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{"sheet":"Cover","index":0,"n_rows":16,"n_cols":14,"rows_kept":16,"cut":false,"hidden":false,"merged":[[15,5,15,6],[1,12,1,16],[2,6,10,10],[12,5,12,6],[13,5,13,6],[14,5,14,6]]}
[]
[null,null,null,null,null,null,null,null,null,null,null,null,"Example and Worksheet Checklist"]
[null,null,null,null,null,null,"Statistical Measurement Methods in Excel: Basic"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Reference Slides"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Data from Worksheets"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Bayes Theorem"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"The Beta Distribution"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Catch and Recatch"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Estimating a Distribution and Mean"]
[]
[]
[]
[null,null,null,null,null,"Hubbard Decision Research"]
[null,null,null,null,null,"2S410 Canterbury Ct"]
[null,null,null,null,null,"Glen Ellyn, IL 60137"]
[null,null,null,null,null,"www.hubbardresearch.com"]

{"sheet":"Reference Slides","index":1,"n_rows":2,"n_cols":19,"rows_kept":2,"cut":false,"hidden":false,"merged":[[1,1,1,15],[1,18,1,32],[0,1,0,32]]}
[null,"Reference Slides"]
[null,"Mathless Table",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Laplace's Rule of Succession"]

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["Data for the Worksheets"]
["Instructions: This page contains data that is on the designated worksheets so the user can use them to see the original results or reset the worksheets after using them."]
["Worksheet: A Simple Bayesian Illustration",null,null,null,null,null,"Population Mean Worksheet"]
["Your \"prior probabiltiy\" for H:",null,null,null,"P(H)",0.65200000000000002,"Sample Value","Survey Results:\nCase Example (Hours spent per week)"]
["Probability of seeing D, Given H is true:",null,null,null,"P(D|H)",0.2]
["Probability of seeing D, Given H is false:",null,null,null,"P(D|~H)",0.25,19.60341451227848,3.2]
[null,null,null,null,null,null,14,5.8]
[null,null,null,null,null,null,29.777969943565893,6.5]
["Worksheet: A Simple Bayesian Illustration",null,null,null,null,null,19,6.5]
[null,null,null,null,"H","~H",22.472662067192626,7.1]
["H = Illness is present",null,null,"D",55,20,36,7.5]
["D= Patient has the indicating gene",null,null,"~D",30,45,26.248730784373315,8.4]
[null,null,null,null,null,null,32.496312612666316,8.9]
[null,null,null,null,null,null,17,9]
[null,null,null,null,null,null,35,9.5]
["Worksheet: CatchRecatch",null,null,null,null,null,26.446772517453628,10.1]
["First sample size (i.e. the fish that were tagged)",null,null,null,null,1000,39,10.199999999999999]
["The second sample size",null,null,null,null,1000,41.5,10.5]
["Overlap between samples (i.e. the tagged fish that showed up in the second sample) ",null,null,null,null,11,22.851439941356947,11.3]
[null,null,null,null,null,null,30.269414387144479,12.2]
[null,null,null,null,null,null,34]
[null,null,null,null,null,null,23.508369792067629]
[null,null,null,null,null,null,22.527255652526545]
[null,null,null,null,null,null,21.820836119113643]
[null,null,null,null,null,null,28.548208996658332]

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["Example: A Simple Bayesian Illustration"]
["Bayesian methods work out the probability of something given a \"prior\" probability and new data.  The charts below show the simplest example of a Bayesian inference.  Consider two urns, A and B.  Each urn contains a large number of red and green marbles but the proporations of colors are different between the urns.  You know the proportion of marbles in each urn but you don't know which urn is which.  You try to determine the probability you are drawing from urn A by the color of a single randomly drawn marble.  Urn A can be thought of as a hypothesis H being true and the draw of a red marble can be thought of as specific observed data D.  You have a prior for H of P(H) and you would like to know the probability of H given additional data D, written P(H|D). This simple example applies to many practical situations by itself (medical tests, quality control, etc.) and it is also the basis of more elaborate methods shown in some of the other worksheets in this file."]
[]
[]
["Urn of Mystery (Max 10 each)",null,null,null,"Bayes Shown as Sets and Subsets",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"A Few Rules of Probability"]
["Fill in the table below and choose from pull-down to show how the probability is computed on the chart.  The number of dots within the dashed borders are divided by the number of dots within the solid borders. In this example the hypothesis H is that Urn A is the urn being sampled from and D represents the data of drawing a red marble.",null,null,null,"The probability you choose in the pull-down menu to the left is illustrated in a simple 2x2 table below.  The table shows four combinations of the hypothesis being true or not and the data being observed or not. Any of those probabilities can be shown as the number of dots within the dashed line rectangle divided by the total set of dots within a larger solid-line rectangle (the specific number of dots is an approximation for illustration).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The following are a set of basic probability rules that can be used in any probability problem. Using several of the initial rules one can derive Bayes Theorem.  Here H and D are events and ~D and ~H denote not D and not H."]
