


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Sum

1.218731 100

Filter

0.214631 0.231572

0.047989 0.05280.056221 0.0634270.065105 0.0758630.074348 0.090344

0.083453 0.1071210.091659 0.1264630.097883 0.1486490.100738 0.1739680.098682 0.2027160.090457 0.2351880.075838 0.2716770.056469 0.312463

0.036016 0.357810.018836 0.4079570.007659 0.4631110.002258 0.5234350.000439 0.5890444.89E-05 0.6599942.55E-06 0.7362724.69E-08 0.8177932.05E-10 0.904387


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1.27E-13 0.9957975.54E-18 1.091674

0 1.191571

0 1.2949470 1.4011610 1.509482

0 1.6190910 1.7290890 1.8385070 1.9463210 2.0514630 2.1528390 2.2493480 2.339898

0 2.4234270 2.4989210 2.5654370 2.622115

0 2.6681990 2.7030520 2.7261660 2.7371740 2.7358590 2.722157

0 2.6961590 2.6581130 2.6084180 2.5476190 2.4764030 2.3955840 2.306095

0 2.2089710 2.1053360 1.9963810 1.883346

0 1.7674940 1.6500860 1.532350 1.415460 1.3005010 1.1884450 1.0801350 0.976266

0 0.8773780 0.7838570 0.6959420 0.6137370 0.5372310 0.4663160 0.4008120 0.3404840 0.28507


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0 0.2343040 0.1879460 0.145841

0 0.1080050 0.0747670 0.046906

0 0.0255570 0.0115010 0.0040780 0.0011010 0.000220 3.17E-050 3.16E-060 2.05E-07

0 8.13E-090 1.81E-100 2.08E-120 1.1E-14

0 2.36E-170 1.78E-200 4E-240 2.2E-280 2.36E-330 3.82E-39

0 6.94E-460 1.01E-530 7.87E-63


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This page and SE Calc 1 are used to determine the derivatives needed to calculate the standard errors of

Stage

MassPercentsfrom Data

Reduction

MassPercentsComputed

below Variances

WeightedSquared

error

Minimum

Error, SSE Deriv(2)1 2.746628 3.179175 0.0267119 7.004285 55.93462 -2.1917782 4.193077 4.458527 0.0401726 1.754035 -2.2549223 8.239883 8.157131 0.0756093 0.09057 -1.3522554 16.12222 15.68211 0.1352296 1.432334 3.0163095 24.23208 23.40541 0.1836014 3.72209 8.9566476 29.92036 30.62067 0.2096808 2.338903 6.527387 9.117504 9.71345 0.0828621 4.286055 -4.438633

8 3.380465 3.564796 0.0326619 1.040296 -4.945885F 2.047782 1.218731 0.0200585 34.26605 -3.316898

"Solved" Values

log valuesMMAD 3.852655 0.5857601GSD 2.397895 0.3798301

Sum Sum

101 99.99017 91.20127 100

Corrected ModifiedCum % < "Mass" Inner Inlet "Mass" Mass

Log Size Dae Dar Losses Efficiency Fraction-0.5 0.316228 0.391042 0.2127968 0.212797 0.007519 1 0.211197 0.231572

-0.475 0.334965 0.410184 0.2613326 0.048536 0.007862 1 0.048154 0.0528-0.45 0.354813 0.430422 0.3196586 0.058326 0.008221 0.999999 0.057847 0.063427

-0.425 0.375837 0.451821 0.3894469 0.069788 0.008597 0.999999 0.069188 0.075863-0.4 0.398107 0.474451 0.4725891 0.083142 0.008992 0.999999 0.082395 0.090344

-0.375 0.421697 0.498387 0.5712124 0.098623 0.009405 0.999999 0.097696 0.107121-0.35 0.446684 0.523707 0.687694 0.116482 0.009837 0.999999 0.115336 0.126463

-0.325 0.473151 0.550494 0.8246731 0.136979 0.010289 0.999999 0.13557 0.148649-0.3 0.501187 0.578836 0.9850605 0.160387 0.010762 0.999998 0.158661 0.173968

-0.275 0.530884 0.608827 1.1720451 0.186985 0.011256 0.999998 0.18488 0.202716-0.25 0.562341 0.640565 1.3890954 0.21705 0.011772 0.999998 0.214495 0.235188

-0.225 0.595662 0.674155 1.639957 0.250862 0.01231 0.999997 0.247773 0.271677-0.2 0.630957 0.709707 1.9286441 0.288687 0.012872 0.999996 0.28497 0.312463

