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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,"The Mathless Table"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Simple Bayes"]
[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,"The Rule of Succession"]
[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":"Simple Bayes","index":1,"n_rows":31,"n_cols":15,"rows_kept":31,"cut":false,"hidden":false,"merged":[[0,0,0,12],[1,2,2,12],[12,0,16,5],[5,0,9,2],[19,0,23,5],[26,0,30,2],[5,3,5,4],[5,8,5,9],[12,6,12,7],[19,6,19,7],[26,3,26,4],[26,8,26,9],[18,0,18,4]]}
["The Urn of Mystery: A Simple Bayesian Example"]
[null,null,"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."]
[]
[]
["\"It Depends\" - If I knew this, I would change this probability."]
["If we knew which urn we drew from, we would know the probability of drawing a red marble.  This is a Conditional Probability. The probability of drawing Red given we are drawing from urn A, can be written as P(R|A).",null,null,"Urn A",null,null,null,null,"Urn B"]
[null,null,null,"P(R|A)=",0.95,null,null,null,"P(R|B)=",{"$f":"1/6^3","v":4.6296296296296294E-3}]
[null,null,null,"P(G|A)=",{"$f":"1-E7","v":5.0000000000000044E-2},null,null,null,"P(G|B)=",{"$f":"1-J7","v":0.99537037037037035}]
[null,null,null,null,null,null,{"$f":"E7","v":0.95},null,null,null,null,{"$f":"J7","v":4.6296296296296294E-3},null,null,"p-value"]
[null,null,null,null,null,null,{"$f":"1-G9","v":5.0000000000000044E-2},null,null,null,null,{"$f":"1-L9","v":0.99537037037037035},null,null,"P(observe|fluke)"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"P(True|observe)"]
["\"To Be or Not To Be\" -  What is my current uncertainty?"]
["The probability we are drawing from urn A or B is written P(A) and P(B) respectively.  This is the \"prior\" probability, or \"What do I know now?\"\n\nThese are mutually exclusive and colletively exhaustive, so they follow the Compliment Rule: P(A)+P(~A)=1.\n\n\n",null,null,null,null,null,"Which Urn?"]
[null,null,null,null,null,null,"P(A)=",{"$f":"10^-6","v":9.9999999999999995E-7},null,null,"B",{"$f":"H15","v":0.99999899999999997}]
[null,null,null,null,null,null,"P(B)=",{"$f":"1-H14","v":0.99999899999999997},null,null,"A",{"$f":"H14","v":9.9999999999999995E-7}]
[null,null,null,null,null,null,"Change Yellow Cells!"]
[null,null,null,null,null,null,"Blue Cells Are Computed Output!"]
[]
["\"What might I see if I look?\" What's the chance of a particular observation?"]
["The chance of drawing a red marble, without knowing which urn you draw from, is the probability weighted average of drawing red from each urn.  This is the Law of Total Probability: P(R )=P(R|A)P(A)+P(R|B)P(B)",null,null,null,null,null,"Total Probability"]
[null,null,null,null,null,null,"P(R )=",{"$f":"H14*E7+H15*J7","v":4.6305749999999996E-3}]
[null,null,null,null,null,null,"P(G )=",{"$f":"1-H21","v":0.99536942500000003},null,null,{"$f":"H21","v":4.6305749999999996E-3}]
[null,null,null,null,null,null,null,null,null,null,{"$f":"1-K22","v":0.99536942500000003}]
[]
[]
["What did I learn?"]