[]
["Your \"prior probabiltiy\" for H:","P(H)",0.5]
["…and \"not H:","P(~H)",{"$f":"1-C8","v":0.5},null,null,null,"Hypothesis True (Urn A)",null,null,null,null,null,"Hypothesis False (Urn B)"]
[null,"Urn A","Urn B",null,"Data Observed","(Draw Red)"]
["Number of Red Marbles",9,3,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Probability: between impossible and inescapable"]
["Number of Green Marbles",3,9]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"To be or not to be…adds up to a probability of 1"]
[null,"P(H|~D)","P(D)"]
["Probability of seeing D, Given H is true:","P(D|H)",{"$f":"B11/(B11+B12)","v":0.75},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The \"It depends\" Rule: conditional probability"]
["…and \"not D\" given H is true:","P(~D|H)",{"$f":"1-C15","v":0.25}]
["Probability of seeing D, Given H is false:","P(D|~H)",{"$f":"C11/(C11+C12)","v":0.25},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The probability of more than one thing; the Chain Rule"]
["…and \"not D\" given H is false:","P(~D|~H)",{"$f":"1-C17","v":0.75},null,"Data Not Observed","(Draw Green)"]
["Probability of seeing D:","P(D)",{"$f":"C15*C8+C17*C9","v":0.5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The law of total probability"]
["…and not seeing D:","P(~D)",{"$f":"C16*C8+C18*C9","v":0.5}]
["Probability of H, given D:","P(H|D)",{"$f":"C15*C8/C19","v":0.75},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bayes Theorem"]
["..and not H, given D:","P(~H|D)",{"$f":"C17*C9/C19","v":0.25}]
["Probability of H, given not D:","P(H|~D)",{"$f":"C8*C16/C20","v":0.25}]
["..and not H, given not D:","P(~H|~D)",{"$f":"1-C23","v":0.75}]
[]
[]
[]
[]
[]
[]
[null,null,"Random Dot Coordinates",null,null,null,null,null,"Lookup Table for Chart Lines"]
[null,null,null,"Initial",null,"By Quadrant",null,null,{"$f":"SUM(J33:J44)","v":7},null,{"$f":"OFFSET(K33,$I32-1,)","v":0},0,0,0,0,0,0,0,0,0,0.02,0.98,0.98,0.02,0.02,0.52,0.52,0.98,0.98,0.52]
[null,null,1,0.49770747233673041,0.72102160361426415,{"$f":"IF(C33-INT((C33-1)/100)*100<=CHOOSE(INT((C33-1)/100)+1,C$11,C$12,B$11,B$12),CHOOSE(INT((C33-1)/200)+1,D33*0.46+0.52,D33*0.46+0.02),100)","v":0.74894543727489604},{"$f":"IF(C33-INT((C33-1)/100)*100<=CHOOSE(INT((C33-1)/100)+1,C$11,C$12,B$11,B$12),CHOOSE(INT((C33-1)/100)+1,E33*0.46+0.52,E33*0.46+0.02,E33*0.46+0.52,E33*0.46+0.02),100)","v":0.8516699376625616},null,1,{"$f":"IF(B8=C$14,I33,0)","v":0},0,1,1,0,0,0,0,1,1,0,0.02,0.48,0.48,0.02,0.02,0.02,0.02,0.98,0.98,0.02]
[null,null,2,0.85363509632246393,0.8921108830541884,0.91267214430833343,0.93037100620492663,null,2,{"$f":"IF(B9=C$14,I34,0)","v":0},0,1,1,0,0,0,0,1,1,0,0.52,0.98,0.98,0.52,0.52,0.02,0.02,0.98,0.98,0.02]
[null,null,3,4.0788600151707488E-2,0.28852159480883055,0.53876275606978541,0.65271993361206204,null,3,{"$f":"IF(B15=C$14,I35,0)","v":0},0,0.5,0.5,0,0,0,0,1,1,0,0.02,0.48,0.48,0.02,0.02,0.52,0.52,0.98,0.98,0.52]
[null,null,4,0.41210323636492119,0.61363956280346599,100,100,null,4,0,0,0.5,0.5,0,0,0,0,1,1,0,0.02,0.48,0.48,0.02,0.02,0.02,0.02,0.48,0.48,0.02]
[null,null,5,0.71265790074014779,0.40129960165930256,100,100,null,5,0,0.5,1,1,0.5,0.5,0,0,1,1,0,0.52,0.98,0.98,0.52,0.52,0.52,0.52,0.98,0.98,0.52]
[null,null,6,0.67950437645236961,8.3484986002820505E-2,100,100,null,6,0,0.5,1,1,0.5,0.5,0,0,1,1,0,0.52,0.98,0.98,0.52,0.52,0.02,0.02,0.48,0.48,0.02]
[null,null,7,0.35851955959086212,0.87765089416044595,100,100,null,7,7,null,null,null,null,null,null,null,null,null,null,0.02,0.98,0.98,0.02,0.02,0.52,0.52,0.98,0.98,0.52]
[null,null,8,0.76358118271624997,0.20063736453167469,100,100,null,8,0,null,null,null,null,null,null,null,null,null,null,0.02,0.98,0.98,0.02,0.02,0.02,0.02,0.48,0.48,0.02]
[null,null,9,9.31051555571627E-3,0.77343463854847483,100,100,null,9,0,0,1,1,0,0,0.5,0.5,1,1,0.5,0.02,0.48,0.48,0.02,0.02,0.52,0.52,0.98,0.98,0.52]
[null,null,10,0.22314714066313746,0.57688176823482573,100,100,null,10,0,0,1,1,0,0,0.5,0.5,1,1,0.5,0.52,0.98,0.98,0.52,0.52,0.52,0.52,0.98,0.98,0.52]
[null,null,101,0.35883593442545192,0.79242005210396127,0.68506452983570787,0.38451322396782223,null,11,0,0,1,1,0,0,0,0,0.5,0.5,0,0.02,0.48,0.48,0.02,0.02,0.02,0.02,0.48,0.48,0.02]
