class: title-slide, center, middle # Methods of Empirical Finance ## Seminar (UE) ### Christoph Huber ### University of Innsbruck #### Master in Banking and Finance ### Winter term 2019/20 (this version: 2019-11-19) --- class: center, middle, inverse # Hypothesis Testing ### Methods of Empirical Finance --- <footer></footer> # Hypothesis Testing Things to consider: - Null Hypothesis ( `\(H_0\)` ) vs. Alternative Hypothesis ( `\(H_1, H_A\)` ) - Exploratory vs. Directional Hypotheses - Exploratory: e.g. `\(H_1\)`: `\(\mu_x \neq \mu_y\)` - Directional: e.g. `\(H_1\)`: `\(\mu_x > \mu_y\)` - Type I and Type II errors - Statistical significance and power --- <footer></footer> # Hypothesis Testing ### Review Exploratory Hypothesis: `\(H_1\)`: `\(\mu_x \neq \mu_y\)` .smaller[ `\(\alpha = 0.05\)` ] .center[ <img 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RX9BdbjZo9nzmIwg07X6wWBqUg5MwILoIMqEJgKg073F5iDwQyCnkHKmRFYAB1U0TfpXq8RRGCzQGC+pJwZgQXQQRXdBdblds8ElsJg4zs940pPCExFypkRWAAdVJFfYFm2YOM7PUMucwQ22mDjg55DypkRWAAdVHEfAstgsPGdVgjMYAs2Pug5pJwZgQXQQRVdk+5mltOZEVgRczZHCExFypkRWAAdVIHAVAzv9By1zBLYYIMND3oWKWdGYAF0UAUCUzG80xqBjd+CDQ96FilnRmABdFBFz6RnPTlVeTHf4m8ZzvBOzzDLnGQR2CxSzozAAuigis4C6/RNZzOnMNjoTs8RCwKTkXJmBBZAB1UgMBWjO60S2HCDjQ56HilnRmABdFBFx6TnvbwdgXUCgVmTcmYEFkAHVfQVWK/vuhSYv8EGd3rWqwMRmIyUMyOwADqo4i4ElmILNl5g9d80V2BDDcbioQKBRdBBFQhMxWoENnoLxuKhAoFF0EEV/ZKeKZW5ArM32NhOz9sWITAZKWdGYAF0UMV9CCzDFmy4wGZ812yBjTQYi4cKBBZBB1UgMBXrEdjgLRiLhwoEFkEHVSAwFQhMBIuHCgQWQQdV3InAEhhsaKdnKgWByUg5MwILoIMquiXd1SgIrJK5Spk58lCDsXioQGARdFAFAlOBwESweKhAYBF0UMUdCczcYCM7Pft1gQhMRcqZEVgAHVTRK+m+QpmYGYFdYbZQEJiKlDMjsAA6qKKjwLrc7gEEVscAgY0zGIuHCgQWQQdV3JPAvA02sNPzfTJ3ZARWS8qZEVgAHVTRKenOOpmaGYGFzNcJAlORcmYEFkAHVfQTWI+bfQaBVTFEYMMMxuKhAoFF0EEVCEzFqgQ2cgvG4qECgUXQQRUITMW4Ti+QCQJTkXJmBBZAB1Xcj8DcDYbARLB4qEBgEXRQRZ+ke7sEgdUwQmADDcbioQKBRdBBFXYCm3kx32U/VEFGgS2IFIHVkXJmBBZAB1UgMBXDOr3gFYEITEbKmRFYAB1U0SXpJe8CQ2CtWaASBCYj5cwILIAOquglsL7fOz2zt8HWJ7BBBmPxUIHAIuigCgSmYlSnl5hkSaIIrIqUMyOwADqookfSi64jhcAas0QkCExGypkRWAAdVNFJYJ2/GYGVM1BgYwzG4qECgUXQQRV3JjBjg61NYMO2YCweKhBYBB1UcU8C896CDer0Io0gMBkpZ0ZgAXRQBQJTgcBEsHioQGARdFBFh6SXaWShwHwNtjqBjTIYi4cKBBZBB1XclcCst2AITASLhwoEFkEHVdgJrAgEVswyiywaGYFVkHJmBBZAB1W0T1pxHg+BFYPAcpByZgQWQAdVdBFY41u8JJzZ2GBjOr1QIghMRcqZEVgAHVSBwFQgMBEsHioQWAQdVNE8ackrARFYKSMFNshgLB4qEFgEHVTRQ2Btb3AKBFYKAktCypkRWAAdVHF/AnM12JBOL70gIQJTkXJmBBZAB1XcmcCMt2CjBLbo+xGYipQzI7AAOqgCgalYp8AGGIzFQwUCi6CDKlonrRHIVYGZGmxEpxcbZOHICKyYlDMjsAA6qOLeBOa7BRsksGU3gMBUpJwZgQXQQRUITMVKBaY3GIuHCgQWQQdV2Als0cV8WwzQi4wCWxwmAisl5cwILIAOqmic9PKnoBBYOxbrA4HJSDkzAguggyraC0xxC9dmdjUYAhPB4qECgUXQQRUITAUCE8HioQKBRdBBFW2TbvAidgTWjvECG2EwFg8VCCyCDqpoLjDJTSCwEpa/BhCByUg5MwILoIMq7lJglgYbIrCFt4DAZKScGYEF0EEV9ycw1y0YAhPB4qECgUXQQRUITIW80w3eRdxEYGqDsXioQGARdFBF06RbqKOJwBwNNkJgS2+iQZIIrIyUMyOwADqo4g4FZroFQ2AiWDxUILAIOqgCgalYr8DEBmPxUIHAIuigCjuBFYHACmhhjgYjI7AiUs6MwALooAoEpkLd6SbiQGAqUs6MwALooIp7FJinwRCYCBYPFQgsgg6qaJm0zhsI7DYILBUpZ0ZgAXRQBQJTsVaByQ3G4qECgUXQQRUITIW4021e/YfAVKScGYEF0EEV9yowP4PpBdbgVhCYipQzI7AAOqiiYdJCbdyaGYEhsGSknBmBBdBBFW0F1uqmboHAbtHo/cONBCY1GIuHCgQWQQdV3K3A7AwmF1iLm2kyMgIrIOXMCCyADqpol7RSGjdnRmAILBcpZ0ZgAXRQRVOBNbql2yCwW5gJTGkwFg8VCCyCDqqwE1iDi/m2G6YlGQXWKEYEdpuUMyOwADqoAoGpkHa6kTIQmIyUMyOwADqo4k4FZmgwBCaCxUMFAouggyqaJd3KGAisBQgsGylnRmABdFAFAlOxYoFpDcbioQKBRdBBFQhMBQITweKhAoFF0EEVCEyFstOtXriOwGSknBmBBdBBFa2SbvY2ZgTWgFbCQGAyUs6MwALooIqGAmtyO60E5mewlQtMZzAWDxUILIIOqkBgKoSdbuaLZiEisFuknBmBBdBBFY2SbnchRAS2nGa6QGAyUs6MwALooIp2AmtxM6W3hMCuYikwmcFYPFQgsAg6qMJOYEUgsKu0s0WzkRHYDVLOjMAC6KCKexaYl8EQmAgWDxUILIIOqrhbgdltwXSdbigLBKYi5cwILIAOqkBgKhCYCBYPFQgsgg6qaJO0WhaFArMy2LoFJjQYi4cKBBZBB1Xcr8DctmAIrNltXYfFQwUCi6CDKhCYClmnW75kHYGpSDkzAguggyoQmAqlwJrdFgJTkXJmBBZAB1U0SVr+dBMCuwICS3kgjh5gBggsgg6qaCWw5TdSQ9nMXgZTdbrpRS+aCkxkMBYPFQgsgg6qQGAqhAJrd2MNR0ZgV0k5MwILoIMqWiStf8E6AotBYCweIhBYBB1U0UhgDSapuTEEFtNSFC0TlJ1DZPFQgcAi6KCKOxeYkcHWLjDZFozFQwUCi6CDKu5ZYF5bMASGwK6QcmYEFkAHVSAwFaJON9UEApORcmYEFkAHVdy7wHwMhsAQ2BVSzozAAuigigZJt7VES4FZbcFWLzCVwVg8VCCwCDqoAoGpQGAI7AopZ0ZgAXRQBQJTgcAQ2BVSzozAAuigCgSmAoEhsCuknBmBBdBBFcuTbvxKCQS2iLaSQGAyUs6MwALooIomAmsySc3NFc9sZDAEhsCukHJmBBZAB1UgMBUIDIFdIeXMCCyADqpYnPSQ91ohsIjGkmg7ssZgLB4qEFgEHVTRQmBtJqkBgUUgMBYPGQgsgg6quH+BuRhM0unWl3xHYCpSzozAAuigijsXmNEWTCWwpreHwFSknBmBBdBBFQhMBQIT/UkwFg8VCCyCDqpYgcBMDKbodHNDNB4ZgYWknBmBBdBBFUuTHuOHipnXJrC2N4jAVKSc2VNg3/mth4fPf/Xy458+fOnWlyCwbCAwFQhMdA6RxUOFp8A+etjzxfOP//zLLwKLvgSBpQOBqUBgW80WjMVDhaXAPn747Fe373/v4XW7deDnX3n5UPQlk6PMgg6qQGAqENgWgcWknNlQYM/7rI8fPvf7xx//yQcPz8KKvmR6lFnQQRUITAUC2yKwmJQzGwrs0ycrPVrqa68fff+7Dw9f+MqTwKa/JBplFnRQxd0LzMZggk631wMCU5FyZkOBffz8zNZHxycIf/LBZ//6+68/fWT6S6JRZkEHVSxMur0d2l7Mt/QGBWQUWPPsEFhEypkNBfbRq52OXqPxk7/2ze2LwKa/JBplFnRQBQJTgcB2CAzG4qHCUGAvlnrcZ/36H0x+avJLfuWFt7AiHlc491tsP6Itj3Zoe4Pts2s+IuQHgcEgcghsJQZ7g8AgIwgMBpFAYOvZgrWXAwIDAQYCe4bnwJKxLOkOVxps/hyYy5Ng/Tvd/vmlLs+B9X4SjMVDRaukEZgHKWdeKrBmk9TcZK3AHAzWvdMd3NAhOQQ2TcqZ/QT2+tL4i5cYHr0KMfoSBJaOFQjMZAumEFjrm0RgMlLObCiw+E1evA/sFilnXpJ0j70NAptLGoF1NhiLhwpHgcWX2XgRGFfiCEg580KBtZuk5jYR2AQ5BNZ/C8biocJRYPGFDl8ExrUQA1LOjMBEILADCGySlDMbCuxRSw/Tl5o/fvFG8CUILB0ITAUCO4DAJkk5s6PA3h//sa9Hab280PBVYO/5e2CTpJzZTWBFVM5sYbDene4ihg4jI7BJUs7sKLCTP7c8LTD+IvM0KWdGYCIQ2AEENknKmT0FtgQElowlSY/zAgK7JIvAuhuMxUMFAouggyoQmAoE9gQCmyLlzAgsgA6qQGAqENgTCGyKlDMjsAA6qAKBqejc6T5vEEZgKlLOjMAC6KAKBKaiv8A63CoCU5FyZgQWQAdVLEh64EVya2d2MBgCe6L3xaRYPFQgsAg6qGKZwFpOUgMCO6eTFbqMjMAmSDkzAguggyoQmIruAutxswhMRcqZEVgAHVQxP+mRf2YLgZ2TTGA9DcbioQKBRdBBFYsE1nSSGhDYOZkE1nkLxuKhAoFF0EEVdgLrcDFfjz/KnFFgnWJDYJeknBmBBdBBFesQmMMWDIG9gMAuSTkzAguggyoQmIqune6kBAQmI+XMCCyADqpYj8BGGwyBvYDALkk5MwILoIMqZifdywh9BGawBUNgr3Q1GIuHCgQWQQdVIDAVCOwVBHZBypkRWAAdVIHAVPTsdK93ViEwGSlnRmABdFAFAlPRWWBdbheByUg5MwILoIMq5ibd7VURnQQ23mAI7JWu1+Jg8VCBwCLooIoFAms8Sc0NI7ATuvmgW2gI7JyUMyOwADqoAoGp6CuwPjeMwGSknBmBBdBBFTOT7ve+KgRWT0qBdTMYi4cKBBZBB1XMF1jrSWpAYCf0s0HCkVk8ZCCwCDqoYk0CG2swBHYMAjsj5cwILIAOqliNwEaPjMBOQGBnpJwZgQXQQRUITEW/TveUQa8bRmBnpJwZgQXQQRWrEtjYmRHYEQjsjJQzI7AAOqhiXtLDdzNzvgmB1ZPvvdcsHjoQWAQdVIHAVCCwExDYKSlnRmABdFAFAlOBwE5AYKeknBmBBdBBFQhMBQI7AYGdknJmBBZAB1UgMBUI7AQEdkrKmRFYAB1UMSvp0S/om5n02Km7dbrrdQW73TICOyXlzAgsgA6qmCuw9pPUgMCOQGCnsHioQGARdFCFncB6Xcy39Ka7kVFgPRPrNjaLhwoEFkEHVcxJuusZRARWCwI7hcVDBQKLoIMqZgqswyQ1N47AjkBgp7B4qEBgEXRQxcoENtBgvTrd809rITAZKWdGYAF0UMWaBDZ2C9ZRYF1udwcCk5FyZgQWQAdVIDAVCOyUbjtHFg8VCCyCDqpYm8DGGaxTp3ueQez7m0Zgx6ScGYEF0EEVM5Lua4GeAhu6BesnsB43ewCByUg5MwILoIMqEJgKBHZGr70ji4cKBBZBB1UgMBUI7BwEdkTKmRFYAB1UgcBUILBzENgRKWdGYAF0UAUCU4HAzkFgR6ScGYEF0EEV9UkPvxT9dkHSA2fv0+mu/upcaQR2RMqZEVgAHVQxS2BdJqkBgT2DwC5g8VCBwCLooAoEpgKBXdBneBYPFQgsgg6qqE7a4QwiAnsBgV3A4qECgUXQQRVzBNZnkhoQ2DMI7AIWDxUILIIOqlifwEaN36XTXS8ktUVgOlLOjMAC6KCKlQls4Pi9BNb+Ro9AYCpSzozAAuigCgSmAoFd0Gf/yOKhAoFF0EEVKxTYoPl7dLr3GcTelUZgL6ScGYEF0EEVtUlb+GtJ0vcmsOa3eQICU5FyZgQWQAdVIDAVCOySLjtIFg8VCCyCDqpAYCoQ2AQI7JmUMyOwADqowk5gXS/mW3r7PcgosO5hIbBnUs6MwALooAoEpgKBTYDAnkk5MwILoIMqViewYQbr0OnuZxARmIyUMyOwADqoAoGpQGATILBnUs6MwALooIrKpPuv/gisnPwC63EXWDxUILAIOqgCgalAYFMgsCdSzozAAuigCgSmAoFNgcCeSDkzAguggypWKbAhh0f7Tne/kBQC05FyZgQWQAdVrE9go7ZgXQTW+BbPQWAyUs6MwALooIq6pAW7FwRWzJ0IrPWdYPFQgcAi6KCKaoF1m6TmRywV2Ijjo3mn+59BVPy+EdiBlDMjsAA6qGKFAhu0BeshsLY3eAkCk5FyZgQWQAdVVCU97o9pnYHAthKBCSrdfh/J4qECgUXQQRW1Aus3SQ0IbHsvAmt/N1g8VCCwCDqoAoGpQGDTILA9KWdGYAF0UAUCU4HApkFge1LOjMAC6KCKNQpszP1o3WmFvxCYjJQzI7AAOqgCgalAYNMgsD0pZ0ZgAXRQRU3SNv5CYNv7EVjzO8LioQKBRdBBFQhMBQILQGA7Us6MwALooAoEpgKBBSCwHSlnRmABdFAFAlPRuNOCC0ltEZiOlDMjsAA6qAKBqWgvsJY3F4DAVKScGYEF0EEVFUnbXEhqedIj7gkCC2i9l2TxUIHAIuigijqB9Zyk5qcgMM0ZRE1OCGx794vHVRCYBylnRmAimgus4a1FIDAZKWdGYIn1rlYAACAASURBVAF0UEV50qIziAisiDsTWMs7w+KhAoFF0EEVVQLrOknNj0Fg9ySwxneGxUMFAouggypWKzD5IYLAQhDYvS8e10FgHqSceZUCG7EFQ2AhCOzeF4/rIDAPUs6MwEQ07bTGXwhMR8qZEVgAHVSxXoGpjxEEFoLA7n3xuA4C8yDlzKVJq1Z8jcAGbMEQWEzTu8PioQKBRdBBFQhMBQKLQWD3vXjcAIF5kHJmBCYCgcUgsPtePG6AwDxIOTMCE4HAYhDYfS8eN0BgHqSc2U1gRSAwjcBUlUZg97143ACBeZByZgQmAoHFILD7XjxugMA8SDlzYdJGf0tl2yRp+f1p2WmVvxCYjJQzI7AAOqiiQmCdJ6kBgd2XwJreIRYPFQgsgg6qQGAqENgVEFjKmRFYAB1UUZi01xlEBIbAYlg8VCCwCDqoolxgvSepAYEhsBAWDxUILIIOqlizwLR3qWGnG/8FyCsgMBUpZ0ZgAXRQxWoFJr9LbQXW6qZuIBRYs7vE4qECgUXQQRUITAUCuwYCGz3ADBBYBB1UsWqBSe9Tu07rziAiMBkpZ0ZgAXRQRVnSZv5qk3RmgTW6pZsgMBUpZ0ZgAXRQhZ3ARBfzLf1J7cgoMF1EDXeVLB4qEFgEHVSBwFQgsKsgsHwgsAg6qAKBqUBgV0Fg+UBgEXRQBQJTgcCugsDygcAi6KCKoqSVL9jTCUxssGadFr6GA4HJSDkzAguggypKBdZ/kpqfhcA0IDAZKWdGYAF0UAUCU4HArtPsbrF4qEBgEXRQRUnS0rf8IrBbILDrsHioQGARdFBFocAEk9T8MASmAYHJSDkzAguggypWLjDhHWvVaeGFpBCYjpQzI7AAOqhizQLT3rGGAmtyOyUgMBkpZ0ZgAXRQBQJTgcCu02xnyeKhAoFF0EEVdgIrop3AdPesUaeVZxC1lUZg2UBgEXRQRUHSfv5qlnROgbW4mUIQmIqUMyOwADqoAoGpQGA3aLW3ZPFQgcAi6KAKBKYCgd0CgSUDgUXQQRUITAUCuwUCSwYCi6CDKhCYCgR2CwSWDAQWQQdVrFtgyvvWptNafyEwGSlnRmABdFAFAmt1U7dAYLdAYMlAYBF0UMXtpA39hcBUaCvd5s6xeKhAYBF0UAUCa3VTt0BgN0FguUBgEXRQBQJrdVO3QGA3QWC5QGARdFAFAlPduyad1l5ICoHpSDkzAguggyrsBKa8mG/pj2tCK4Etv5FyxL97BJYLBBZBB1XcTFr7R7MQ2HXuXmAN7h6LhwoEFkEHVZQITDNJzc9rKjDR/WvRafUZRPUvH4GlAoFF0EEVaxeY7v41EliDScpBYDJSzozAAuigiltJq88gIrBrrEBgy+8gi4cKBBZBB1UUCEw0Sc0PRGAa5L99BJYJBBZBB1UgMAQWg8BkpJwZgQXQQRUIDIHFIDAZKWdGYAF0UMXqBSa7hw06rfYXAtORcmYEFkAHVSAwBBaDwGSknBmBBdBBFTeS1l9HCoHF3L/AWtxFFg8VCCyCDqpAYAgsBoHJSDkzAguggyrsBFYEAhMhrzQCSwQCi6CDKhBYHoGpLyS1RWA6Us6MwALooAoElkpgTSapAIGpSDkzAguggyquJy2/kFQhTZMW3UcEVkKDXSaLhwoEFkEHVdwUmGySGlYpsAFnEAdUGoHlAYFF0EEVCCyTwNpMUgECU5FyZgQWQAdVXE3a9QwiAlMxRGAL7yaLhwoEFkEHVdwSmG6SGhCYiAGVRmBpQGARdFAFAlPtMxFYGQgsDQgsgg6qQGCqu4nAykBgaUBgEXRQBQLLIrAR/kJgMlLOjMAC6KAKBKY6h4jAykBgabhLgb2Fe+FxXV/HDx1yR2t5XNjlP3NIMCPuKIzESmBNbuYtD6JEXEt6yAZMfjX60p+5lKWdHrEDG9KApXeUxUNFq6QRmAcpZ0ZgCCwEgclIOTMCC6CDKhBY6c9cCgIrBIFlAYFF0EEVCKz0Zy5lYadHXAkRgelIOTMCC6CDKq4kPeZCUiMEJlmolwus1STljBLYorvK4qECgUXQQRXXBaacpOanIjANYyqAwJKAwCLooAoEVvxDF7Ks00POICIwHSlnRmABdFAFAiv+oQtZLLBmk5QzTGBL7iyLhwoEFkEHVcRJD/pbKghskjUJbOGdZfFQgcAi6KCKqwKTTlLzYzsIrPudRWDFILAcILAIOqgCgZX/1GUgsGIQWA4QWAQdVGEnsCIQmIgxlUZgOUBgEXRQBQLb4y6wQf5CYDJSzozAAuigCgS2R/AkGAIrZ9HdZfFQgcAi6KCKMGlnf3VIGoFNgsBUpJwZgQXQQRUI7AACmwSBqUg5MwILoIMqENgBBDYJAlORcmYEFkAHVSCwAwhsEgSmIuXMCCyADqpAYAcQ2CQITEXKmRFYAB1UESU96EJShXRIuvv9XdLpUf5CYDJSzozAAuigiisCE09SAwITMarSS+4wi4cKBBZBB1UgsCcQ2BQITEXKmRFYAB1UESTtfQYRgalAYCpSzozAAuigilhg6klqfjIC0zCsBggsAwgsgg6qQGCvP7fvXV7Q6TF/jnmLwISknBmBBdBBFQis6gcvYJnAWk5SzkiBzb7LLB4qEFgEHVSBwKp+8AIQWA0ILAEILIIOqkBgRz+4632e3+lhZxARmI6UMyOwADqoYjrpga9BHCaw3nd6kcCaTlLOUIHNvdMsHioQWAQdVIHA6n7yfBBYFQjMHwQWQQdVILC6nzwfBFYFAvMHgUXQQRUIrO4nzweBVYHA/EFgEXRQBQKr+8nzQWBVIDB/EFgEHVSBwCp/9Gxmd3qcvxCYjpQzI7AAOqgCgVX+6NkgsDpm320WDxUILIIOqphM2vtKvlsEJmNgpRGYPQgsgg6qQGCvILALEJiKlDMjsAA6qAKBvYLALkBgKlLOjMAC6KAKBPZK34tJze30uAtJbRGYjpQzI7AAOqgCgR3hKrDGk1QwVmDz7jiLhwoEFkEHVUwlbf7nmLcITMbISiMwdxBYBB1UEQhswCQ19BNYv3s+s9NDzyAiMBkpZ0ZgAXRQBQI7xlNgrSepYLDAZt11Fg8VCCyCDqqYSNr/DCICUzG00gjMHAQWQQdVTAtsxCQ1IDARCExFypkRWAAdVIHAjkFgZyAwFSlnRmABdFAFAjsGgZ2BwFSknBmBBdBBFXYCG3gx39KfPo95nR7rr7FVQGDmILAIOqgCgdX/9HkgsGrm3XkWDxUILIIOqrhMevCihcBOQGDVsHioQGARdFAFAqv/6fNAYNUgMG8QWAQdVIHA6n/6PBBYNQjMGwQWQQdVILD6nz6PWZ0eeyGp0V1AYN4gsAg6qOIi6dHX4RgrsI5L9lyBtZ+knPECm3H3WTxUILAIOqhiSmBjJqn5+QhMw+gyIDBrEFgEHVSBwGb8+FnM6fTgM4jDy4DArEFgEXRQxXnSo88gIrBjBvvLQWD1AbB4qEBgEXRQxYTABk1SMwAC0zC8DQjMGQQWQQdVILCLH98pAAQ2AwTmDAKLoIMq7ARWRMekEdgxoyuNwJxBYBF0UAUCO8NJYMP9NbzSCMwZBBZBB1UgsDO6nUNEYDNAYM4gsAg6qOIs6Rz+6po0AjtieKVnRMDioQKBRdBBFQjsHAR2xPBKIzBjEFgEHVSBwM5BYEcMrzQCMwaBRdBBFQjsHB+Bjb4Ox9ag0gjMGAQWQQdVILBzrATWZZIKhlcagRmDwCLooIrTpIdfSKqQrkl3ygCBzWHGLpTFQwUCi6CDKi4ENmySGlYhMIMziAaVRmC+ILAIOqgCgV1gJLAec1QxvtIIzBcEFkEHVZwkneUMIgJTMb7S9ftQFg8VCCyCDqo4F9i4SWpmQGAaHAqBwGxBYBF0UAUCm5qgRwwIbB4IzBYEFkEHVSCwmSNUg8DmgcBsQWARdFAFAps5QjW1nTbwl0UhEJgtCCyCDqpAYJMjdMgBgc0DgdmCwCLooIrjpB2WKweB9QkCgc2kNggWDxUILIIOqkBgc2eoBYHNBIG5gsAi6KAKBDZ3hloQ2EwQmCsILIIOqkBgc2eoBYHNBIG5gsAi6KAKBDZ3hloQ2EwQmCsILIIOqjhK2uNCUg4C67JwV3bawV8ITEfKmRFYAB1UcSqwkZM8gcAOILBnEJgrCCyCDqqwE1gRCEyERaUro2DxUIHAIuigitekPc4gloHARFhUGoGZgsAi6KCKE4ENnaQGBCbCotIIzBQEFkEHVSCwKXrsRus67fDnmLcmlUZgpiCwCDqoAoFN4iCw1gPMwaLSCMwUBBZBB1UgsEkQ2AGLSlfuRlk8VCCwCDqoAoFN0uEcYlWnTc4gmlQagXmCwCLooIqXpDP5S5D0eIE1/vHz8Kg0AvMEgUXQQRUIbBoEtsej0nX7URYPFQgsgg6qQGDTILA9JpVGYJYgsAg6qAKBTYPA9phUGoFZgsAi6KCK56QzXYfj/gXm4i+XSiMwSxBYBB1UcSSwwZM8YXEx39I5asgoMJdWIDBLEFgEHVSBwJbMUQMCW0BNICweKhBYBB1U8ZS0zxlEBLZFYBcgMEcQWAQdVPEqsNGTPIHAtgjsAgTmCAKLoIMqEFg8R9tIKjrtch0On1ogMEcQWAQdVIHAIsYKrOmPno1NLRCYIwgsgg6qQGARCMyoFjV7UhYPFQgsgg6qQGARrc8hlnfa5gyiUS0QmCEILIIOqjgk7bNQ+QisdShVAmv5gxfg0wsEZggCi6CDKhBYCAIz6kXFrpTFQwUCi6CDKhBYCAJz6gUC8wOBRdBBFQgsBIE59QKB+YHAIuigCjuBFYHARPhUGoH5gcAi6KAKBBbTNpXiThv5y6jSCMwPBBZBB1Xsk87mLwSmwqfSCMwPBBZBB1UgsBgE5lTp4lhYPFQgsAg6qAKBxSAwp0ojMDsQWAQdVIHAYsYIzOc6HFurSiMwOxBYBB1UgcBihgms4U9diFGlEZgdCCyCDqrYJe3z1yxLESXdNBcEtozinSmLhwoEFkEHVTwJbPQYldyxwKzOIFpVGoG5gcAi6KAKBHaFQQJr9zMX41RpBOYGAouggyoek853BhGBqXCqdOnelMVDBQKLoIMqDgIbPUUtCEyEVaURmBkILIIOqrATmM/FfBv/TcuMAvOqBgIzA4FF0EEVCOwaCMypGgjMDAQWQQdVILBr6AVm5S8EpiPlzAgsgA6qQGDXaHkOEYEtBYGZgcAi6KAKN395CazlCo7AFlMWDouHCgQWQQdVILCrILDRIxyDwLxAYBF0UAUCu4paYF7X4UBgOlLOjMAC6KAKBHaVAQJr9fNaYNYNBOYFAouggyrsrsOBwIww60bZ/pTFQwUCi6CDKtw2YGYCa7iEl3Ta7Ayim8DK/M7ioQKBRdBBFQjsOnKBNfppbXArBwKzAoFF0EEVbmcQEZgTbuUo2qGyeKhAYBF0UIXbElUGAhPhVmkE5gQCi6CDKhDYddrtUBFYAxCYEwgsgg6qQGA3QGBOIDAnEFgEHVSBwG6gFJidv+wqjcCcQGARdFDE4/KccGqxwNocTQisAQjMCQQWQQdFILCbIDAnCiJi8VCBwCLooAgEdhME5gQCMwKBRdBBEQjsJgjMCQRmBAKLoIMiENhNEJgTCMwIBBZBBzVsENhNdALz85dfpRGYEQgsgg5q2Pkr39TipBsZDIG1AIEZgcAi6KAGBFYAAnPidkgsHioQWAQdlLAxFJjZxXy3qxaY4dvcEZgPCCyCDkrY+8ts6vUKzO2PgW0RmJCUMyOwADooAYGV0OhaHCUCa/BjmoLAZKScGYEF0EEJCKwIBGYEAvMBgUXQQQkIrAiNwAzPIJoK7EZMdpUuIuXMCCyADirYLU92SXsKrMEBVSCw5T+kMYYCu52TXaWLSDkzAguggwoQWCEIzAgEZgMCi6CDChBYIQjMiJvnEO0qXUTKmRFYAB1UgMAKQWBOIDAXEFgEHRSwQWCFIDAnEJgLCCyCDgrYr052STsKrMlCfiNpR38hMB0pZ0ZgAXRQAAIrBoEZgcBcQGARdLA/G0+BFYHARFiW40ZUVFoFAougg/05LMokXQICcwKBmWAqsO/81sPD57965YPvv/5w4Nf/4PYos6CD/UFg5fQXmON1OLamlUZgJngK7KODnL4Yf/DnX0ZgU+SaGYGV0+JaHDcFtvQH9MCyHAjMBEuBffzw2a9u3//ew8OXwg/+5INLc4WjzIIO9geBVYDAjLixW6XSKhwF9ri