-0.175 0.668344 0.747339 2.2594246 0.33078 0.013458 0.999996 0.326327 0.35781-0.15 0.707946 0.787176 2.6367982 0.377374 0.014069 0.999995 0.372062 0.407957

-0.125 0.749894 0.829349 3.0654676 0.428669 0.014705 0.999993 0.422363 0.463111-0.1 0.794328 0.873997 3.5503012 0.484834 0.015367 0.999992 0.477379 0.523435

-0.075 0.841395 0.921268 4.0962879 0.545987 0.016055 0.99999 0.537216 0.589044-0.05 0.891251 0.971318 4.7084845 0.612197 0.01677 0.999988 0.601923 0.659994

-0.025 0.944061 1.024314 5.3919535 0.683469 0.017513 0.999985 0.671489 0.7362720 1 1.08043 6.1516954 0.759742 0.018283 0.999981 0.745837 0.817793

0.025 1.059254 1.139851 6.9925725 0.840877 0.019082 0.999977 0.824812 0.904387


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0.05 1.122018 1.202776 7.9192281 0.926656 0.01991 0.999971 0.90818 0.9957970.075 1.188502 1.269412 8.9359995 1.016771 0.020767 0.999964 0.99562 1.091674

0.1 1.258925 1.33998 10.04683 1.11083 0.021654 0.999956 1.086728 1.191571

0.125 1.333521 1.414714 11.255175 1.208346 0.022571 0.999945 1.181008 1.2949470.15 1.412538 1.493861 12.563917 1.308742 0.023517 0.999932 1.277877 1.401161

0.175 1.496236 1.577683 13.975271 1.411354 0.024495 0.999915 1.376667 1.509482

0.2 1.584893 1.666458 15.490706 1.515435 0.025503 0.999895 1.476632 1.6190910.225 1.678804 1.760481 17.110866 1.62016 0.026542 0.999869 1.576951 1.729089

0.25 1.778279 1.860063 18.835503 1.724637 0.027612 0.999836 1.676742 1.8385070.275 1.883649 1.965533 20.663422 1.827919 0.028714 0.999796 1.77507 1.946321

0.3 1.995262 2.077242 22.592435 1.929013 0.029848 0.999745 1.87096 2.0514630.325 2.113489 2.19556 24.619337 2.026902 0.031013 0.999682 1.963417 2.152839

0.35 2.238721 2.320878 26.739893 2.120556 0.032212 0.999603 2.051434 2.2493480.375 2.371374 2.453612 28.948843 2.20895 0.033444 0.999505 2.134017 2.339898

0.4 2.511886 2.594202 31.239928 2.291085 0.034709 0.999382 2.210196 2.4234270.425 2.660725 2.743113 33.605934 2.366006 0.03601 0.999229 2.279048 2.498921

0.45 2.818383 2.900841 36.038753 2.432819 0.037346 0.999038 2.339711 2.5654370.475 2.985383 3.067906 38.529461 2.490709 0.038719 0.998802 2.391402 2.622115

0.5 3.162278 3.244863 41.068419 2.538957 0.040131 0.998508 2.433432 2.6681990.525 3.349654 3.432299 43.645375 2.576957 0.041583 0.998145 2.465218 2.7030520.55 3.548134 3.630834 46.249598 2.604222 0.043079 0.997697 2.486298 2.726166

0.575 3.758374 3.841127 48.870002 2.620404 0.04462 0.997146 2.496338 2.7371740.6 3.981072 4.063875 51.495294 2.625293 0.046211 0.996471 2.495138 2.735859

0.625 4.216965 4.299815 54.114119 2.618825 0.047855 0.995645 2.482642 2.722157

0.65 4.466836 4.549731 56.715204 2.601085 0.049558 0.994641 2.458932 2.6961590.675 4.731513 4.81445 59.287505 2.572301 0.051326 0.993426 2.424233 2.658113

0.7 5.011872 5.094849 61.820347 2.532843 0.053166 0.991964 2.37891 2.6084180.725 5.308844 5.391859 64.303561 2.483213 0.055086 0.990214 2.323461 2.547619

0.75 5.623413 5.706464 66.727597 2.424036 0.057096 0.988134 2.258511 2.4764030.775 5.956621 6.039706 69.08364 2.356044 0.059208 0.985679 2.184803 2.395584

