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[]
[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 Decision Analysis Examples"]
[]
[null,null,null,null,"1) Risk Tolerance from Chapter 6\n2) Dawes Linear Model from Chapter 8\n3) Information Value Example from Chapters 10 and 11"]

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["Risk Tolerance (Chapter 6)"]
[null,"This tab allows a user to define an unambiguous risk tolerance by assessing just-barely-acceptable bets representing a typical investment, a relative safe one, and a longshot.  Three different models are used to represent risk tolerance of the decision maker: Constand Absolute Risk Aversion (CARA), Relative Risk Aversion (RRA), and exponential (Exp).  These three models try to find a best fit solution for the risk tolerance of the investor but minimizing the \"fit\" in row 9 by changing values in rows 7 and 8.  Notes that two of the models require an \"initial wealth\" assumption while one (CARA) does not.  Also the exponential only varies initial wealth to try to find a fit.  Since RRA varies two parameters to fit the stated preferences, it will usually find the best fit of the three."]
[null,"$Gain","$Loss","P(Gain)","CARA CME","RRA CME","Exp CME"]
["Safe bet",5,-3,0.8,{"$f":"-E$7*LN(1-(1-EXP(-B4/E$7))*D4-(1-EXP(-C4/E$7))*(1-D4))","v":7.7469571499453188E-2},{"$f":"EXP(LN((B4+$F$8)^(1-$F$7)*D4+(C4+$F$8)^(1-$F$7)*(1-D4))/(1-$F$7))-$F$8","v":2.3333333333333339},{"$f":"EXP(LN(B4+$G$8)*D4+LN(C4+$G$8)*(1-D4))-$G$8","v":2.9288090127379842}]
["Typical investment",2,-1,0.6,{"$f":"-E$7*LN(1-(1-EXP(-B5/E$7))*D5-(1-EXP(-C5/E$7))*(1-D5))","v":0.25517550112045867},{"$f":"EXP(LN((B5+$F$8)^(1-$F$7)*D5+(C5+$F$8)^(1-$F$7)*(1-D5))/(1-$F$7))-$F$8","v":0.60714285714285587},{"$f":"EXP(LN(B5+$G$8)*D5+LN(C5+$G$8)*(1-D5))-$G$8","v":0.70485428222119673}]
["longshot",15,-3,0.2,{"$f":"-E$7*LN(1-(1-EXP(-B6/E$7))*D6-(1-EXP(-C6/E$7))*(1-D6))","v":-2.5537746013217699},{"$f":"EXP(LN((B6+$F$8)^(1-$F$7)*D6+(C6+$F$8)^(1-$F$7)*(1-D6))/(1-$F$7))-$F$8","v":-1.7142857142857153},{"$f":"EXP(LN(B6+$G$8)*D6+LN(C6+$G$8)*(1-D6))-$G$8","v":-0.87332996673613295}]
[null,"Utility Coeficients:",null,null,2,2,"NA"]
[null,"Initial Wealth:",null,null,"NA",11,11]
[null,"Fit (lower is better fit):",null,null,{"$f":"SUMSQ(E4:E6)","v":6.5928807852365505},{"$f":"SUMSQ(F4:F6)","v":8.7518424036281228},9.8374470230601396]

{"sheet":"Dawes Linear Model","index":2,"n_rows":27,"n_cols":11,"rows_kept":27,"cut":false,"hidden":false,"merged":[[1,0,4,4],[1,10,5,10],[6,5,9,5]]}
["Dawes Linear Model Example (Chapter 8)"]
["The primary purpose of this is to show how z-scores are computed from a set of inputs.  This example is one that estimates relative risks in R&D projects based on four factors.  The z-scores, row 7 columns G to J, convert these inputs to a standardized unit.  The primary reason this might improve on human experts is simply because experts tend to be inconsistent.  This avoids the errors introduced by ordinal scales but may not perform as well as a Lens Model.",null,null,null,null,"Mean",{"$f":"AVERAGE(A7:A27)","v":18.523809523809526},{"$f":"AVERAGE(B7:B27)","v":5.2857142857142856},{"$f":"AVERAGE(C7:C27)","v":0.52380952380952384},{"$f":"AVERAGE(D7:D27)","v":4.0476190476190474},"Total Weighted z-scores.  In this case, a negative z-score means the risk is lower than average.  A positive z-score means it is higher than average.  Color coding is added with Excel's \"Conditional Formating\" function so that the riskiest are shown as red, the least risky are green and yellow is in between."]
