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{"sheet":"Cover","index":0,"n_rows":7,"n_cols":9,"rows_kept":7,"cut":false,"hidden":false,"merged":[[1,8,3,8],[6,4,15,8]]}
[]
[null,null,null,null,null,null,null,null,"Hubbard Decision Research\n2S410 Canterbury Ct\nGlen Ellyn, IL 60137\nwww.hubbardresearch.com"]
[]
[]
[null,null,null,null,"Table of Contents for Examples for Measurement"]
[]
[null,null,null,null,"1) Controlled Experiment Example from Chapter 3\n2) Irrational Belief in Small Samples from Chapter 7\n3) Survey Example using a Normal Distribution from Chapter 10\n4) Beta Distribution Population Proportion Example Chapter 12 \n\n"]

{"sheet":"Comparing Risks","index":1,"n_rows":9,"n_cols":4,"rows_kept":9,"cut":false,"hidden":false,"merged":[[1,0,1,3],[6,0,6,2],[7,0,7,2],[8,0,8,2]]}
["The Drug Company Experiment Example: The Difference Between Population Proportions (Chapter 3)"]
["This worksheet explains the example in Chapter 3 of a hypothetical major experiment in the pharmacutical industry.  The problem was to compare the outcomes of different risk management approaches to determine if risks actually decreased.  The event being observed is fairly rare so a large number of samples were needed to determine if a reduction in risk really happened.\nThis is a standard problem in statistics where we need to compare the observed proportions between two groups. We could apply this to determining whether the number of customers complained under one policy or another.   In this case we are trying to determine if the difference between the number of acccidents in two groups was just chance of if the risk management method can really be credited for it."]
[]
[null,"Number of incidents","Number of Samples","Proportion"]
["Control Group (Where new risk management methods were not used)",12,100,{"$f":"B5/C5","v":0.12}]
["Test Group (Where new risk management methods were used)",4,{"$f":"C5","v":100},{"$f":"B6/C6","v":0.04}]
["Difference between the proportions",null,null,{"$f":"D5-D6","v":7.9999999999999988E-2}]
["Standard error of the difference between the proportions.   For now, just know that this quantity is like a unit of measure for how much uncertainty we have from these random samples.",null,null,{"$f":"(D5*(1-D5)/C5+D6*(1-D6)/C6)^0.5","v":3.7947331922020551E-2}]
["Chance the difference in proportions could just be a coincidence.  Given how much uncertainty we have from the random sample, this shows us the likelihood that the result was an accident.",null,null,{"$f":"NORMDIST(0,D7,D8,1)","v":1.7507490509831272E-2}]

{"sheet":"Small Samples","index":2,"n_rows":18,"n_cols":3,"rows_kept":18,"cut":false,"hidden":false,"merged":[[1,0,2,3],[3,0,3,2],[4,1,5,1],[4,2,5,2],[9,0,9,2]]}
["An Example of Irrational Belief in Small Numbers (Chapter 7)"]
["This is the problem in the book about the a pharmacutical manufacturer evaluating production methods of an overseas supplier.  There were two possible production methods used.  Historically, the preferred production method produced a batch acceptance rate of 70%.  A cheaper production method produced a batch acceptance rate of only 30%.  There are currently two suppliers being used, one with more total batches produced.  The question is, based on the rate of batch acceptance, which of the suppliers is more likely to be using the preferred production method?  Although many people might believe that Supplier B has a better acceptance rate (although it has fewer batches in total, it has rejected none of them), the two suppliers have exactly the same probability of using the preferred method.  Sample size affects this calculation.  This assumes that either production method is equally likely at first.  "]
[]
["Assumptions"]
[null,"Batch acceptance rate with given method","Initial probability that given method is used"]
[]
["Good Method",0.7,0.5]
["Bad Method",0.3,{"$f":"1-C7","v":0.5}]
[]
["Comparison of Suppliers - Who is more likely to be using the preferred method?"]
