MTB > # CHAPTER 3 EXERCISES MTB > #-------------------------------------------- MTB > # Exercise 2 MTB > #-------------------------------------------- MTB > MTB > # p1 - prob of preferring Bush pre-debate MTB > # p2 - prob of preferring Bush post-debate MTB > # want posterior of p2-p1 and P(p2>p1) MTB > # we'll assign uniform priors to p1 and p2 MTB > MTB > exec 'pp_beta' FOR PROPORTION P1, ENTER VALUES OF BETA PARAMETERS A1 AND B1: DATA> 295 308 FOR PROPORTION P2, ENTER VALUES OF BETA PARAMETERS A2 AND B2: DATA> 289 333 HOW MANY VALUES OF (P1, P2) DO YOU WISH TO SIMULATE? DATA> 1000 TYPE 'y' TO SEE A PLOT OF THE DISTRIBUTION OF THE DIFFERENCE IN PROPORTIONS P2-P1: y Each dot represents 4 points . : : : ::..: :. . .::::::::: :: ::::::::::: .::::::::::::::.:: .::::::::::::::::::: : .. :.:::::::::::::::::::::::. . ....:::::::::::::::::::::::::::::::::... .. . +---------+---------+---------+---------+---------+-------P2-P1 -0.120 -0.080 -0.040 0.000 0.040 0.080 TYPE 'y' to COMPUTE PROBABILITIES OF IMPROVEMENT FOR P2-P1: ----------------------------------------------------------- Input values of possible improvement. The output is the probabilty PdALx that P2-P1 exceeds each improvement value x. The column sim_se gives simulation standard errors for the estimated probabilities. ------------------------------------------------------------ y DATA> 0 DATA> end Row x PdALx sim_se 1 0 0.189 0.012 MTB > #-------------------------------------------- MTB > # Exercise 3 MTB > #-------------------------------------------- MTB > MTB > # comparison of two normal means (Behren's Fisher problem) MTB > MTB > exec 'mm_tt' OBSERVED DATA IN WORKSHEET? (TYPE 'y' OR 'n'.) n NOTE: FOR FIRST SAMPLE, INPUT MEAN, STANDARD DEVIATION, AND SAMPLE SIZE DATA> 1.013 .24 32 NOTE: FOR SECOND SAMPLE, INPUT MEAN, STANDARD DEVIATION, AND SAMPLE SIZE DATA> 1.173 .20 36 INPUT NUMBER OF SIMULATED VALUES: DATA> 1000 Simulated values of M1 and M2: Each dot represents 6 points :::. ::::.: ::::::: . ::::::::: ::::::::::: ..:::::::::::: .:::::::::::::::. . ...::::::::::::::::::::.: .. +---------+---------+---------+---------+---------+-------m1 Each dot represents 9 points . ..: :::: .::::. .:::::::. :::::::::: .:::::::::::. .. ....::::::::::::::::... . +---------+---------+---------+---------+---------+-------m2 0.80 0.90 1.00 1.10 1.20 1.30 Simulated values of M2-M1: Each dot represents 4 points : . :. .: . :::::.:: ..: ::::::::. : : ::::::::::::::::. ..:.:::::::::::::::::::: :.::::::::::::::::::::::::::: .......:::::::::::::::::::::::::::::::::.:.... .. ---+---------+---------+---------+---------+---------+---m_diff 0.000 0.070 0.140 0.210 0.280 0.350 Variable N Mean Median TrMean StDev SEMean m_diff 1000 0.16042 0.16181 0.16095 0.05601 0.00177 Variable Min Max Q1 Q3 m_diff -0.00439 0.34831 0.12309 0.19822 MTB > sort 'm_diff' 'm_diff' MTB > let k1='m_diff'(25) MTB > let k2='m_diff'(976) MTB > prin k1 k2 K1 0.0474259 K2 0.263079 MTB > MTB > #-------------------------------------------- MTB > # Exercise 4 MTB > #-------------------------------------------- MTB > MTB > # observe independent binomials with probabilities p0 and p1 MTB > # interested in posterior distribution of odds ratio MTB > MTB > exec 'pp_beta' FOR PROPORTION P1, ENTER VALUES OF BETA PARAMETERS A1 AND B1: DATA> 40 636 FOR PROPORTION P2, ENTER VALUES OF BETA PARAMETERS A2 AND B2: DATA> 23 659 HOW MANY VALUES OF (P1, P2) DO YOU WISH TO SIMULATE? DATA> 1000 TYPE 'y' TO SEE A PLOT OF THE JOINT DISTRIBUTION OF P1 AND P2: y TYPE 'y' TO SEE A PLOT OF THE DISTRIBUTION OF THE DIFFERENCE IN PROPORTIONS P2-P1: y Each dot represents 4 points : . ::.:::::.: :::::::::::. ::::::::::::: :.:::::::::::::::. ..::::::::::::::::::. . ....::::::::::::::::::::: : . ....:..:::::::::::::::::::::::::::::::.: . . .. -+---------+---------+---------+---------+---------+-----P2-P1 -0.064 -0.048 -0.032 -0.016 0.000 0.016 MTB > name c1 'odds_rat' MTB > let 'odds_rat'=('p2'/(1-'p2'))/('p1'/(1-'p1')) MTB > dotplot 'odds_rat' Each dot represents 5 points :: . .::::.. :::::::: .:::::::::: . :::::::::::.: ::::::::::::::::. .:::::::::::::::::::. . .:::::::::::::::::::::::::.:....:.. . . . . -+---------+---------+---------+---------+---------+-----odds_rat 0.25 0.50 0.75 1.00 1.25 1.50 MTB > MTB > #-------------------------------------------- MTB > # Exercise 8 MTB > #-------------------------------------------- MTB > # MTB > # model: y_i independent binomial(n_i, py) MTB > # z_i independent binomial(m_i, pz) MTB > # interested in posterior density of py - pz MTB > MTB > name c1 'bikes_y' c2 'other_y' c3 'bikes_n' c4 'other_n' MTB > read c1 c2 DATA> 16 58 DATA> 9 90 DATA> 10 48 DATA> 13 57 DATA> 19 103 DATA> 20 57 DATA> 18 86 DATA> 17 112 DATA> 35 273 DATA> 55 64 DATA> read c3 c4 10 rows read. DATA> 12 113 DATA> 1 18 DATA> 2 14 DATA> 4 44 DATA> 9 208 DATA> 7 67 DATA> 9 29 DATA> 8 154 DATA> end 8 rows read. MTB > sum c1 Sum of bikes_y = 212.00 MTB > sum c2 Sum of other_y = 948.00 MTB > sum c3 Sum of bikes_n = 52.000 MTB > sum c4 Sum of other_n = 647.00 MTB > exec 'pp_beta' FOR PROPORTION P1, ENTER VALUES OF BETA PARAMETERS A1 AND B1: DATA> 213 959 FOR PROPORTION P2, ENTER VALUES OF BETA PARAMETERS A2 AND B2: DATA> 53 648 HOW MANY VALUES OF (P1, P2) DO YOU WISH TO SIMULATE? DATA> 1000 TYPE 'y' TO SEE A PLOT OF THE JOINT DISTRIBUTION OF P1 AND P2: n TYPE 'y' TO SEE A PLOT OF THE DISTRIBUTION OF THE DIFFERENCE IN PROPORTIONS P2-P1: y Each dot represents 3 points . : . . .: :.::. :. : . : .::.:::::.:: :. : :::::::::::::: :::. .::::::::::::::::::::::. . ::::::::::::::::::::::::::.: .: :::::::::::::::::::::::::::::::. :. . . . .. :::.:::::::::::::::::::::::::::::::::.::::.:..... ---+---------+---------+---------+---------+---------+---P2-P1 -0.144 -0.128 -0.112 -0.096 -0.080 -0.064 TYPE 'y' to COMPUTE PROBABILITIES OF IMPROVEMENT FOR P2-P1: ----------------------------------------------------------- Input values of possible improvement. The output is the probabilty PdALx that P2-P1 exceeds each improvement value x. The column sim_se gives simulation standard errors for the estimated probabilities. ------------------------------------------------------------ y DATA> -.14:-.06/.01 DATA> end Row x PdALx sim_se 1 -0.14 0.993 0.003 2 -0.13 0.937 0.008 3 -0.12 0.806 0.013 4 -0.11 0.592 0.016 5 -0.10 0.349 0.015 6 -0.09 0.139 0.011 7 -0.08 0.052 0.007 8 -0.07 0.012 0.003 9 -0.06 0.000 0.000