[null,null,null,null,null,"Standard Devation",{"$f":"STDEV(A7:A27)","v":17.162805853411754},{"$f":"STDEV(B7:B27)","v":3.8877095717511767},{"$f":"STDEV(C7:C27)","v":0.51176631571915898},{"$f":"STDEV(D7:D27)","v":4.0555664274696639}]
[null,null,null,null,null,"Direction:  This shows whether more of a given factor increases risk (+1) or decreases risk (-1).",1,1,-1,1]
[null,null,null,null,null,"Weight (optional): Dawes research shows that even equally weighted z-scores might outperform unaided human experts.  But if some factors are obviously more important than others, the relative weights can be used to reflect that.",1,1,1,1]
["Estimated Cost ($millions)","Estimated Duration (Years)","Currently patented","Related new patents per year",null,null,"Estimated Cost z-score","Estimated Duration z-score","Currently patented z-score","Related new patents per year z-score"]
[12,2,1,1,null,"Weighted z-scores ====>>>",{"$f":"(A7-G$2)/G$3*G$4*G$5","v":-0.38011322737841685},{"$f":"(B7-H$2)/H$3*H$4*H$5","v":-0.84515425472851646},{"$f":"(C7-I$2)/I$3*I$4*I$5","v":-0.93048421039847085},{"$f":"(D7-J$2)/J$3*J$4*J$5","v":-0.75146569588320322},{"$f":"SUM(G7:J7)","v":-2.9072173883886072}]
[4,1,1,5,null,null,{"$f":"(A8-G$2)/G$3*G$4*G$5","v":-0.84623747701034391},-1.1023751148632823,-0.93048421039847085,0.23483302996350106,{"$f":"SUM(G8:J8)","v":-2.6442637723085962}]
[25,5,0,12,null,null,0.37733867827346468,-7.3491674324218798E-2,1.023532631438318,1.9608558001952336,3.2882354355827976]
[6,4,0,2,null,null,-0.72970641460236219,-0.33071253445898469,1.023532631438318,-0.50489101442152717,-0.54177733204455614]
[9,2,0,1,null,null,-0.55490982099038955,-0.84515425472851646,1.023532631438318,-0.75146569588320322,-1.1279971401637914]
[50,5,1,9,null,null,1.8339769583732368,-7.3491674324218798E-2,-0.93048421039847085,1.2211317558102053,2.0511328294607525]
[1,7,0,15,null,null,-1.0210340706223167,0.44095004594531295,1.023532631438318,2.700579844580262,3.1440284513415762]
[3,2,0,4,null,null,-0.90450300821433482,-0.84515425472851646,1.023532631438318,-1.1741651498175009E-2,-0.73786628300270829]
[44,9,1,2,null,null,1.4843837711492915,0.95539176621484478,-0.93048421039847085,-0.50489101442152717,1.0044003125441381]
[29,7,1,3,null,null,0.61040080308942823,0.44095004594531295,-0.93048421039847085,-0.25831633295985107,-0.13744969432358073]
[3,3,1,1,null,null,-0.90450300821433482,-0.5879333945937506,-0.93048421039847085,-0.75146569588320322,-3.1743863090897593]
[15,4,0,0,null,null,-0.20531663376644418,-0.33071253445898469,1.023532631438318,-0.99804037734487927,-0.5105369141319902]
[11,3,1,1,null,null,-0.43837875858240771,-0.5879333945937506,-0.93048421039847085,-0.75146569588320322,-2.7082620594578324]
[8,2,1,1,null,null,-0.61317535219438035,-0.84515425472851646,-0.93048421039847085,-0.75146569588320322,-3.1402795132045709]
[19,10,0,5,null,null,2.7745491049519372E-2,1.2126126263496106,1.023532631438318,0.23483302996350106,2.4987237788009491]
[33,15,1,2,null,null,0.84346292790539179,2.4987169270234402,-0.93048421039847085,-0.50489101442152717,1.9068046301088337]
[62,12,0,3,null,null,2.5331633328211276,1.7270543466191424,1.023532631438318,-0.25831633295985107,5.0254339779187367]
[31,10,0,1,null,null,0.72693186549740996,1.2126126263496106,1.023532631438318,-0.75146569588320322,2.2116114274021355]
[13,4,0,9,null,null,-0.32184769617442593,-0.33071253445898469,1.023532631438318,1.2211317558102053,1.5921041566151126]
[4,2,1,6,null,null,-0.84623747701034391,-0.84515425472851646,-0.93048421039847085,0.48140771142517713,-2.1404682307121545]
[7,2,1,2,null,null,-0.67144088339837127,-0.84515425472851646,-0.93048421039847085,-0.50489101442152717,-2.9519703629468861]

{"sheet":"SimpleInfoValue","index":3,"n_rows":12,"n_cols":4,"rows_kept":12,"cut":false,"hidden":false,"merged":[[5,0,5,1],[6,0,6,1],[8,0,8,3],[0,0,0,3],[1,0,1,3],[2,0,2,1],[3,0,3,1],[4,0,4,1],[4,2,4,3]]}
["Simple Expected Opportunity Loss (EOL) Example (Chapters 10 and 11)"]
["This is the simple Expected Opportunity Loss (EOL) Example.  The values are for a proposed advertising campaign but you could change them to any simple, binary decision problem.  Remember the EOL is also the Expected Value of Perfect Information (EVPI).  The more elaborate calculation for ranges is on the next worksheet."]