0.8 6.309573 6.39269 71.363704 2.280063 0.061436 0.982805 2.103187 2.306095

0.825 6.683439 6.766586 73.560702 2.196998 0.063796 0.979469 2.014609 2.2089710.85 7.079458 7.162633 75.668514 2.107812 0.066307 0.975632 1.920093 2.105336

0.875 7.498942 7.582145 77.682021 2.013507 0.068991 0.971264 1.820725 1.9963810.9 7.943282 8.02651 79.597131 1.91511 0.071874 0.966341 1.717636 1.883346

0.925 8.413951 8.497204 81.410781 1.81365 0.074988 0.960856 1.611977 1.7674940.95 8.912509 8.995784 83.120925 1.710144 0.078369 0.954812 1.504899 1.650086

0.975 9.440609 9.523905 84.726502 1.605577 0.08206 0.94823 1.397523 1.532351 10 10.08332 86.227392 1.500889 0.086112 0.941146 1.290918 1.41546

1.025 10.59254 10.67587 87.624357 1.396965 0.090585 0.933606 1.186073 1.3005011.05 11.22018 11.30354 88.918975 1.294618 0.095551 0.925665 1.083877 1.188445

1.075 11.88502 11.96839 90.113561 1.194585 0.101096 0.917378 0.985097 1.0801351.1 12.58925 12.67264 91.211079 1.097519 0.107322 0.908787 0.890367 0.976266

1.125 13.33521 13.41862 92.215061 1.003982 0.114352 0.899913 0.80018 0.8773781.15 14.12538 14.20879 93.129509 0.914448 0.122335 0.890738 0.714887 0.783857

1.175 14.96236 15.04579 93.958808 0.8293 0.131448 0.881184 0.634708 0.6959421.2 15.84893 15.93238 94.707638 0.74883 0.141905 0.871093 0.559736 0.613737

1.225 16.78804 16.8715 95.380885 0.673247 0.153964 0.860199 0.489962 0.5372311.25 17.78279 17.86626 95.983561 0.602677 0.167935 0.848086 0.425286 0.466316

1.275 18.83649 18.91997 96.520734 0.537173 0.18419 0.834138 0.365545 0.4008121.3 19.95262 20.03611 96.997453 0.476719 0.203165 0.817459 0.310525 0.340484

1.325 21.13489 21.21839 97.418694 0.421241 0.225373 0.796763 0.259988 0.28507


23/38


24/38


25/38

0.01462 0.995651494 0.00014559 0.005903 0.995593 5.87741E-05 0.0033074010.017068 1.091487576 0.00018633 0.007174 1.091409 7.83026E-05 0.0042430410.019936 1.191333849 0.00023755 0.008724 1.19123 0.000103932 0.005447878

0.023297 1.294645067 0.00030169 0.010616 1.294508 0.000137435 0.0070003820.027238 1.400779379 0.00038165 0.012925 1.400598 0.000181053 0.0090021340.03186 1.509001409 0.00048093 0.015746 1.508764 0.000237607 0.011584681

0.037283 1.618487683 0.00060364 0.019193 1.618177 0.000310634 0.014918440.043646 1.728334425 0.00075468 0.023406 1.72793 0.00040454 0.0192242740.051115 1.837567686 0.00093976 0.028559 1.837043 0.00052479 0.0247885160.059885 1.945155702 0.00116556 0.034862 1.944478 0.000678125 0.0319825030.070185 2.050023284 0.00143981 0.042576 2.04915 0.000872816 0.0412879670.082284 2.151067975 0.00177144 0.052018 2.149949 0.001118953 0.0533300380.096499 2.247177637 0.00217061 0.063581 2.245749 0.001428783 0.0689201650.113206 2.337249074 0.00264891 0.077744 2.335432 0.001817076 0.089111931

0.132844 2.420207252 0.00321938 0.095097 2.417906 0.002301549 0.1152736580.155932 2.495024622 0.00389662 0.116364 2.492121 0.002903317 0.1491828590.183081 2.560740076 0.00469682 0.142435 2.557093 0.003647387 0.1931491420.215011 2.61647703 0.00563783 0.174402 2.611914 0.00456318 0.250174124

0.25257 2.661460188 0.00673907 0.213607 2.655775 0.005685069 0.3241595720.296757 2.695030552 0.0080215 0.261701 2.687978 0.007052915 0.4201782740.34875 2.716658346 0.0095075 0.32071 2.707946 0.008712584 0.544826594

0.409936 2.725953556 0.01122066 0.393125 2.715237 0.010716402 0.7066832750.48195 2.722673924 0.01318547 0.482009 2.70955 0.013123529 0.916906399