[null,null,102,0.55583211323732196,0.41083979669725923,0.77568277208916814,0.20898630648073924,null,12,0,0,1,1,0,0,0,0,0.5,0.5,0,0.52,0.98,0.98,0.52,0.52,0.02,0.02,0.48,0.48,0.02]
[null,null,103,0.73139636705605238,8.7164936487212574E-2,0.85644232884578408,6.009587078411778E-2]
[null,null,104,0.41267513076201989,0.14974595043131211,0.70983056015052914,8.8883137198403572E-2]
[null,null,105,0.14960204538177624,0.2473403913015948,0.58881694087561709,0.1337765799987336]
[null,null,106,0.17608817568644053,0.9489090469205621,0.6010005608157627,0.45649816158345863]
[null,null,107,0.79618818220490362,4.9604649683987478E-3,0.88624656381425571,2.2281813885463426E-2]
[null,null,108,0.97969371218087831,0.5,0.97065910760320406,0.25]
[null,null,109,0.91764031159697634,0.7939134204858691,0.9421145433346092,0.38520017342349983]
[null,null,110,0.87496985361640023,0.89030089916793953,100,100]
[null,null,201,0.39406049755007944,0.1542733535101718,0.20126782887303654,0.59096574261467905]
[null,null,202,0.32897033043414214,0.4,0.17132635199970539,0.70400000000000007]
[null,null,203,0.9,0.1,0.43400000000000005,0.56600000000000006]
[null,null,204,0.4,0.8,0.20400000000000001,0.88800000000000012]
[null,null,205,0.11962398716444245,0.6,7.5027034095643527E-2,0.79600000000000004]
[null,null,206,5.1750585615658817E-2,0.4,4.380526938320306E-2,0.70400000000000007]
[null,null,207,0.47555063956103505,4.9039400692435287E-2,0.23875329419807612,0.54255812431852024]
[null,null,208,0.65004365242393336,0.7,0.31902008011500937,0.84200000000000008]
[null,null,209,0.56165518475552367,0.26363964779807125,0.27836138498754093,0.64127423798711281]
[null,null,210,7.8428929208097409E-2,5.6455038241601252E-2,100,100]
[null,null,301,0.16595240411079459,7.3376346764288169E-2,9.6338105890965517E-2,5.3753119511572564E-2]
[null,null,302,0.77968873229184288,0.1,0.37865681685424774,6.6000000000000003E-2]
[null,null,303,0.920823996332224,0.68793844313871522,0.44357903831282308,0.33645168384380902]
[null,null,304,0.92143015525604888,0.43902243996548551,100,100]
[null,null,305,0.80011798352787078,0.592169081786448,100,100]
[null,null,306,0.37599041049011417,0.47159473485738213,100,100]
[null,null,307,0.71928227898036812,0.38770687662804049,100,100]
[null,null,308,0.4,0.69288967375826671,100,100]
[null,null,309,4.0890308434982092E-2,6.613682395086784E-2,100,100]
[null,null,310,7.1092097282392186E-2,0.345887696250752,100,100]

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["Example: A Simple Bayesian Illustration"]
["This worksheet can be used to create an example like the ones seen in the other Bayesian examples. The user should define H (hypothesis) and D (data) as well as their frequencies here. In the current example the sheet calculates the probability of someone developing an illness given they have a gene or not. Even though it appears that the gene predicts the illness some people without the gene can get the illness and some people with the gene will not get the illness."]
["H=","Illness is present","D=","Patient has the indicating gene",null,null,null,null,"N=","Number of people sampled"]
[]
["Observed Events ",null,null,null,null,"Bayes Shown as Sets and Subsets",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"A Few Rules of Probability"]
["Fill in the number of observed events to calculate the probabilities below.  You should use the space above to fomulate the ecperiment you want to calculate the probabilities for.",null,"H","~H",null,"The probability you choose in the pull-down menu to the left is illustrated in a simple 2x2 table below.  The table shows four combinations of the hypothesis being true or not and the data being observed or not. Any of those probabilities can be shown as the number of dots within the dashed line rectangle divided by the total set of dots within a larger solid-line rectangle (the specific number of dots is an approximation for illustration).",null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The following are a set of basic probability rules that can be used in any probability problem. Using several of the initial rules one can derive Bayes Theorem.  Here H and D are events and ~D and ~H denote not D and not H."]