[null,"Supplier A","Supplier B"]
["Total number of batches from this supplier to date (including both accepted and rejected)",12,4]
["Number of batches that were rejected",4,0]
["Probability of observing this result if the preferred method is used",{"$f":"BINOMDIST(B12-B13,B12,B7,0)","v":0.23113969609500007},{"$f":"BINOMDIST(C12-C13,C12,B7,0)","v":0.24009999999999992}]
["Probability of observing this result if cheaper method is used",{"$f":"BINOMDIST(B12-B13,B12,B8,0)","v":7.7977156950000074E-3},{"$f":"BINOMDIST(C12-C13,C12,B8,0)","v":8.0999999999999961E-3}]
["Overall probability of observing this result - this is is the weighted average of the two probabilities above given our assumptions about the initial likelihood of each",{"$f":"C7*B14+C8*B15","v":0.11946870589500004},{"$f":"C14*C7+C8*C15","v":0.12409999999999996}]
["Probability that prefered method is used",{"$f":"C7*B14/B16","v":0.96736502820306203},{"$f":"C7*C14/C16","v":0.96736502820306203}]
["Probability that bad method is used",{"$f":"1-B17","v":3.2634971796937973E-2},{"$f":"1-C17","v":3.2634971796937973E-2}]

{"sheet":"Survey with Normal Dist","index":3,"n_rows":1065,"n_cols":7,"rows_kept":1065,"cut":false,"hidden":false,"merged":[[7,0,7,3],[8,0,8,3],[9,0,9,3],[10,0,10,3],[13,6,14,15],[6,0,6,3],[0,0,0,16],[1,0,1,16],[3,0,3,4],[4,0,4,3],[5,0,5,3]]}
["Normal Distribution Illustration (Chapter 10)"]
["The \"Normal\" distribution, also known as the Guasian distribution.  If you enter the mean and standard deviation of an estimated value, this spreadsheet will compute the probability that the true value is below an amount you want to check against.  The values are currently set to show the lower bound of the example in the book on page 182.  But you can change these values and see how the chart changes."]
[]
["Variables and Estimates"]
["Mean",null,null,null,25]
["Standard Deviation",null,null,null,2]
["The number of standard deviations the lower bound is from the mean.  Note that a negative value here means it is below mean.  The standard deviations for the upper bound would be the same number but a positve value.",null,null,null,{"$f":"NORMINV(E10,0,1)","v":-1.6448536269514726}]
["The upper bound from the example in the book. ",null,null,null,{"$f":"E5-E6*E7","v":28.289707253902947}]
["The lower bound from the example in the book. ",null,null,null,{"$f":"E5+E7*E6","v":21.710292746097053}]
["The probability that the value is below the lower bound.  If you change this value, you will see the chart below change so that you get a sense of how different probabilities look on a normal distribution.",null,null,null,0.05]
["The probability that the value is above the lower bound.",null,null,null,{"$f":"1-E10","v":0.95}]
[]
[]
["Percentile","Standard Normal","Weight Below","Weight Above",null,null,"The size of the area in blue shows the probability (shown in row 7) that the estimated value is below the given amount  (in this case, the lower bound of a range)"]
[-5,{"$f":"NORMDIST(A15,0,1,1)","v":2.8665157187919333E-7}]
[-4.99,{"$f":"NORMDIST(A16,0,1,1)","v":3.0189646252084792E-7},{"$f":"IF(A16<E$7,B16-B15,0)","v":1.5244890641654589E-8},{"$f":"IF(A16>=E$7,B16-B15,0)","v":0}]
[-4.9800000000000004,{"$f":"NORMDIST(A17,0,1,1)","v":3.1792136618528084E-7},1.6024903664432925E-8,0]
[-4.97,{"$f":"NORMDIST(A18,0,1,1)","v":3.3476450827361611E-7},1.6843142088335266E-8,0]
[-4.96,3.524658981764237E-7,1.7701389902807594E-8,0]
[-4.95,3.7106740796333271E-7,1.8601509786909003E-8,0]
[-4.9400000000000004,3.9061285431832542E-7,1.954544635499271E-8,0]
[-4.93,4.1114808384392932E-7,2.0535229525603904E-8,0]
[-4.92,4.3272106186170034E-7,2.157297801777102E-8,0]
[-4.91,4.5538196484073046E-7,2.2660902979030124E-8,0]
[-4.9000000000000004,4.7918327659031834E-7,2.3801311749587874E-8,0]
[-4.8899999999999997,5.0417988835753554E-7,2.4996611767217205E-8,0]
[-4.88,5.3042920297509319E-7,2.6249314617557653E-8,0]
[-4.87,5.5799124320978072E-7,2.756204023468753E-8,0]