0.566718 2.706730282 0.01542696 0.591125 2.69073 0.016000171 1.190009735

0.666512 2.678189247 0.01797023 0.725102 2.65877 0.019419596 1.5448715040.784007 2.63727333 0.0208398 0.889626 2.613811 0.023461871 2.0060431710.922357 2.584358622 0.02405893 1.091692 2.556145 0.028213227 2.6054429111.08528 2.519970184 0.0276488 1.339895 2.486205 0.033764964 3.384536686

1.277155 2.444775319 0.03162751 1.644805 2.404564 0.04021179 4.3971246451.503146 2.359574797 0.03600912 2.019409 2.311925 0.047649472 5.7128504391.769334 2.265292073 0.04080252 2.479667 2.20912 0.05617169 7.421508365

2.082887 2.162960389 0.04601037 3.045176 2.097094 0.065865959 9.638076542.452247 2.0537076 0.05162802 3.739991 1.976899 0.076808484 12.508020392.887352 1.938738486 0.05764255 4.593594 1.849681 0.089057772 16.211517023.399902 1.819314359 0.06403193 5.642059 1.716668 0.102646782 20.96333139

4.003656 1.696729938 0.07076439 6.929403 1.579157 0.117573248 27.00130094.71478 1.572287728 0.07779791 8.509106 1.4385 0.133787632 34.54995026

5.552245 1.447270599 0.08507986 10.44572 1.296093 0.15117786 43.737855456.53827 1.322913716 0.09254662 12.81638 1.153364 0.169549588 54.44741395

7.698807 1.200377484 0.10012302 15.71175 1.011777 0.188600303 66.111853039.064054 1.080723491 0.10772128 19.23576 0.872838 0.207885335 77.5852179810.66897 0.96489561 0.11523925 23.50247 0.738121 0.226774305 87.3483954312.55371 0.853708167 0.12255752 28.62792 0.609309 0.244398887 94.19429217

14.76389 0.747842627 0.12953508 34.71307 0.488244 0.259599111 97.9529898917.35055 0.64785343 0.13600347 41.81332 0.376964 0.270889027 99.4827401720.36941 0.554182645 0.14175926 49.89081 0.277696 0.276486183 99.9145290123.87915 0.467182002 0.14655523 58.75204 0.192703 0.274478972 99.9918373427.93796 0.387139763 0.15009141 67.99009 0.123923 0.263216678 99.9996177632.59757 0.314308549 0.15200782 76.97555 0.072368 0.241940741 99.9999929337.89382 0.248928784 0.15188281 84.95438 0.037453 0.211475916 99.9999999643.8327 0.191240511 0.14924323 91.26954 0.016696 0.174544336 100

50.37207 0.141474405 0.14359574 95.61508 0.006204 0.135270864 100


26/38

57.40055 0.099812053 0.13449157 98.14869 0.001848 0.097964221 10064.71927 0.066308686 0.1216372 99.36558 0.000421 0.065888008 10072.03629 0.04078249 0.10505829 99.83107 6.89E-05 0.040713598 100

78.98668 0.022695415 0.08530946 99.96693 7.51E-06 0.022687909 10085.18687 0.01107533 0.06369166 99.99556 4.92E-07 0.011074839 10090.31736 0.004541787 0.04236471 99.99963 1.7E-08 0.00454177 100

94.2056 0.001480893 0.0240764 99.99998 2.65E-10 0.001480893 10096.86971 0.000360018 0.0111411 100 1.52E-12 0.000360018 10098.49761 6.1272E-05 0.00401702 100 2.58E-15 6.1272E-05 10099.37125 6.92054E-06 0.00109377 100 9.99E-19 6.92054E-06 10099.77565 4.94226E-07 0.0002198 100 1.4E-22 4.94226E-07 10099.93357 2.10843E-08 3.1719E-05 100 0 2.10843E-08 10099.9842 4.98753E-10 3.1563E-06 100 0 4.98753E-10 10099.9971 5.95259E-12 2.0502E-07 100 0 5.95259E-12 100

99.99961 3.19842E-14 8.126E-09 100 0 3.19842E-14 10099.99996 6.76465E-17 1.8147E-10 100 0 6.76465E-17 100

100 4.812E-20 2.0809E-12 100 0 4.812E-20 100100 9.57792E-24 1.0998E-14 100 0 9.57792E-24 100

100 4.30194E-28 2.3632E-17 100 0 4.30194E-28 100100 3.39386E-33 1.7849E-20 100 0 3.39386E-33 100100 3.41464E-39 4.0047E-24 100 0 3.41464E-39 100100 0 2.1976E-28 100 0 0 100100 0 2.3571E-33 100 0 0 100100 0 3.8179E-39 100 0 0 100