["New information (even one draw) updates my prior to a posterior probability. This is computed using the priors, the conditionals, and the total probabilities with Bayes Rule: P(A|R)=P(A)P(R|A)/P(R )",null,null,"If Red is drawn",null,null,null,null,"If Green is drawn"]
[null,null,null,"P(A|R)=",{"$f":"H14*E7/H21","v":2.0515810671460887E-4},null,null,null,"P(A|G)=",{"$f":"H14*E8/H22","v":5.0232605848828479E-8}]
[null,null,null,"P(B|R)=",{"$f":"1-E28","v":0.99979484189328538},null,null,null,"P(B|G)=",{"$f":"1-J28","v":0.99999994976739415}]
[null,null,null,null,null,"B",{"$f":"E29","v":0.99979484189328538},null,null,null,"B",{"$f":"J29","v":0.99999994976739415}]
[null,null,null,null,null,"A",{"$f":"1-G30","v":2.051581067146202E-4},null,null,null,"A",{"$f":"1-L30","v":5.0232605852684742E-8}]

{"sheet":"BetaDistPopProportion Ws","index":2,"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,{"$f":"B6+C15","v":3}]
["beta",1,{"$f":"B7+C16","v":5}]
[]
["P5",{"$f":"_xlfn.BETA.INV(0.05,B6,B7)","v":5.000000000000001E-2},{"$f":"_xlfn.BETA.INV(0.05,C6,C7)","v":0.12875639280424281}]
["Median",{"$f":"_xlfn.BETA.INV(0.5,B6,B7)","v":0.5},{"$f":"_xlfn.BETA.INV(0.5,C6,C7)","v":0.36411608644808263}]
["Mean",{"$f":"B6/(B6+B7)","v":0.5},{"$f":"C6/(C6+C7)","v":0.375}]
["P95",{"$f":"_xlfn.BETA.INV(0.95,B6,B7)","v":0.95},{"$f":"_xlfn.BETA.INV(0.95,C6,C7)","v":0.658738563844664}]
[]
["Observations"]
["\"Hits\"",null,2]
["\"Misses\"",null,4]
["Total Observations",null,{"$f":"C16+C15","v":6}]
[]
["Calcs for Chart Boundaries"]
[{"$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":0.12875639280424281},0]
[{"$f":"C9","v":0.12875639280424281},{"$f":"VLOOKUP(A25,D$31:F$1029,3)","v":9.9466097424290301E-4}]
[{"$f":"A27","v":0.658738563844664},0]
[{"$f":"C12","v":0.658738563844664},{"$f":"VLOOKUP(A27,D$31:F$1029,3)","v":6.2193667006993358E-4}]
[]
[null,null,null,"Chart Distribution Calculations",null,null,"Prob. of sample result if the hypothetical proportion was the actual proportion","Bayesian Inversion: Prob. that actual proportion is equal to hypothetical proportion"]
[null,null,null,"Population Proportion","Prior","w/Data"]
[null,null,null,1E-3,{"$f":"_xlfn.BETA.DIST(D31+D$31/2,B$6,B$7,1)-_xlfn.BETA.DIST(D31-D$31/2,B$6,B$7,1)","v":1.0000000000000005E-3},{"$f":"_xlfn.BETA.DIST(D31+D$31/2,C$6,C$7,1)-_xlfn.BETA.DIST(D31-D$31/2,C$6,C$7,1)","v":1.1322595207900628E-7},{"$f":"BINOMDIST(C$15,C$15+C$16,D31,0)","v":1.4940089940015008E-5},{"$f":"(G31*E31/SUMPRODUCT($G$31:$G$1029,$E$31:$E$1029))","v":1.045806295804738E-7}]
[null,null,null,{"$f":"D31+D$31","v":2E-3},9.999999999999998E-4,4.2519133159139821E-7,5.9521438080959998E-5,{"$f":"(G32*E32/SUMPRODUCT($G$31:$G$1029,$E$31:$E$1029))","v":4.1665006656818879E-7}]
[null,null,null,3.0000000000000001E-3,1.0000000000000005E-3,{"$f":"_xlfn.BETA.DIST(D33+D$31/2,C$6,C$7,1)-_xlfn.BETA.DIST(D33-D$31/2,C$6,C$7,1)","v":9.4214876137360369E-7},1.333872754309349E-4,9.3371092801983655E-7]
[null,null,null,4.0000000000000001E-3,9.9999999999999872E-4,1.6616158757539881E-6,2.3618297862143978E-4,1.6532808503559049E-6]
[null,null,null,5.0000000000000001E-3,1.0000000000000018E-3,2.5811252782169033E-6,3.6755606273437472E-4,2.572892439149698E-6]