[null,"D",55,20]
[null,"~D",30,45]
["Number of people sampled:","N",{"$f":"SUM(C7:D8)","v":150}]
["Probability for H:","P(H)",{"$f":"SUM(C7:C8)/SUM(C7:D8)","v":0.56666666666666665}]
["Probability of seeing D, Given H is true:","P(D|H)",{"$f":"C7/(C7+C8)","v":0.6470588235294118},null,null,null,null,"H",null,null,null,null,null,"~H"]
["Probability of seeing D, Given H is false:","P(D|~H)",{"$f":"D7/(D7+D8)","v":0.30769230769230771},null,null,null,"D",null,null,null,null,null,null,null,null,null,null,null,null,null,"Probability: between impossible and inescapable"]
[]
["Calculated Probabilities and Inputs",null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"To be or not to be…adds up to a probability of 1"]
["This table calculates the probabilities of all of the different combinations. "]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The \"It depends\" Rule: conditional probability"]
[null,null,"P(H|~D)","P(H|D)"]
[null,"Your \"prior probability\" for H:","P(H)",{"$f":"C10","v":0.56666666666666665},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"The probability of more than one thing; the Chain Rule"]
[null,"…and \"not H:","P(~H)",{"$f":"1-D18","v":0.43333333333333335}]
[null,"Probability of seeing D, Given H is true:","P(D|H)",{"$f":"C11","v":0.6470588235294118},null,null,"~D",null,null,null,null,null,null,null,null,null,null,null,null,null,"The law of total probability"]
[null,"…and \"not D\" given H is true:","P(~D|H)",{"$f":"1-D20","v":0.3529411764705882}]
[null,"Probability of seeing D, Given H is false:","P(D|~H)",{"$f":"C12","v":0.30769230769230771},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Bayes Theorem"]
[null,"…and \"not D\" given H is false:","P(~D|~H)",{"$f":"1-D22","v":0.69230769230769229}]
[null,"Probability of seeing D:","P(D)",{"$f":"D20*D18+D22*D19","v":0.5}]
[null,"…and not seeing D:","P(~D)",{"$f":"D21*D18+D23*D19","v":0.5}]
[null,"Probability of H, given D:","P(H|D)",{"$f":"D20*D18/D24","v":0.73333333333333339}]
[null,"..and not H, given D:","P(~H|D)",{"$f":"D22*D19/D24","v":0.26666666666666666}]
[null,"Probability of H, given not D:","P(H|~D)",{"$f":"D18*D21/D25","v":0.39999999999999997}]
[null,"..and not H, given not D:","P(~H|~D)",{"$f":"1-D28","v":0.60000000000000009}]
[]
[]
[]
[null,null,null,"Random Dot Coordinates",null,null,null,null,null,"Computing Number of Dots By quadrant"]
[null,null,null,null,"Initial",null,"By Quadrant",null,null,"Initial Calc",null,null,"Normalized"]
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{"sheet":"BetaDistPopProportion Ws","index":5,"n_rows":1029,"n_cols":8,"rows_kept":1029,"cut":false,"hidden":false,"merged":[[0,0,0,9],[28,3,28,5],[18,0,18,1],[13,0,13,2],[1,0,2,9],[28,6,29,6],[28,7,29,7]]}
["Worksheet: The Beta Distribution"]
["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 distribution, 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. This distribution is confirmed using the probability of seeing that outcome from a Binomial distribution."]
[]
[]
[null,"Prior","w/Data"]
["alpha",1,{"$f":"B6+C15","v":2}]
["beta",1,{"$f":"B7+C16","v":1}]
[]
["P5",{"$f":"_xlfn.BETA.INV(0.05,B6,B7)","v":5.000000000000001E-2},{"$f":"_xlfn.BETA.INV(0.05,C6,C7)","v":0.22360679774997899}]
["Median",{"$f":"_xlfn.BETA.INV(0.5,B6,B7)","v":0.5},{"$f":"_xlfn.BETA.INV(0.5,C6,C7)","v":0.70710678118654757}]
["Mean",{"$f":"B6/(B6+B7)","v":0.5},{"$f":"C6/(C6+C7)","v":0.66666666666666663}]
["P95",{"$f":"_xlfn.BETA.INV(0.95,B6,B7)","v":0.95},{"$f":"_xlfn.BETA.INV(0.95,C6,C7)","v":0.97467943448089644}]
[]
["Observations"]
["\"Hits\"",null,1]
["\"Misses\"",null,0]
["Total Observations",null,{"$f":"C16+C15","v":1}]
[]
["Calcs for Chart Boundaries"]
[{"$f":"A21","v":5.000000000000001E-2},0]
[{"$f":"B9","v":5.000000000000001E-2},{"$f":"VLOOKUP(A21,D$31:E$1029,2)","v":1.0000000000000148E-3}]
[{"$f":"A23","v":0.95},0]
[{"$f":"B12","v":0.95},{"$f":"VLOOKUP(A23,D$31:E$1029,2)","v":9.9999999999988987E-4}]
[{"$f":"A25","v":0.22360679774997899},0]
[{"$f":"C9","v":0.22360679774997899},{"$f":"VLOOKUP(A25,D$31:F$1029,3)","v":4.4600000000000195E-4}]
[{"$f":"A27","v":0.97467943448089644},0]
[{"$f":"C12","v":0.97467943448089644},{"$f":"VLOOKUP(A27,D$31:F$1029,3)","v":1.9479999999997277E-3}]
[]
[null,null,null,"Chart Distribution Calculations",null,null,"Prob. of sample result if the hypothetical proportion was the actual proportion","Bayesian Inversion: Prob. that actual proportion is equal to hypothetical proportion"]
[null,null,null,"Population Proportion","Prior","w/Data"]
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[null,null,null,{"$f":"D31+D$31","v":2E-3},9.999999999999998E-4,4.0000000000000015E-6,2.0000000000000005E-3,{"$f":"(G32*E32/SUMPRODUCT($G$31:$G$1029,$E$31:$E$1029))","v":4.0040040040043324E-6}]
[null,null,null,3.0000000000000001E-3,1.0000000000000005E-3,{"$f":"_xlfn.BETA.DIST(D33+D$31/2,C$6,C$7,1)-_xlfn.BETA.DIST(D33-D$31/2,C$6,C$7,1)","v":6.0000000000000044E-6},2.9999999999999992E-3,6.0060060060064999E-6]
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[null,null,null,0.97100000000000075,9.9999999999988987E-4,1.9419999999997772E-3,0.97100000000000075,1.9439439439438908E-3]
[null,null,null,0.97200000000000075,9.9999999999988987E-4,1.9439999999998347E-3,0.97200000000000075,1.9459459459458927E-3]
[null,null,null,0.97300000000000075,9.9999999999988987E-4,1.9459999999997812E-3,0.97300000000000075,1.9479479479478947E-3]
[null,null,null,0.97400000000000075,9.9999999999988987E-4,1.9479999999997277E-3,0.97400000000000075,1.9499499499498966E-3]
[null,null,null,0.97500000000000075,9.9999999999988987E-4,1.9499999999997852E-3,0.97500000000000075,1.9519519519518985E-3]
[null,null,null,0.97600000000000076,9.9999999999988987E-4,1.9519999999997317E-3,0.97600000000000076,1.9539539539539007E-3]
[null,null,null,0.97700000000000076,9.9999999999988987E-4,1.9539999999997892E-3,0.97700000000000076,1.9559559559559022E-3]
[null,null,null,0.97800000000000076,9.9999999999988987E-4,1.9559999999998468E-3,0.97800000000000076,1.9579579579579042E-3]
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{"sheet":"CatchRecatch Ws","index":6,"n_rows":16,"n_cols":3,"rows_kept":16,"cut":false,"hidden":false,"merged":[[0,0,0,13],[5,1,5,2],[6,1,7,1],[6,2,7,2],[1,0,1,2],[2,0,2,2],[3,1,3,2],[4,1,4,2]]}
["Worksheet: Computing a 90% Confidence with Catch/Recatch"]
["This shows the calculations for the estimation of the size of a population when you can't actually count or even see the entire population.  Note the similarities to and differences from the 90% CI calculation on other worksheets."]