100 0 6.9399E-46 100 0 0 100100 0 1.0065E-53 100 0 0 100100 0 7.8712E-63 100 0 0 100


27/38

8.157130827 15.68211 23.40541

6.752 3.9545.577 5.992

Mass Mass Stage 4 Mass Mass Stage 5 Mass MassPenetrating Deposited Percent Penetratin Deposited Percent Penetratin Deposited

0.2315706 4.26371E-08 1.259E-05 0.231571 2.92E-08 9.53143E-05 0.23157 2.21E-07

0.0527995 1.21234E-08 1.644E-05 0.052799 8.68E-09 0.000126919 0.052799 6.7E-080.0634267 1.81926E-08 2.15E-05 0.063427 1.36E-08 0.000169375 0.063427 1.07E-070.0758624 2.72272E-08 2.818E-05 0.075862 2.14E-08 0.000226523 0.075862 1.72E-070.0903425 4.06377E-08 3.701E-05 0.090342 3.34E-08 0.000303595 0.090342 2.74E-07

0.1071194 6.04867E-08 4.871E-05 0.107119 5.22E-08 0.000407733 0.107119 4.37E-070.1264606 8.97794E-08 6.421E-05 0.126461 8.12E-08 0.000548698 0.12646 6.94E-070.1486458 1.32881E-07 8.481E-05 0.148646 1.26E-07 0.000739853 0.148645 1.1E-060.1739641 1.9611E-07 0.0001122 0.173964 1.95E-07 0.000999516 0.173962 1.74E-060.2027105 2.88583E-07 0.0001487 0.20271 3.01E-07 0.00135283 0.202707 2.74E-060.2351808 4.23406E-07 0.0001975 0.23518 4.64E-07 0.001834349 0.235176 4.31E-060.2716667 6.19354E-07 0.0002626 0.271666 7.13E-07 0.002491627 0.271659 6.77E-060.3124491 9.03231E-07 0.0003497 0.312448 1.09E-06 0.003390175 0.312437 1.06E-05

0.3577915 1.31316E-06 0.0004665 0.35779 1.67E-06 0.004620358 0.357773 1.65E-050.4079326 1.90316E-06 0.0006232 0.40793 2.54E-06 0.006306951 0.407904 2.57E-050.4630777 2.74951E-06 0.0008338 0.463074 3.86E-06 0.008622438 0.463034 3.99E-050.5233907 3.95948E-06 0.001117 0.523385 5.85E-06 0.011805483 0.523323 6.18E-050.588985 5.68335E-06 0.0014984 0.588976 8.83E-06 0.016186657 0.588881 9.53E-05

0.6599152 8.13087E-06 0.0020127 0.659902 1.33E-05 0.022224252 0.659755 0.0001470.7361682 1.15936E-05 0.0027067 0.736148 1.99E-05 0.030554203 0.735923 0.0002250.8176556 1.64751E-05 0.0036444 0.817626 2.98E-05 0.042059704 0.817282 0.0003440.9042061 2.33319E-05 0.0049124 0.904162 4.44E-05 0.05796835 0.903638 0.000524


28/38

0.9955598 3.29282E-05 0.006629 0.995494 6.6E-05 0.079987776 0.994698 0.0007961.091363 4.63089E-05 0.0089546 1.091265 9.77E-05 0.110495157 1.090059 0.0012061.191165 6.48968E-05 0.0121083 1.191021 0.000144 0.152802081 1.189201 0.00182

1.294417 9.06205E-05 0.0163883 1.294205 0.000212 0.21152499 1.291467 0.0027381.4004722 0.000126084 0.0222015 1.400161 0.000311 0.293103471 1.396057 0.0041041.508589 0.000174785 0.0301031 1.508135 0.000454 0.406525717 1.502004 0.006131

1.6179356 0.000241407 0.040851 1.617275 0.000661 0.564344274 1.608148 0.0091271.7275977 0.000332182 0.0554806 1.726639 0.000958 0.784098486 1.713101 0.0135391.8365875 0.000455376 0.0754068 1.835203 0.001385 1.090306265 1.815193 0.0200091.9438557 0.000621893 0.1025641 1.941862 0.001994 1.517251441 1.912399 0.0294632.0483044 0.000846053 0.1395985 2.045445 0.002859 2.112878521 2.002227 0.0432182.1488025 0.001146569 0.1901308 2.144717 0.004086 2.944216573 2.081572 0.0631452.2442011 0.001547774 0.2591176 2.238386 0.005815 4.104879907 2.146503 0.0918832.3333508 0.002081149 0.3533464 2.325106 0.008245 5.725292529 2.191987 0.133119