[null,null,null,6.0000000000000001E-3,9.9999999999999655E-4,3.6982244912671716E-6,{"$f":"BINOMDIST(C$15,C$15+C$16,D36,0)","v":5.2715617413984E-4},3.6900932189918766E-6]
[null,null,null,7.0000000000000001E-3,1E-3,5.0104759063704941E-6,7.1463508334473522E-4,5.0024455834307819E-6]
[null,null,null,8.0000000000000002E-3,1.0000000000000044E-3,6.5154567339689652E-6,9.2964667785215961E-4,6.5075267449880872E-6]
[null,null,null,9.0000000000000011E-3,9.9999999999999742E-4,8.2107589535727695E-6,1.1718469550316146E-3,8.2029286852502004E-6]
[null,null,null,1.0000000000000002E-2,1.0000000000000061E-3,1.0093989263926991E-5,1.4408940150000009E-3,1.0086258105035625E-5]
[null,null,null,1.1000000000000003E-2,9.9999999999999568E-4,1.2162769033254141E-5,1.7364480535134146E-3,1.2155136374636703E-5]
[null,null,null,1.2000000000000004E-2,1.0000000000000044E-3,1.4414734249572812E-5,2.0581713548697596E-3,1.4407199484139173E-5]
[null,null,null,1.3000000000000005E-2,9.9999999999999742E-4,1.6847535471090601E-5,2.4057282848221357E-3,1.6840097993814277E-5]
[null,null,null,1.4000000000000005E-2,1.0000000000000061E-3,1.9458837776674859E-5,2.7787852835030389E-3,1.9451496984589967E-5]
[null,null,null,1.5000000000000006E-2,9.9999999999999395E-4,2.2246320716395556E-5,3.1770108583593763E-3,2.2239076008593901E-5]
[null,null,null,1.6000000000000007E-2,1.0000000000000078E-3,2.5207678262149479E-5,3.6000755770982432E-3,2.5200529039776741E-5]
[null,null,null,1.7000000000000008E-2,9.9999999999999742E-4,2.8340618758351512E-5,4.0476520606435367E-3,2.833356442460457E-5]
[null,null,null,1.8000000000000009E-2,1.0000000000000009E-3,3.1642864872710578E-5,4.5194149761033633E-3,3.16359048328351E-5]
[null,null,null,1.900000000000001E-2,1.0000000000000009E-3,3.5112153547075213E-5,5.01504102974822E-3,3.5105287208361332E-5]
[null,null,null,2.0000000000000011E-2,1.0000000000000044E-3,3.8746235948358058E-5,5.5342089600000062E-3,3.8739462720136787E-5]
[null,null,null,2.1000000000000012E-2,9.9999999999999742E-4,4.2542877419530492E-5,6.0765995304318237E-3,4.2536196713172614E-5]
[null,null,null,2.2000000000000013E-2,9.9999999999999742E-4,4.6499857430703346E-5,6.6418955227785636E-3,4.6493268659613731E-5]
[null,null,null,2.3000000000000013E-2,1.0000000000000009E-3,5.0614969530268826E-5,7.229781729958344E-3,5.060847210988687E-5]
[null,null,null,2.4000000000000014E-2,1.0000000000000009E-3,5.488602129613459E-5,7.8399449491046522E-3,5.4879614643926089E-5]
[null,null,null,2.5000000000000015E-2,1.0000000000000009E-3,5.9310834287016505E-5,8.4720739746093794E-3,5.930451782247478E-5]
[null,null,null,2.6000000000000016E-2,1.0000000000000078E-3,6.3887243993820475E-5,9.1258595911766511E-3,6.3881017138462274E-5]
[null,null,null,2.7000000000000017E-2,1.0000000000000044E-3,6.8613099791093712E-5,9.8009945668873482E-3,6.8606961968453611E-5]
[null,null,null,2.8000000000000018E-2,9.9999999999999742E-4,7.348626488855065E-5,1.0497173646274567E-2,7.348021552418084E-5]
[null,null,null,2.9000000000000019E-2,1.0000000000000044E-3,7.8504616282680018E-5,1.1214093543409829E-2,7.8498654804145889E-5]
[null,null,null,3.000000000000002E-2,9.9999999999999395E-4,8.3666044708417451E-5,1.1951452935000011E-2,8.3660170545294516E-5]