["90% Confidence Interval Calculations"]
["First sample size (i.e. the fish that were tagged)",1000]
["The second sample size",1000]
["Overlap between samples (i.e. the tagged fish that showed up in the second sample) - THIS APPROXIMATION IS ONLY VALID WHERE THIS VALUE >10",250]
[null,null,"Beta Distribution"]
[]
[]
[]
["Computing bounds for 90% CI for the percentage of tagged fish"]
["Upper bound",null,{"$f":"_xlfn.BETA.INV(0.95,B6+1,B5-B6+1)","v":0.27328466821058062}]
["Lower bound",null,{"$f":"_xlfn.BETA.INV(0.05,B6+1,B5-B6+1)","v":0.22827984726670153}]
["Computing bounds for 90% CI for the total population of fish"]
["Upper bound",null,{"$f":"(B5-B6)/C13+B5","v":4285.4411328029664}]
["Lower bound",null,{"$f":"(B5-B6)/C12+B5","v":3744.3910590040286}]

{"sheet":"EstimatingDistAndMean Ex ","index":7,"n_rows":225,"n_cols":75,"rows_kept":225,"cut":false,"hidden":false,"merged":[[24,10,24,12],[12,0,14,1],[22,19,22,20],[22,8,22,12],[22,13,22,18],[7,0,7,1],[0,0,0,16],[1,0,2,16],[3,0,3,1],[3,3,3,8],[3,10,3,16],[4,0,4,1],[4,3,4,8],[4,10,4,16]]}
["Example Estimating a Population Distribution and Mean "]
["This worksheet computes a distribution for he estimate of the mean of several different population data sets. For each data set it will also compute an estimate of the underlying distribution. The graph on the right also shows how the 90% confidence interval for the mean narrows as more samples are taken. The user can also explore different groups of sample points by changing the scenario. Different populations can be selected from the drop down menu. "]
[]
["Scenario",null,null,"Estimate of True Population Distribution and Its Mean",null,null,null,null,null,null,"90% Confidence Interval for Estimate of Mean as Samples Increase"]
["Different scenarios will randomly changes the samples to show how different random samples could change the estimates.",null,null,"The chart below shows the \"true\" shape of the distribution for a population (dashed line). It also shows an estimate of that true shape (dark blue) and an estimate of the true mean (light blue) based on a random sample of values from the population (green diamonds)",null,null,null,null,null,null,"This chart shows how the estimate of the mean of a population improves with sample size.  The true mean is shown as a dashed grey line.  The estimate of the mean is shown with blue lines representing upper and lower bounds of the 90% confidence interval."]
[null,46]
["Number of Samples"]
["Enter number of samples or use slider bar below.  For a given scenario, increasing the number of samples improves estimates."]
[null,5]
["True, Hidden Distribution"]
["Population #",10]
["Reveal Distribution?",false]
[{"$f":"IF(B12,OFFSET(W18,,B11-1),\"\")","v":""}]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Make new tab"]
[]
["Estimates Based on Samples"]
["Average of sample",{"$f":"AVERAGE(L26:L227)","v":179.75999999999954}]
["Standard Deviation of Sample",{"$f":"_xlfn.STDEV.S(L26:L227)","v":43.645194466286625},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Normal","Beta","Uniform","lognormal","MLB Player Batting","book ratings w/>10 reviews","Book num of pages","NJ teacher salary","age of working adults","Work hours per month"]
["Error of the Estimate of the Mean",{"$f":"B18/B9^0.5","v":19.518724343562909},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,100,{"$f":"6/9*100","v":66.666666666666657},50,{"$f":"EXP((LN(120)+LN(10))/2+((LN(120)-LN(10))/3.29)^2/2)","v":46.07499961946349},278.87,3.9449999999999998,348.18,73990,38.643585438761718,201.05]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,0,0,140,null,0,0,0,90]
["Increments for chart",{"$f":"OFFSET(W23,,B11-1)","v":1.1000000000000001},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,200,100,100,200,400,null,1800,300000,98,310]
[null,"Distribution curves",null,null,null,null,null,null,"Sample Values",null,null,null,null,"Running Calculations for Chart Above",null,null,null,null,null,"True Mean Plot",null,null,{"$f":"(W22-W21)/200","v":1},0.5,0.5,1,1.3,0,9,1500,0.49,1.1000000000000001]