[null,null,"Good Outcome (eg. Campaign succeeds)","Bad Outcome (eg. Campaign Fails)"]
["Chance of Outcome:",null,0.6,{"$f":"1-C4","v":0.4}]
["Choice",null,"Payoff"]
["A (eg. Invest in the new ad campaign)",null,40000000,-5000000]
["B (eg. Don't Invest in the ad campaign)",null,0,0]
[]
["Expected Opportunity Loss (EOL) Results for Exhibit 7.1"]
[null,"Opportunity Loss","Chance of being wrong","Expected Opportunity Loss (EOL)"]
["If initially desired choice is A",{"$f":"ABS(MIN(C6:D6))","v":5000000},{"$f":"D4","v":0.4},{"$f":"C11*B11","v":2000000}]
["If initially desired choice is B",{"$f":"ABS(MAX(C6:D6))","v":40000000},{"$f":"C4","v":0.6},{"$f":"C12*B12","v":24000000}]

{"sheet":"InfoValUniform ","index":4,"n_rows":19,"n_cols":26,"rows_kept":19,"cut":false,"hidden":false,"merged":[[12,0,12,2],[14,2,14,3],[14,4,14,5],[14,6,14,7],[6,0,6,1],[7,0,7,1],[8,0,8,1],[9,0,9,1],[10,0,10,1],[11,0,11,1],[5,0,5,1],[0,0,0,3],[1,0,1,3],[2,0,2,3],[3,0,3,3],[4,0,4,1]]}
["Continuous Information Value Calculation using a Uniform (Chapters 10 and 11)"]
["This is an example of an information value calculation for a continuous quantity with a uniform distribution.  This calculation is different from the information value calculation for a normal because it can be calculated exactly without have to \"slice up\" the distribution as we did with the normal distribution.  Input values are the yellow cells."]
["As with the normal distribution, this spreadsheet can give a slightly more accurate answer than the chart in Doug's book.  The lower and upper bounds of this spreadsheet are \"absolute\" bounds.  Unlike the 90% confidence interval, there is no chance the value can be outside of the stated bounds. The only problem in using this spreadsheet is that for many special cases the \"loss rate\" may change depending on the quantity estimated.   For example, the rate of loss in this spreadsheet (cell B9) is fixed and many loss functions accelerate as things get worse, or it may level off.   Hubbard's more advanced Monte Carlo simulation tools address of of these issues.  See Hubbard's tools on the catalog page at www.howtomeasureanything.com for more info."]