[-4.8600000000000003,5.8692876446663605E-7,2.893752125685533E-8,0]
[-4.8499999999999996,6.1730737200919715E-7,3.0378607542561092E-8,0]
[-4.84,6.4919564286133376E-7,3.1888270852136613E-8,0]
[-4.83,6.8266525256166203E-7,3.3469609700328276E-8,0]
[-4.82,7.1779110694689841E-7,3.5125854385236374E-8,0]
[-4.8099999999999996,7.5465147914637197E-7,3.6860372199473559E-8,0]
[-4.8,7.933281519755948E-7,3.8676672829222833E-8,0]
[-4.79,8.339065659229098E-7,4.0578413947315001E-8,0]
[-4.78,8.764759729292021E-7,4.25694070062923E-8,0]
[-4.7699999999999996,9.2112959616714115E-7,4.4653623237939052E-8,0]
[-4.7600000000000096,9.6796479603268433E-7,4.6835199865543174E-8,0]
[-4.7500000000000098,1.0170832425686521E-6,4.9118446535967807E-8,0]
[-4.74000000000001,1.0685910945458807E-6,5.1507851977228531E-8,0]
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[-4.7000000000000099,1.3008074539172174E-6,6.2223496564807194E-8,0]
[-4.6900000000000102,1.3660252446060695E-6,6.521779068885206E-8,0]
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[-4.6600000000000099,1.5810469189704335E-6,7.5048241374349492E-8,0]
[-4.6500000000000101,1.659675144371382E-6,7.8628225400948528E-8,0]
[-4.6400000000000103,1.7420458903445675E-6,8.23707459731855E-8,0]
[-4.6300000000000097,1.8283286635240718E-6,8.6282773179504284E-8,0]
[-4.6200000000000099,1.9187002199708018E-6,9.0371556446730008E-8,0]
[-4.6100000000000101,2.0133448548092414E-6,9.464463483843962E-8,0]
[-4.6000000000000103,2.112454702502744E-6,9.910984769350258E-8,0]
[-4.5900000000000096,2.2162300481174329E-6,1.0377534561468884E-7,0]
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[-4.5600000000000103,2.5576810394513957E-6,1.1905996567209501E-7,0]
[-4.5500000000000096,2.6822957796387278E-6,1.2461474018733207E-7,0]
[-4.5400000000000098,2.8127114117240744E-6,1.3041563208534663E-7,0]
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[-4.5000000000000098,3.3976731247299031E-6,1.5629183737666457E-7,0]
[-4.49000000000001,3.5611586795973878E-6,1.6348555486748467E-7,0]
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[-4.4700000000000104,3.9109798602805006E-6,1.7882789976620607E-7,0]
[-4.4600000000000097,4.0979826466361746E-6,1.8700278635567402E-7,0]
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[-4.4100000000000099,5.1685309572238896E-6,2.3348589469085049E-7,0]
[-4.4000000000000101,5.4125439077036103E-6,2.440129504797208E-7,0]
[-4.3900000000000103,5.6675330418264613E-6,2.5498913412285098E-7,0]
[-4.3800000000000097,5.9339654456243863E-6,2.6643240379792496E-7,0]
[-4.3700000000000099,6.2123268269012112E-6,2.7836138127682492E-7,0]
[-4.3600000000000101,6.5031222009924885E-6,2.9079537409127731E-7,0]
[-4.3500000000000103,6.8068765993337144E-6,{"$f":"IF(A80<E$7,B80-B79,0)","v":3.0375439834122587E-7},{"$f":"IF(A80>=E$7,B80-B79,0)","v":0}]
[-4.3400000000000096,{"$f":"NORMDIST(A81,0,1,1)","v":7.124135801495022E-6},3.1725920216130762E-7,0]
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[-4.3200000000000101,7.8014600381009772E-6,3.4599294674619218E-7,0]
[-4.3100000000000103,8.1627273027626718E-6,3.612672646616946E-7,0]
[-4.3000000000000096,8.5399054709914283E-6,3.7717816822875646E-7,0]
[-4.2900000000000196,8.9336559128261899E-6,3.9375044183476161E-7,0]
[-4.2800000000000198,9.3446656701955222E-6,4.110097573693323E-7,0]
[-4.27000000000002,9.7736483729166705E-6,4.2898270272114837E-7,0]
[-4.2600000000000202,1.0221345183983147E-5,4.4769681106647635E-7,0]
[-4.2500000000000204,1.0688525774933443E-5,4.6718059095029606E-7,0]
[-4.2400000000000198,1.117598933211957E-5,4.8746355718612685E-7,0]
[-4.23000000000002,1.1684565594706375E-5,5.0857626258680511E-7,0]
[-4.2200000000000202,1.2215115925251905E-5,5.3055033054553038E-7,0]
[-4.2100000000000204,1.2768534413733763E-5,5.5341848848185736E-7,0]
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[-4.1900000000000199,1.3947722726880003E-5,6.0197371097484264E-7,0]
[-4.1800000000000201,1.4575454790865707E-5,6.2773206398570398E-7,0]