["True Population Cumulative Distribution","True Population Distribution","Horizontal axis values","Estimated Distribution pdf",null,"Error of the Mean Estimate pdf",null,null,"Y-axis Value for Samples","Sample Count","Random Number","For Calcs","For Chart",null,"Running Average",null,null,null,null,"Mean","Count",null,{"$f":"NORMDIST(C25,100,15,1)","v":0.25249253754692291},{"$f":"IFERROR(BETADIST(C25,6,3,0,100),\"\")","v":0.96190820999999993},{"$f":"C25/100","v":0.9},0,1.5610514094811206E-6,1.2485100129659449E-4,2.2492764901592502E-11,1.4319415685426138E-4,1.8801106744299012E-18,4.3636970020232717E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
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[0.99745912053583075,"",306.70000000000022,5.5199887439572048E-4,null,4.637769132864733E-5,null,null,"","","","",{"$error":"#N/A"},null,{"$f":"IF(K222=\"\",\"\",AVERAGE(L$26:L222))","v":""},{"$f":"IFERROR(_xlfn.STDEV.S(L$26:L222)/J222^0.5,\"\")","v":""},"","","",201.05,197,null,1,"",3.0780000000000025,0.99808690443290893,0.99998576013802287,0.99999978910303833,1,0.99999793965241934,1,0.99831121029863656]
[0.99831121029863656,"",307.80000000000024,5.3602154218079789E-4,null,4.4583987468427289E-5,null,null,"","","","",{"$error":"#N/A"},null,{"$f":"IF(K223=\"\",\"\",AVERAGE(L$26:L223))","v":""},{"$f":"IFERROR(_xlfn.STDEV.S(L$26:L223)/J223^0.5,\"\")","v":""},"","","",201.05,198,null,1,"",3.0890000000000026,0.99811547044589743,0.99999334325212619,1,1,1,1,0.99901933702195589]
[0.99901933702195589,"",308.90000000000026,5.2055458049182768E-4,null,4.2871669484578767E-5,null,null,"","","","",{"$error":"#N/A"},null,{"$f":"IF(K224=\"\",\"\",AVERAGE(L$26:L224))","v":""},{"$f":"IFERROR(_xlfn.STDEV.S(L$26:L224)/J224^0.5,\"\")","v":""},"","","",201.05,199,null,1,"",3.1000000000000028,0.99814354878644307,1,1,1,1,1,0.99958116301096644]
[0.99958116301096644,"",310.00000000000028,5.05580844530229E-4,null,4.1236526830301656E-5,null,null,"","","","",{"$error":"#N/A"},null,{"$f":"IF(K225=\"\",\"\",AVERAGE(L$26:L225))","v":""},{"$f":"IFERROR(_xlfn.STDEV.S(L$26:L225)/J225^0.5,\"\")","v":""},"","","",201.05,200,null,1.3083924686052984E-11,0,0,{"$error":"#NUM!"}]

{"sheet":"PopMean Ws","index":8,"n_rows":620,"n_cols":15,"rows_kept":620,"cut":false,"hidden":false,"merged":[[0,1,0,15],[6,1,6,2],[7,1,7,2],[11,1,11,2],[15,1,15,2],[15,10,15,11],[5,1,5,2],[2,1,2,3],[3,1,3,2],[4,1,4,2],[15,3,15,4],[12,1,12,2],[13,1,13,2],[1,1,1,3]]}
[null,"Worksheet: Computing 90% Confidence Intervals with Small Samples"]
[null," The \"t-stat\" is used for small samples.  Note that two excel formulas are introduced here that give the same answers as the steps in the book: VAR() and TINV().  This will slightly simplify the calculation.  You can use this spreadsheet to compute ranges for larger samples, too.  Just add however many rows you need and don't forget to change the references in the cells to capture all the new rows.  See how close the answers would be if you just used the \"Mathless\" table.\n\nThis sheet will also calculate an estimate of the underlying distribution using a t-distribution. One will notice from the previous example that this may or ay not be a good assumption."]
[null,"90% Confidence Interval Calculations (by steps described in book)"]
[null,"Average of Sample Values (step 1.a in book)",null,{"$f":"AVERAGE(C18:C117)","v":27.103569366319892}]
[null,"Population Variance",null,{"$f":"VAR(C18:C117)","v":57.071368573250624}]
[null,"SD of the estimate of the mean",null,{"$f":"SQRT(D5/COUNT(C18:C117))","v":1.6892508483533555}]
[null,"t-stat using Excel's \"Tinv()\" formula (same answer as step 3 in book)",null,{"$f":"TINV(0.1,COUNT(C18:C117)-1)","v":1.7291328115213698}]
[null,"Sample error (step 4 in book)",null,{"$f":"D7*D6","v":2.9209390687780967}]
[null,"SD",null,{"$f":"_xlfn.STDEV.S(C18:C117)","v":7.5545594559345828}]
[null,"Sample size",null,{"$f":"COUNT(C18:C1001)","v":20}]
[]
[null,"Computing bounds for 90% CI (step 5 in book)"]
[null,"Upper bound",null,{"$f":"D4+D8","v":30.024508435097989}]
[null,"Lower bound",null,{"$f":"D4-D8","v":24.182630297541795}]
[]
[null,"Data ",null,"Chart Data",null,"Std Error for Estimate of Mean (Normalized)","cpf for Sample","Incremental P ","Sample","Error of the mean","Confidence Interval Bars",null," Estimate of Distribution"," Estimate of Distribution","Error of the Mean"]