["Inputs to Information Value Calculation"]
["Upper Bound",null,null,700]
["Lower Bound",null,null,450,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"over"]
["Interval Range",null,null,{"$f":"D5-D6","v":250},null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"under"]
["Threshold",null,null,500]
["Loss rate (on the undesirable side of the threshold)",null,null,75000]
["Mean",null,null,{"$f":"(D5+D6)/2","v":575}]
["Standard deviation",null,null,{"$f":"(D5-D6)/12^0.5","v":72.168783648703226}]
["Does the loss occur under or over the threshold?",null,null,"under"]
["Information Value if it were a uniform distribution with the absolute constraints above",null,null,{"$f":"IF(EXACT(D12,\"under\"),MAX(0,D8-D6)^2/2*D9/(D5-D6),MAX(0,D5-D8)^2/2*D9/(D5-D6))","v":375000}]
[]
["Confidence Interval Bars",null,"Mean Bar",null,"Threshold Bar",null,"Loss Function"]
[{"$f":"D6","v":450},0,{"$f":"D10","v":575},0,{"$f":"D8","v":500},0,{"$f":"IF(D12=\"under\",D9*ABS(H16-D8),0)","v":13125000},{"$f":"D10-D7","v":325}]
[{"$f":"D6","v":450},0.1,{"$f":"D10","v":575},0.1,{"$f":"D8","v":500},0.15,0,{"$f":"D8","v":500}]
[{"$f":"D5","v":700},0.1,null,null,null,null,{"$f":"IF(D12=\"over\",D9*ABS(D8-H18),0)","v":0},{"$f":"D10+D7","v":825}]
[{"$f":"D5","v":700},0]

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["Continuous Information Value Calculation using a Normal Distribution (Chapter 10 and 11)"]
["This is an example of an information value calculation for a continuous quantity that is normally distributed (See the next worksheet tab for the example with a uniform distribution).  As mentioned in the book, one way to compute  the value of reducing uncertainty about a range is to chop up the range into hundreds of small slices, compute the probability and loss for each slice, multiply each probability and loss, and add them all up.  This is what this spreadsheet does.  It slices the possible range of values of the quantity into 2000 pieces up to 5 standard deviations from the mean.  For each slice, it computes the loss and the probability of that slice.  The product of each loss & probability pair is added to all the other such products to get the Expected Value of Perfect Information (EVPI) for the uncertain quantity.  "]
["This spreadsheet can give a slightly more accurate answer than the chart in the book for two reasons.  First, it doesn't depend on \"eyeballing\" the lines on the chart.  Second, the chart doesnt allow for truncated values.  That is, the quantity which we are computing the informatin value for, could be much farther beyond either of the bounds of the 90% CI.  But, in reality, we might want to put realistic \"hard stops\" on these values.  This spreadsheet asks for \"absolute\" min and max bounds in addition to the 90% CI bounds.  However, even this is still less accurate than the VIA calculation tools for many special cases.   For example, the rate of loss in this spreadsheet (cell B9) is fixed and many loss functions accelerate as things get worse, or it may level off.   Hubbard's more sophisticated Monte Carlo tool handles all of these issues.  See Hubbard's tools on the catalog page at www.howtomeasureanything.com for more info.  Input values into yellow shaded cells"]
["Inputs to Information Value Calculation"]
["90% CI Upper Bound",null,null,1000000]
["90% CI Lower Bound",null,null,-1000000]
["Interval Range",null,null,{"$f":"D5-D6","v":2000000}]
["Threshold",null,null,0]
["Loss rate (on the undesirable side of the threshold)",null,null,1]
["Mean",null,null,{"$f":"(D5+D6)/2","v":0}]
["Standard deviation",null,null,{"$f":"(D5-D6)/3.29","v":607902.73556230997}]
["Does the loss occur under or over the threshold?",null,null,"under"]
["The absolute minimum the quantity can reach",null,null,-9999999999,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"over"]
["The absolute maximum the quantity can reach",null,null,9999999999,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,null,"under"]