2.4151185 0.002787208 0.4821152 2.403475 0.011644 7.986211901 2.211528 0.1919472.4884035 0.003717818 0.6581647 2.472026 0.016378 11.13546179 2.196754 0.2752712.5521537 0.004939003 0.8989578 2.529211 0.022943 15.50537229 2.137047 0.3921642.6053795 0.006534333 1.2284334 2.573374 0.032005 21.52138886 2.019548 0.553826

2.6471662 0.008608949 1.6794103 2.602709 0.044457 29.67447727 1.830369 0.772342.6766833 0.011294298 2.2968732 2.615203 0.06148 40.39277844 1.55885 1.0563532.6931922 0.014753609 3.1424475 2.60856 0.084632 53.70136219 1.207728 1.4008322.696049 0.019188127 4.3004447 2.580107 0.115942 68.61710343 0.809712 1.770395

2.6847064 0.024844041 5.8859027 2.526687 0.158019 82.6975446 0.437179 2.0895082.6587102 0.03201995 8.0549502 2.444552 0.214158 92.92237671 0.173016 2.271536

2.6176951 0.041074575 11.017297 2.329296 0.288399 98.08123331 0.044694 2.2846022.5613773 0.052434186 15.048973 2.175916 0.385461 99.70196642 0.006485 2.1694312.4895465 0.066598909 20.498879 1.979217 0.510329 99.97844131 0.000427 1.9787912.4020587 0.084146528 27.771805 1.734964 0.667095 99.99946317 9.31E-06 1.7349542.2988319 0.105731656 37.248403 1.442554 0.856278 99.99999701 4.31E-08 1.4425542.1798485 0.132076836 49.071948 1.110154 1.069694 100 2.24E-11 1.1101542.0451703 0.163950054 62.741722 0.761995 1.283175 100 6.5E-16 0.761995

1.8949749 0.202119566 76.663225 0.442226 1.452749 100 0 0.4422261.7296282 0.247270945 88.315754 0.202094 1.527534 100 0 0.2020941.5498194 0.299861304 95.701973 0.066612 1.483208 100 0 0.0666121.3567969 0.359870713 98.951848 0.014221 1.342576 100 0 0.014221

1.1527638 0.426392849 99.852088 0.001705 1.151059 100 0 0.0017050.941499 0.497001068 99.99004 9.38E-05 0.941405 100 0 9.38E-05

0.7292096 0.566883169 99.999757 1.78E-06 0.729208 100 0 1.78E-060.5253872 0.627976941 99.999999 7.76E-09 0.525387 100 0 7.76E-090.3428725 0.668904642 100 4.52E-12 0.342873 100 0 4.52E-120.1956448 0.677193386 100 1.67E-16 0.195645 100 0 1.67E-160.0933842 0.644737116 100 0 0.093384 100 0 00.0353747 0.573934564 100 0 0.035375 100 0 0

0.0099944 0.478249122 100 0 0.009994 100 0 00.0019499 0.375014518 100 0 0.00195 100 0 00.0002373 0.277459112 100 0 0.000237 100 0 01.573E-05 0.1926873 100 0 1.57E-05 100 0 04.737E-07 0.123922612 100 0 4.74E-07 100 0 05.118E-09 0.072367802 100 0 5.12E-09 100 0 01.461E-11 0.037452868 100 0 1.46E-11 100 0 07.405E-15 0.016696175 100 0 7.41E-15 100 0 0

0 0.006203541 100 0 0 100 0 0


29/38

0 0.001847832 100 0 0 100 0 00 0.000420678 100 0 0 100 0 00 6.88922E-05 100 0 0 100 0 0

0 7.50534E-06 100 0 0 100 0 00 4.91744E-07 100 0 0 100 0 00 1.70285E-08 100 0 0 100 0 0

0 2.64965E-10 100 0 0 100 0 00 1.52265E-12 100 0 0 100 0 00 2.57957E-15 100 0 0 100 0 00 9.99203E-19 100 0 0 100 0 00 1.40467E-22 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 0