[null,null,null,3.1000000000000021E-2,9.9999999999999395E-4,8.8968454590908136E-5,1.270895245349523E-2,8.8962667174779703E-5]
[null,null,null,3.2000000000000021E-2,1.0000000000000078E-3,9.4409763997333439E-5,1.3486294680207374E-2,9.4404062761785175E-5]
[null,null,null,3.3000000000000022E-2,1.0000000000000009E-3,9.9987904588808973E-5,1.4283184138439545E-2,9.9982288969429391E-5]
[null,null,null,3.4000000000000023E-2,1.0000000000000078E-3,1.057008215723835E-4,1.5099327286626262E-2,1.0569529100675728E-4]
[null,null,null,3.5000000000000024E-2,9.9999999999999395E-4,1.1154647365307717E-4,1.5934432511484384E-2,1.1154102758078326E-4]
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[null,null,null,3.7000000000000026E-2,9.9999999999999395E-4,1.2362788512869415E-4,1.7660372338476144E-2,1.2362260636976808E-4]
[null,null,null,3.8000000000000027E-2,1.0000000000000078E-3,1.2985962899314334E-4,1.8550633293965786E-2,1.298544330582193E-4]
[null,null,null,3.9000000000000028E-2,9.9999999999998701E-4,1.3621607679838209E-4,1.9458709019216428E-2,1.3621096313499342E-4]
[null,null,null,4.0000000000000029E-2,1.0000000000000009E-3,1.426952540228585E-4,2.0384317440000022E-2,1.4269022208050332E-4]
[null,null,null,4.1000000000000029E-2,1.0000000000000148E-3,1.4929519935689018E-4,2.1327178369503635E-2,1.4929024858705394E-4]
[null,null,null,4.200000000000003E-2,1.0000000000000009E-3,1.5601396465531004E-4,2.2287013501556194E-2,1.5600909451144352E-4]
[null,null,null,4.3000000000000031E-2,9.9999999999998701E-4,1.6284961489010938E-4,2.3263546403865763E-2,1.6284482482763234E-4]
[null,null,null,4.4000000000000032E-2,1.0000000000000148E-3,1.698002281031734E-4,2.4256502511267878E-2,1.6979551757947625E-4]
[null,null,null,4.5000000000000033E-2,9.9999999999999395E-4,1.7686389535908091E-4,2.5265609118984411E-2,1.7685926383351333E-4]
[null,null,null,4.6000000000000034E-2,1.0000000000000078E-3,1.8403872069802998E-4,2.6290595375893459E-2,1.8403416763190444E-4]
[null,null,null,4.7000000000000035E-2,9.9999999999998701E-4,1.9132282108875586E-4,2.733119227780996E-2,1.9131834594534171E-4]
[null,null,null,4.8000000000000036E-2,1.0000000000000009E-3,1.9871432638163267E-4,2.8387132660776998E-2,1.987099286261397E-4]
[null,null,null,4.9000000000000037E-2,1.0000000000000148E-3,2.0621137926169408E-4,2.9458151194368055E-2,2.062070583613064E-4]
[null,null,null,5.0000000000000037E-2,1.0000000000000009E-3,2.13812135201922E-4,3.0543984375000034E-2,2.1380789062575418E-4]
[null,null,null,5.1000000000000038E-2,9.9999999999998701E-4,2.2151476241647058E-4,3.1644370519257045E-2,2.2151059363557734E-4]
[null,null,null,5.2000000000000039E-2,1.0000000000000078E-3,2.2931744181398702E-4,3.2759049757225003E-2,2.2931334830138524E-4]
[null,null,null,5.300000000000004E-2,9.9999999999999395E-4,2.3721836695107194E-4,3.3887764025836979E-2,2.372143481816937E-4]
[null,null,null,5.4000000000000041E-2,1.0000000000000078E-3,2.4521574398575323E-4,3.5030257062229467E-2,2.4521179943647265E-4]
[null,null,null,5.5000000000000042E-2,1.0000000000000009E-3,2.5330779163102238E-4,3.6186274397109419E-2,2.5330392078065921E-4]
[null,null,null,5.6000000000000043E-2,1.0000000000000078E-3,2.6149274110857067E-4,3.7355563348131893E-2,2.6148894343784715E-4]