["Estimated Information Value for a normally distributed uncertain quantity with the 90% confidence interval adjusted for absolute constraints",null,null,{"$f":"SUMPRODUCT(C18:C2018,D18:D2018)*SUM(D18:D2018)","v":241757.68846667936}]
[]
["Standard deviation","Quantity","Loss","Incremental Probability"]
[-5,{"$f":"A18*D$11+D$10","v":-3039513.67781155},{"$f":"IF(EXACT(D$12,\"under\"),IF(B18<D$8,D$9*(D$8-B18),0),IF(B18>D$8,D$9*(B18-D$8),0))","v":3039513.67781155},0,null,"cpf for Data","Incremental \nP for Data","Parameter Values","Confidence Interval Bars",null,"Threshold Bars",null,null,null,"Truncated probabilities"]
[-4.9950000000000001,-3036474.1641337383,3036474.1641337383,{"$f":"IF(OR(B19<D$13,B19>D$14),0,NORMDIST(B19,D$10,D$11,1)-NORMDIST(B18,D$10,D$11,1))","v":7.5272651805013383E-9},null,{"$f":"NORMDIST(B18,D$10,D$11,1)","v":2.8665157187919333E-7},null,null,{"$f":"D6","v":-1000000},0,{"$f":"D8","v":0},0,null,"Absolute lower",{"$f":"NORMDIST(D13,D10,D11,1)","v":0}]
[-4.99,-3033434.650455927,3033434.650455927,7.7176254611532507E-9,null,2.9417883705969467E-7,{"$f":"IF(AND(H20>=D$13,H20<=D$14),(F20-F19)/(1-O$19-O$20),0)","v":7.5272651805013383E-9},{"$f":"D$10+A19*D$11","v":-3036474.1641337383},{"$f":"D6","v":-1000000},5.0000000000000001E-4,{"$f":"D8","v":0},1.9E-3,null,"Absolute upper",{"$f":"1-NORMDIST(D14,D10,D11,1)","v":0}]
[-4.9850000000000003,-3030395.1367781153,3030395.1367781153,7.91260202856633E-9,null,3.0189646252084792E-7,7.7176254611532507E-9,-3033434.650455927,{"$f":"D5","v":1000000},0]
[-4.9800000000000004,-3027355.623100304,3027355.623100304,8.1123016358665947E-9,null,3.0980906454941425E-7,7.91260202856633E-9,-3030395.1367781153,{"$f":"D5","v":1000000},5.0000000000000001E-4]
[-4.9749999999999996,-3024316.1094224919,3024316.1094224919,8.3168333731134181E-9,null,3.1792136618528084E-7,8.1123016358665947E-9,-3027355.623100304]
[-4.97,-3021276.5957446806,3021276.5957446806,8.5263087152218476E-9,null,3.2623819955839426E-7,8.3168333731134181E-9,-3024316.1094224919,null,null,null,null,null,{"$f":"IF(AND(H20>=D$13,H20<=D$14),(F20-F19)/(1-O$19-O$20),0)","v":7.5272651805013383E-9}]
[-4.9649999999999999,-3018237.0820668689,3018237.0820668689,8.7408415708179294E-9,null,3.3476450827361611E-7,8.5263087152218476E-9,-3021276.5957446806]
[-4.96,-3015197.5683890576,3015197.5683890576,8.9605483319896649E-9,null,3.4350534984443404E-7,8.7408415708179294E-9,-3018237.0820668689]
[-4.9550000000000001,-3012158.0547112459,3012158.0547112459,9.1855479249943741E-9,null,3.524658981764237E-7,8.9605483319896649E-9,-3015197.5683890576]
[-4.95,-3009118.5410334347,3009118.5410334347,9.4159618619146285E-9,null,3.6165144610141808E-7,9.1855479249943741E-9,-3012158.0547112459]
[-4.9450000000000003,-3006079.027355623,3006079.027355623,9.6519142932855733E-9,null,3.7106740796333271E-7,9.4159618619146285E-9,-3009118.5410334347]
[-4.9400000000000004,-3003039.5136778117,3003039.5136778117,9.8935320617071365E-9,null,3.8071932225661828E-7,9.6519142932855733E-9,-3006079.027355623]
[-4.9349999999999996,-2999999.9999999995,2999999.9999999995,1.0140944756460502E-8,null,3.9061285431832542E-7,9.8935320617071365E-9,-3003039.5136778117]
[-4.93,-2996960.4863221878,2996960.4863221878,1.0394284769143402E-8,null,4.0075379907478592E-7,1.0140944756460502E-8,-2999999.9999999995]
[-4.9249999999999998,-2993920.9726443766,2993920.9726443766,1.0653687350356795E-8,null,4.1114808384392932E-7,1.0394284769143402E-8,-2996960.4863221878]
[-4.92,-2990881.4589665649,2990881.4589665649,1.0919290667414224E-8,null,4.2180177119428611E-7,1.0653687350356795E-8,-2993920.9726443766]
[-4.915,-2987841.9452887536,2987841.9452887536,1.1191235863163965E-8,null,4.3272106186170034E-7,1.0919290667414224E-8,-2990881.4589665649]
[-4.91,-2984802.4316109419,2984802.4316109419,1.1469667115866159E-8,null,4.439122977248643E-7,1.1191235863163965E-8,-2987841.9452887536]
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{"sheet":"Validation","index":6,"n_rows":6,"n_cols":1,"rows_kept":6,"cut":false,"hidden":true,"merged":[]}
["Normal"]
["Binary"]
["Uniform"]
["Lognorm"]
["Triangular"]
["Constant"]