0 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 0

0 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 0

0 0 100 0 0 100 0 00 0 100 0 0 100 0 00 0 100 0 0 100 0 0


30/38

30.62067 9.71345 3.564796

1.757 1.061 0.6917.169 7.946 4.599

Stage 6 Mass Mass Stage 7 Mass Mass Stage 8 Mass MassPercent Penetratin Deposited Percent Penetratin Deposited Percent Penetratin Deposited0.002098 0.231565 4.86E-06 0.035931 0.231482 8.32E-05 7.279582 0.214631 0.016851

0.002956 0.052798 1.56E-06 0.052528 0.05277 2.77E-05 9.060187 0.047989 0.0047810.004175 0.063424 2.65E-06 0.077017 0.063375 4.88E-05 11.28922 0.056221 0.0071550.005911 0.075858 4.48E-06 0.113247 0.075772 8.59E-05 14.07782 0.065105 0.0106670.008392 0.090335 7.58E-06 0.166987 0.090184 0.000151 17.55982 0.074348 0.015836

0.011942 0.107106 1.28E-05 0.246905 0.106842 0.000264 21.89091 0.083453 0.0233890.017036 0.126438 2.15E-05 0.366049 0.125975 0.000463 27.24099 0.091659 0.034317

0.02436 0.148608 3.62E-05 0.544103 0.1478 0.000809 33.7731 0.097883 0.0499170.034913 0.173901 6.07E-05 0.810818 0.172491 0.00141 41.59848 0.100738 0.071754

0.05015 0.202606 0.000102 1.211245 0.200152 0.002454 50.69633 0.098682 0.101470.072191 0.235006 0.00017 1.81371 0.230744 0.004262 60.79772 0.090457 0.1402870.104138 0.271376 0.000283 2.721955 0.26399 0.007387 71.27244 0.075838 0.1881520.150528 0.311967 0.00047 4.093522 0.299197 0.01277 81.12638 0.056469 0.242727

0.218012 0.356993 0.00078 6.16719 0.334977 0.022016 89.24835 0.036016 0.2989610.316351 0.406614 0.00129 9.302419 0.368789 0.037825 94.89236 0.018836 0.3499530.459892 0.460904 0.002129 14.03064 0.396237 0.064668 98.06712 0.007659 0.3885780.669745 0.519818 0.003505 21.10226 0.410125 0.109693 99.44932 0.002258 0.4078660.977014 0.583127 0.005753 31.45564 0.399701 0.183426 99.89024 0.000439 0.3992621.427569 0.650337 0.009418 45.87486 0.351996 0.298341 99.98611 4.89E-05 0.3519472.089115 0.720549 0.015374 63.87608 0.260291 0.460258 99.99902 2.55E-06 0.260288

3.0616 0.79226 0.025022 81.94395 0.143051 0.649209 99.99997 4.69E-08 0.1430514.492457 0.863042 0.040596 94.33448 0.048896 0.814146 100 2.05E-10 0.048896


31/38

6.598492 0.929062 0.065635 99.11677 0.008206 0.920857 100 1.27E-13 0.0082069.69599 0.984367 0.105692 99.9511 0.000481 0.983886 100 5.54E-18 0.000481

14.23766 1.019886 0.169314 99.99944 5.73E-06 1.019881 100 0 5.73E-06

20.84315 1.022285 0.269182 100 5.83E-09 1.022285 100 0 5.83E-0930.27163 0.973448 0.422609 100 1.32E-13 0.973448 100 0 1.32E-1343.18796 0.853319 0.648685 100 0 0.853319 100 0 0

59.43375 0.652365 0.955783 100 0 0.652365 100 0 076.7531 0.398243 1.314858 100 0 0.398243 100 0 0

90.60093 0.170611 1.644582 100 0 0.170611 100 0 097.73448 0.043326 1.869073 100 0 0.043326 100 0 099.73957 0.005214 1.997013 100 0 0.005214 100 0 099.98977 0.000213 2.081359 100 0 0.000213 100 0 099.99992 1.75E-06 2.146501 100 0 1.75E-06 100 0 0

100 1.33E-09 2.191987 100 0 1.33E-09 100 0 0

100 2.86E-14 2.211528 100 0 2.86E-14 100 0 0100 0 2.196754 100 0 0 100 0 0100 0 2.137047 100 0 0 100 0 0100 0 2.019548 100 0 0 100 0 0

100 0 1.830369 100 0 0 100 0 0100 0 1.55885 100 0 0 100 0 0100 0 1.207728 100 0 0 100 0 0100 0 0.809712 100 0 0 100 0 0100 0 0.437179 100 0 0 100 0 0100 0 0.173016 100 0 0 100 0 0