[null,null,null,5.7000000000000044E-2,9.9999999999998701E-4,2.6976883610238186E-4,3.8537873013288794E-2,2.6976511109396908E-4]
[null,null,null,5.8000000000000045E-2,1.0000000000000078E-3,2.7813433271267271E-4,3.9732954264308215E-2,2.7813067985114025E-4]
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[null,null,null,6.1000000000000047E-2,9.9999999999998701E-4,3.0374997851814484E-4,4.3392362717555463E-2,3.0374653902395511E-4]
[null,null,null,6.2000000000000048E-2,9.9999999999998701E-4,3.1245588930621862E-4,4.463607427361381E-2,3.1245251991639413E-4]
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[null,null,null,0.99600000000000077,9.9999999999988987E-4,2.7495450360959239E-11,3.8093414399970612E-9,2.66653900800705E-11]
[null,null,null,0.99700000000000077,9.9999999999988987E-4,8.9230844935173081E-12,1.2077209349987557E-9,8.454046545020163E-12]
[null,null,null,0.99800000000000078,9.9999999999988987E-4,1.8831602943691905E-12,2.3904095999963006E-10,1.6732867200031251E-12]
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{"sheet":"Rule of Succession","index":3,"n_rows":52,"n_cols":17,"rows_kept":52,"cut":false,"hidden":false,"merged":[[0,0,0,14],[24,0,24,14],[51,0,51,14]]}
["Laplace's Rule of Succession"]
[]
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[]
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[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,{"$f":"1/(12+2)","v":7.1428571428571425E-2}]
[]
["Other Handy \"Naïve\" Estimators"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
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[]
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[]
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[]
["Process for Estimating the Baseline"]

{"sheet":"CatchRecatch Ws","index":4,"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)",20]
["The second sample size",12]
["Overlap between samples (i.e. the tagged fish that showed up in the second sample) - THIS APPROXIMATION IS ONLY VALID WHERE THIS VALUE >10",5]
[null,null,"Beta Distribution"]
[]
[]
[]
["Computing bounds for 90% CI for the percentage of tagged fish"]
["Upper bound",null,{"$f":"_xlfn.BETA.INV(0.95,B6+1,B5-B6+1)","v":0.645200718980387}]
["Lower bound",null,{"$f":"_xlfn.BETA.INV(0.05,B6+1,B5-B6+1)","v":0.22395539421131924}]
["Computing bounds for 90% CI for the total population of fish"]
["Upper bound",null,{"$f":"(B4-B6)/C13+B5","v":78.977623168327611}]
["Lower bound",null,{"$f":"(B4-B6)/C12+B5","v":35.248579176577103}]

{"sheet":"Mathless Table","index":5,"n_rows":1,"n_cols":1,"rows_kept":1,"cut":false,"hidden":false,"merged":[[0,0,0,14]]}
["The \"Mathless Table\""]

{"sheet":"EstimatingDistAndMean Ex ","index":6,"n_rows":225,"n_cols":75,"rows_kept":225,"cut":false,"hidden":false,"merged":[[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],[24,10,24,12],[12,0,14,1],[22,19,22,20],[22,8,22,12],[22,13,22,18]]}
["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,2402]
["Number of Samples"]
["Enter number of samples or use slider bar below.  For a given scenario, increasing the number of samples improves estimates."]