[null,"Data Point","Sample Value","Min",{"$f":"MIN(C18:C117)","v":14},-4.2,{"$f":"NORMDIST(F17+0.05,0,1,1)","v":1.6623763729652213E-5},null,null,null,{"$f":"D14","v":24.182630297541795},0,{"$f":"E17-(E19*100)","v":-3.1875}]
[0,1,19.603414512278501,"Max",{"$f":"MAX(C18:C117)","v":41.5},-4.0999999999999996,{"$f":"NORMDIST(F18+0.05,0,1,1)","v":2.5608816474041486E-5},{"$f":"(G18-G17)","v":8.9850527443892729E-6},{"$f":"D$4+F18*D$6","v":20.177640888071135},null,{"$f":"D14","v":24.182630297541795},{"$f":"_xlfn.T.DIST(((K18+2*E19)-D$4)/D$6,D$10-1,1)-_xlfn.T.DIST((K18-D$4)/D$6,D$10-1,1)","v":2.1786871236267859E-2},{"$f":"M17+$E$19","v":-3.015625},{"$f":"_xlfn.T.DIST((M19-D$4)/D$9,D$10-1,1)-_xlfn.T.DIST((M17-D$4)/D$9,D$10-1,1)","v":4.1048154149605858E-5},{"$f":"_xlfn.T.DIST((M19-D$4)/D$6,D$10-1,1)-_xlfn.T.DIST((M17-D$4)/D$6,D$10-1,1)","v":2.6126249288936221E-14}]
[0,2,14,"Increment",{"$f":"(E18-E17)/160","v":0.171875},-4,{"$f":"NORMDIST(F19+0.05,0,1,1)","v":3.9075596597787456E-5},{"$f":"(G19-G18)","v":1.346678012374597E-5},20.346565972906468,{"$f":"_xlfn.T.DIST((I19-D$4)/D$6,D$10-1,1)-_xlfn.T.DIST((I18-D$4)/D$6,D$10-1,1)","v":7.822297032338601E-5},{"$f":"D13","v":30.024508435097989},0,-2.84375,{"$f":"_xlfn.T.DIST((M20-D$4)/D$9,D$10-1,1)-_xlfn.T.DIST((M18-D$4)/D$9,D$10-1,1)","v":4.3237982524760288E-5},{"$f":"_xlfn.T.DIST((M20-D$4)/D$6,D$10-1,1)-_xlfn.T.DIST((M18-D$4)/D$6,D$10-1,1)","v":2.9105525132326058E-14}]
[0,3,29.777969943565893,null,null,-3.9,{"$f":"NORMDIST(F20+0.05,0,1,1)","v":5.9058912418922381E-5},{"$f":"(G20-G19)","v":1.9983315821134925E-5},20.515491057741805,9.8308714610202143E-5,{"$f":"D13","v":30.024508435097989},{"$f":"L18","v":2.1786871236267859E-2},-2.671875,4.554334619021695E-5,3.2442400224815572E-14]
[0,4,19,null,null,-3.8,8.841728520080376E-5,{"$f":"(G21-G20)","v":2.9358372781881379E-5},20.684416142577142,1.2348137015670525E-4,null,null,-2.5,4.7970182419311471E-5,3.6181948605145834E-14]
[0,5,22.472662067192626,null,null,-3.7,1.3112015442048446E-4,{"$f":"(G22-G21)","v":4.2702869219680701E-5},20.853341227412479,{"$f":"_xlfn.T.DIST((I22-D$4)/D$6,D$10-1,1)-_xlfn.T.DIST((I21-D$4)/D$6,D$10-1,1)","v":1.5498574566802533E-4},null,null,-2.328125,5.0524718820917373E-5,4.0375197884841549E-14]
[0,6,36,null,null,-3.6,{"$f":"NORMDIST(F23+0.05,0,1,1)","v":1.9261557563563276E-4},6.1495421215148298E-5,21.022266312247812,1.9435143169228234E-4,null,null,-2.15625,5.3213486296102542E-5,4.5079951683410054E-14]
[0,7,26.248730784373315,null,null,-3.5,2.8029327681617738E-4,8.7677701180544624E-5,{"$f":"D$4+F24*D$6","v":21.191191397083148},2.4344991409986998E-4,null,null,-1.984375,5.6043332473480799E-5,5.036173067174571E-14]
[0,8,32.496312612666316,null,null,-3.4,{"$f":"NORMDIST(F25+0.05,0,1,1)","v":4.0405780186402075E-4},1.2376452504784337E-4,21.360116481918482,3.0456006189852943E-4,null,null,-1.8125,5.9021435632935137E-5,5.6294850051158251E-14]
[0,9,17,null,null,-3.3,5.7702504239076603E-4,1.7296724052674528E-4,21.529041566753818,3.8044203151619345E-4,null,null,-1.640625,6.2155319126924692E-5,6.2963654083856472E-14]
[0,10,35,null,null,-3.19999999999999,8.1635231282858845E-4,2.3932727043782243E-4,21.697966651589169,4.7441907587551031E-4,null,null,-1.46875,6.5452866307937193E-5,7.046393153218045E-14]
[0,11,26.446772517453628,null,null,-3.0999999999999899,1.1442068310227363E-3,3.2785451819414789E-4,21.866891736424506,5.9046595981379537E-4,null,null,-1.296875,6.8922335969976356E-5,7.8904539635020047E-14]
[0,12,39,null,null,-2.9999999999999898,1.5888696473649174E-3,{"$f":"(G29-G28)","v":4.446628163421811E-4},22.035816821259843,7.3330161798896903E-4,null,null,-1.125,7.2572378311258428E-5,8.8409268640295985E-14]
[0,13,41.5,null,null,-2.8999999999999901,2.1859614549133047E-3,5.9709180754838722E-4,22.20474190609518,9.0848230830345086E-4,null,null,-0.953125,7.6412051424312602E-5,9.9118984027733792E-14]
[0,14,22.851439941356947,null,null,-2.7999999999999901,2.9797632350546427E-3,7.9380178014133804E-4,22.373666990930513,1.1224897898124914E-3,null,null,-0.78125,8.0450838318749411E-5,1.1119408952072801E-13]
[0,15,30.269414387144479,null,null,-2.69999999999999,4.0245885427584224E-3,1.0448253077037797E-3,22.54259207576585,1.3828069940034476E-3,null,null,-0.609375,8.4698664480914215E-5,1.2481736094576051E-13]