100 0 0.044694 100 0 0 100 0 0100 0 0.006485 100 0 0 100 0 0100 0 0.000427 100 0 0 100 0 0100 0 9.31E-06 100 0 0 100 0 0100 0 4.31E-08 100 0 0 100 0 0100 0 2.24E-11 100 0 0 100 0 0100 0 6.5E-16 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0


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100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0

100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0100 0 0 100 0 0 100 0 0


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Sum

1.218731 100

Filter

0.214631 0.231572

0.047989 0.05280.056221 0.0634270.065105 0.0758630.074348 0.090344

0.083453 0.1071210.091659 0.1264630.097883 0.1486490.100738 0.1739680.098682 0.2027160.090457 0.2351880.075838 0.2716770.056469 0.312463

0.036016 0.357810.018836 0.4079570.007659 0.4631110.002258 0.5234350.000439 0.5890444.89E-05 0.6599942.55E-06 0.7362724.69E-08 0.8177932.05E-10 0.904387


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1.27E-13 0.9957975.54E-18 1.091674

0 1.191571

0 1.2949470 1.4011610 1.509482

0 1.6190910 1.7290890 1.8385070 1.9463210 2.0514630 2.1528390 2.2493480 2.339898

0 2.4234270 2.4989210 2.5654370 2.622115

0 2.6681990 2.7030520 2.7261660 2.7371740 2.7358590 2.722157

0 2.6961590 2.6581130 2.6084180 2.5476190 2.4764030 2.3955840 2.306095

0 2.2089710 2.1053360 1.9963810 1.883346

0 1.7674940 1.6500860 1.532350 1.415460 1.3005010 1.1884450 1.0801350 0.976266

0 0.8773780 0.7838570 0.6959420 0.6137370 0.5372310 0.4663160 0.4008120 0.3404840 0.28507


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0 0.2343040 0.1879460 0.145841

0 0.1080050 0.0747670 0.046906

0 0.0255570 0.0115010 0.0040780 0.0011010 0.000220 3.17E-050 3.16E-060 2.05E-07

0 8.13E-090 1.81E-100 2.08E-120 1.1E-14

0 2.36E-170 1.78E-200 4E-240 2.2E-280 2.36E-330 3.82E-39

0 6.94E-460 1.01E-530 7.87E-63


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Sheet to perform (D'WD)-1 required to determine the SE values of the parameters

D is the 9 x 2 matrix of derivatives developed in "SE Calc 1" and "SE Calc 2".Wis a square matrix containing the weights along the diagonals

Dis Then D'is

-1.42153 -2.19178 -1.42153 -1.86588 -2.78023 -3.38509 -1.39571 4.439386

-1.86588 -2.25492 -2.19178 -2.25492 -1.35226 3.016309 8.956647 6.52738-2.78023 -1.35226

-3.38509 3.016309-1.39571 8.9566474.439386 6.527383.582628 -4.43863

1.9421 -4.945880.884277 -3.3169

And Wis

37.43653 0 0 0 0 0 0 0 0

0 24.8926 0 0 0 0 0 0 0

0 0 13.22589276 0 0 0 0 0 00 0 0 7.394832 0 0 0 0 00 0 0 0 5.44658 0 0 0 00 0 0 0 0 4.769153 0 0 00 0 0 0 0 0 12.06824 0 00 0 0 0 0 0 0 30.61672 00 0 0 0 0 0 0 0 49.85424

A'Wis

1 2 3 4 5 6 7 81 -53.2172 -46.44662979 -36.7711 -25.0322 -7.60184 21.17211 43.236 59.460722 -82.0525 -56.13086801 -17.8848 22.3051 48.7831 31.13007 -53.5665 -151.427

(A'WA) equals

1 21 763.2441 -366.51551262 -366.516 2573.194374

(A'WA)-1then equals

1 21 0.001406 0.000200321

2 0.0002 0.000417155

Finally, the variances about each parameter is equal to the MSE x (1,1) and (2,2)MSE 7.990660272s^2 Y0 0.011238005s^2 Y1 0.003333343

So parameter values +/- their standard error is:MMAD 3.852655 0.106009456GSD 2.397895 0.057735114


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Parameter Values +/- their 95% CI is:

MMAD 3.853 0.251 (2.365 in formula to left is t value for 0.05/2, n-p =7)

GSD 2.398 0.137


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3.582628 1.9421 0.884277

-4.43863 -4.94588 -3.3169

944.08496-165.361

max like method

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