[null,8]
["True, Hidden Distribution"]
["Population #",2]
["Reveal Distribution?",true]
[{"$f":"IF(B12,OFFSET(W18,,B11-1),\"\")","v":"Beta"}]
[]
[]
["Estimates Based on Samples"]
["Average of sample",{"$f":"AVERAGE(L26:L227)","v":65.9375}]
["Standard Deviation of Sample",{"$f":"_xlfn.STDEV.S(L26:L227)","v":14.293948519765777},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Normal","Beta","Uniform","lognormal","MLB Player Batting","book ratings w/>10 reviews","Book num of pages","NJ teacher salary","age of working adults","Work hours per month"]
["Error of the Estimate of the Mean",{"$f":"B18/B9^0.5","v":5.0536739641288966},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,100.49999999737008,66.916666695831267,50.250000000000007,43.866708940552002,261.21391772668164,4.637817596061458,354.78107676456682,73281.170998547328,38.069417544485447,201.27406605390445]
[]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,0,0,0,0,140,0,0,0,0,90]
["Increments for chart",{"$f":"OFFSET(W23,,B11-1)","v":0.5},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,200,100,100,200,400,8,1800,300000,98,310]
[null,"Distribution curves",null,null,null,null,null,null,"Sample Values",null,null,null,null,"Running Calculations for Chart Above",null,null,null,null,null,"True Mean Plot",null,null,{"$f":"(W22-W21)/200","v":1},0.5,0.5,1,{"$f":"(AA22-AA21)/200","v":1.3},{"$f":"(AB22-AB21)/200","v":0.04},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,{"$f":"NORMDIST(C25,100,15,1)","v":1.3083924686052984E-11},{"$f":"IFERROR(BETADIST(C25,6,3,0,100),\"\")","v":0},{"$f":"C25/100","v":0},0,1.5610514094811206E-6,1.2485100129659449E-4,2.2492764901592502E-11,1.4319415685426138E-4,1.8801106744299012E-18,4.3636970020232717E-5,null,null,null,null,null,null,null,null,null,null,null,null,null,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]
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{"sheet":"PopMean Ws","index":7,"n_rows":620,"n_cols":15,"rows_kept":620,"cut":false,"hidden":false,"merged":[[0,1,0,15],[6,1,6,2],[7,1,7,2],[11,1,11,2],[15,1,15,2],[15,10,15,11],[5,1,5,2],[2,1,2,3],[3,1,3,2],[4,1,4,2],[15,3,15,4],[12,1,12,2],[13,1,13,2],[1,1,1,3]]}
[null,"Worksheet: Computing 90% Confidence Intervals with Small Samples"]
[null," The \"t-stat\" is used for small samples.  Note that two excel formulas are introduced here that give the same answers as the steps in the book: VAR() and TINV().  This will slightly simplify the calculation.  You can use this spreadsheet to compute ranges for larger samples, too.  Just add however many rows you need and don't forget to change the references in the cells to capture all the new rows.  See how close the answers would be if you just used the \"Mathless\" table.\n\nThis sheet will also calculate an estimate of the underlying distribution using a t-distribution. One will notice from the previous example that this may or ay not be a good assumption."]
[null,"90% Confidence Interval Calculations (by steps described in book)"]
[null,"Average of Sample Values (step 1.a in book)",null,{"$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}]
[0,1,19.60341451227848,"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]
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{"sheet":"Data","index":8,"n_rows":25,"n_cols":2,"rows_kept":25,"cut":false,"hidden":false,"merged":[[0,0,0,7],[1,0,1,7],[2,0,2,1],[3,1,4,1]]}
["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."]
["Population Mean Worksheet"]
["Sample Value","Survey Results:\nCase Example (Hours spent per week)"]
[]
[19.60341451227848,3.2]
[14,5.8]
[29.777969943565893,6.5]
[19,6.5]
[22.472662067192626,7.1]
[36,7.5]
[26.248730784373315,8.4]
[32.496312612666316,8.9]
[17,9]
[35,9.5]
[26.446772517453628,10.1]
[39,10.199999999999999]
[41.5,10.5]
[22.851439941356947,11.3]
[30.269414387144479,12.2]
[34]
[23.508369792067629]
[22.527255652526545]
[21.820836119113643]
[28.548208996658332]