[0,16,34,null,null,-2.5999999999999899,5.386145954066837E-3,1.3615574113084146E-3,22.711517160601183,1.6979713110588874E-3,null,null,-0.4375,8.9165915973287119E-5,1.4019720912541527E-13]
[0,17,23.508369792067629,null,null,-2.4999999999999898,7.1428107352716139E-3,1.7566647812047769E-3,22.880442245436519,2.0775930890862618E-3,null,null,-0.265625,9.3863458075263504E-5,1.5757143948943291E-13]
[0,18,22.527255652526545,null,null,-2.3999999999999901,9.3867055348388212E-3,2.2438947995672073E-3,23.049367330271856,2.5323244361108062E-3,null,null,-9.375E-2,9.8802654465429056E-5,1.7721158719733209E-13]
[0,19,21.820836119113643,null,null,-2.2999999999999901,1.2224472655045003E-2,2.8377671202061815E-3,23.218292415107193,3.0737612113880576E-3,null,null,7.8125E-2,1.0399538694374621E-4,1.9942791956965208E-13]
[0,20,28.548208996658332,null,null,-2.19999999999999,1.5777607391090891E-2,3.5531347360458886E-3,23.387217499942526,3.7142595913896362E-3,null,null,0.25,1.0945407569036623E-4,2.2457521285753085E-13]
[0,21,null,null,null,-2.0999999999999899,2.0182215405704869E-2,4.4046080146139775E-3,23.556142584777863,4.466648298549751E-3,null,null,0.421875,1.1519170005581448E-4,2.5305942823868069E-13]
[0,22,null,null,null,-1.99999999999999,2.5588059521639211E-2,5.4058441159343419E-3,23.725067669613196,5.3438190714124728E-3,null,null,0.59375,1.2122181987514512E-4,2.8534543288155335E-13]
[0,23,null,null,null,-1.8999999999999899,3.2156774795614428E-2,6.5687152739752168E-3,23.893992754448533,6.3581818494570196E-3,null,null,0.765625,1.27558597296391E-4,3.2196593652479522E-13]
[0,24,null,null,null,-1.7999999999999901,4.0059156863817939E-2,7.9023820682035117E-3,24.06291783928387,7.5209780110961494E-3,null,null,0.9375,1.3421681911120415E-4,3.6353184293633036E-13]
[0,25,null,null,null,-1.69999999999999,4.9471468033649123E-2,9.4123111698311834E-3,24.231842924119206,8.84145524041164E-3,null,null,1.109375,1.4121191957282178E-4,4.1074424962890383E-13]
[0,26,null,null,null,-1.5999999999999901,6.0570758002060181E-2,1.1099289968411058E-2,24.40076800895454,1.0325921299566769E-2,null,null,1.28125,1.4856000368367712E-4,4.644083692486438E-13]
[0,27,null,null,null,-1.49999999999999,7.3529259609649775E-2,1.2958501607589594E-2,24.569693093789876,1.1976710777555966E-2,null,null,1.453125,1.562778709318772E-4,5.2544969322697666E-13]
[0,28,null,null,null,-1.3999999999999899,8.8507991437403635E-2,1.4978731827753861E-2,24.73861817862521,1.3791117793889807E-2,null,null,1.625,1.643830394525217E-4,5.9493277391229804E-13]
[0,29,null,null,null,-1.2999999999999801,0.10564977366685889,1.7141782229455255E-2,24.907543263460564,1.5760366983640278E-2,null,null,1.796875,1.7289377058624144E-4,6.7408306704841501E-13]
[0,30,null,null,null,-1.19999999999998,0.12507193563715435,1.9422161970295462E-2,25.076468348295901,1.7868712511736301E-2,null,null,1.96875,1.818290938035024E-4,7.6431235401213631E-13]
[0,31,null,null,null,-1.0999999999999801,0.14685905637590049,2.1787120738746141E-2,25.245393433131234,2.0092767442298071E-2,null,null,2.140625,1.9120883195951777E-4,8.6724835490038014E-13]
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[0,42,null,null,null,0,0.51993880583837249,3.9877611676737035E-2,27.103569366319892,3.9304025117364749E-2,null,null,4.03125,3.3025845427294169E-4,3.6601564011932177E-12]
[0,43,null,null,null,0.10000000000002,0.5596176923702505,3.967888653187801E-2,27.272494451155261,3.9304025117380403E-2,null,null,4.203125,3.4684147956023969E-4,4.1919787930767251E-12]
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[0,45,null,null,null,0.30000000000001997,0.63683065117562654,3.8124325492695066E-2,27.610344620825931,3.8085495442126027E-2,null,null,4.546875,3.8239946313197229E-4,5.5124363315242891E-12]
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[0,47,null,null,null,0.50000000000002998,0.70884031321166396,3.5195533499576825E-2,27.948194790496622,3.5400699041589712E-2,null,null,4.890625,4.2137685479055626E-4,7.2734617816541642E-12]
[0,48,null,null,null,0.60000000000002995,0.74215388919414504,3.3313575982481081E-2,28.117119875331955,3.3610567667198943E-2,null,null,5.0625,4.4223861712597377E-4,8.3656962129073291E-12]
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