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[-4.1600000000000197,1.5912379719080794E-5,6.8239777110430627E-7,0]
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[-4.0800000000000196,2.2517850388523499E-5,9.4919094034482787E-7,0]
[-4.0700000000000198,2.3506568868593539E-5,9.8871848007003996E-7,0]
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[-4.0500000000000203,2.5608816474039273E-5,1.0724585076316484E-6,0]
[-4.0400000000000196,2.672560071948983E-5,1.1167842454505567E-6,0]
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[-4.02000000000002,2.9099070711928416E-5,1.210644271366878E-6,0]
[-4.0100000000000202,3.0359373926615547E-5,1.2603032146871314E-6,0]
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[-3.9700000000000202,3.5936315902850715E-5,1.4786817878005952E-6,0]
[-3.9600000000000199,3.7474881691070286E-5,1.5385657882195704E-6,0]
[-3.9500000000000202,3.9075596597784149E-5,1.6007149067138635E-6,0]
[-3.9400000000000199,4.0740804558547294E-5,1.6652079607631443E-6,0]
[-3.9300000000000201,4.2472930788757602E-5,1.7321262302103085E-6,0]
[-3.9200000000000199,4.4274484312067044E-5,1.8015535233094414E-6,0]
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[-3.8800000000000199,5.2228232401815872E-5,2.1061214056316787E-6,0]
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[-3.80000000000003,7.2348043925111181E-5,2.8646480452543997E-6,0]
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[-3.7700000000000302,8.1623773702676187E-5,3.2095943191005953E-6,0]
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[-3.7500000000000302,8.8417285200793189E-5,3.4606067028055321E-6,0]
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[-3.6700000000000301,1.2127523428534334E-4,4.6582574699889683E-6,0]
[-3.6600000000000299,1.2610762413847187E-4,4.8323898531285229E-6,0]
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[-3.6200000000000299,1.4730150790745559E-4,5.5908980316529797E-6,0]
[-3.6100000000000301,1.530985025737374E-4,5.7969946662818177E-6,0]
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[-3.5400000000000298,2.0006351600729733E-4,7.4479403716860902E-6,0]
[-3.53000000000003,2.0777983348059775E-4,7.7163174733004209E-6,0]
[-3.5200000000000302,2.1577339929469295E-4,7.9935658140952055E-6,0]
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{"sheet":"BetaDistPopProportion","index":4,"n_rows":1013,"n_cols":6,"rows_kept":1013,"cut":false,"hidden":false,"merged":[[0,0,0,12],[1,0,2,12],[3,4,3,5],[12,0,12,2],[13,4,13,5]]}
["The Beta Distribution (Chapter 12)"]
["This spreadsheet computes how uncertainty about an estimate of a \"population proportion\" (e.g., \"what percentage of customers want X?\").  It uses a method called a beta distrubtion, which allows for establishing a \"prior\" uncertainty which is updated with new data.  Enter values in the yellow \"prior\" fields to set the initial estimate.  Enter \"hits\" and \"misses\" from a random sample in the yellow \"Observations\" fields."]
[]
[null,"Prior","w/Data",null,"Observations"]
["alpha",1,{"$f":"B5+F5","v":39},null,"\"Hits\"",38]
["beta",1,{"$f":"B6+F6","v":8},null,"\"Misses\"",7]
[null,null,null,null,"Total Observations",{"$f":"F6+F5","v":45}]
["P5",{"$f":"_xlfn.BETA.INV(0.05,B5,B6)","v":5.000000000000001E-2},{"$f":"_xlfn.BETA.INV(0.05,C5,C6)","v":0.73309479225428753}]
["Median",{"$f":"_xlfn.BETA.INV(0.5,B5,B6)","v":0.5},{"$f":"_xlfn.BETA.INV(0.5,C5,C6)","v":0.83448459862496116}]
["Mean",{"$f":"B5/(B5+B6)","v":0.5},{"$f":"C5/(C5+C6)","v":0.82978723404255317}]
["P95",{"$f":"_xlfn.BETA.INV(0.95,B5,B6)","v":0.95},{"$f":"_xlfn.BETA.INV(0.95,C5,C6)","v":0.91040697881045252}]
[]
["Chart Distribution Calculations"]
["Population Proportion","Prior","w/Data",null,"Calcs for Chart Boundaries"]
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{"sheet":"Validation","index":5,"n_rows":6,"n_cols":1,"rows_kept":6,"cut":false,"hidden":true,"merged":[]}
["Normal"]
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["Triangular"]
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