72kvq44fP/X70wU/PtmdXR5kFHewPAqugt8BMzyCaVhqBeeAosE+fxPXorK9FH/z4ZHd2Y5RZ0MHuPC3JJF1Eg3OItwS28Ob74FkOBOaBo8A+ft5dfXRkqbMPfvTZ3y4fZRZ0sDsIrAoEZsT1/SqVVuEosI9eXfXF4IM///Ln/rN//+Hhs//BxBNhCCwLCKwKBOYEArPAUGDvv/688fr49TWGZx/8yQdPL0L8wuuzZL/ywltIweGPWUIhneN6XJF73vy9QVx3hVhgnz7uvv7T7fY7Hxy9jB6BZQOBVdE3LhbkOsjrrhAL7PkFio87sZfXeSCwbCCwOrrmxYJcB3ndFWKBvfDR5cvpeQ4sCc/P6dglbXkx322DJ8GuJe36FJjlxXx3XAvMrtJFpJw553NgL3x8eSkOBJYEBFYJAnMCgTlgKLDXV8+fvgpx4oMI7JxMMyOwSnoKzPVtzAhMR8qZDQVW8j6w1w8jsGMyzYzAKln8VubrAlt0091AYDJSzmwosNtX4ng5ofh6ZvHaKLOgg53ZILBaEJgRCMwBR4EVXAvx+VOfPlxekQOB5eBlZbJLeoUCsz2DaC2wMDK7SheRcmZDgT3q6WHqavRHH/zJBw9f+Ob2/d/7YOKavggsBwismqXnEK8KbMkNd8RWYNcys6t0ESlndhTY++M//fX+64enuU4+uP306VIcX7y8lhQCS8EGgdWDwIxAYAZYCuzkjy8/C+zszzT/9G99MPFHm6dHmQUd7MvrwmSXNAIzwlpgUWh2lS4i5cyeAlsCAksBApsBAnMCgY0HgUXQwb4gsBn0EpivvxCYjpQzI7AAOtgXBDaHZcs5AmsKAhsPAougg105WpdIupz1Ccy40ghsPAgsgg52BYHNAoE5EcZGpVUgsAg62BUENos+AvN9G/PWutIIbDgILIIOdgWBzaKbwBbcameMy4HAhoPAIuhgTzYIbBYIzAkENhwEFkEHe3K8EJN0BYsMFiRtfQbRudJhcFRaBQKLoIM9QWAz6SSw+bfZHedyILDRILAIOtiRDQKbCQJzAoGNBoFF0MGOnCzDJF0BAnMiOodIpVUgsAg62BEENpdFf1EFgbUGgQ0GgUXQwY4gsNm0F5i3v7wrjcAGg8Ai6GBHENhsEJgTCGwwCCyCDvbjdBG2S9r4Yr7LziFmFJjxxXy3CGw4CCyCDvYDgS0AgTkxHZ5dpYtIOTMCC6CD/UBgC0BgTiCwsSCwCDrYDwS2AATmBAIbCwKLoIPd2CCwBbQWmLe/EJiOlDMjsAA62I2zNckuaW+BLVjSEVhzENhYEFgEHewGAlsEAnNiMj67SheRcmYEFkAHe3H+QnC7pBGYEQhMRsqZEVgAHezF+ZJkl/SqBOb9t1QQmJCUMyOwADrYCwS2jPlvZQ4EtnCeviAwGSlnRmABdLAXCGwhCMyIyR2sXaWLSDkzAgugg71AYAtpKTD3M4j2Apt8BGBX6SJSzozAAuhgJy5WJJKuZPY5xGmBLZ6nL+7lQGAjQWARdLATCGwxCMyIqT0slVaBwCLoYCcQ2GIQmBMIbCAILIIO9uHy/BdJ14LAnEBgA0FgEXSwD5eLL0lXM9Ngl0n7+8u/0ghsIAgsgg72AYE1AIEZgcAGgsAi6GAXJl5BR9LVIDAnLkOk0ioQWAQd7MLE0kvS1SAwJxDYOBBYBB3sAgJrwcx3gl0kbf825m2CSiOwgSCwCDrYBQTWhHYCazJOT/zLgcDGgcAi6GAXEFgTEJgRl/tYKq0CgUXQwR5MLbwkXc+8c4jnSWc4g2hf6e3E4wAqrQKBRdDBHqQQmPvFfHe0ElijcfphfzHfLQIbCAKLoIM9QGCNQGBGXOxk7SpdRMqZEVgAHewBAmsEAnMCgY0CgUXQwR4gsEa0EFgGfyEwHSlnRmABdLAHCKwVcxZ2BNYJBDYKBBZBBzswuRrZJY3AjEghsPMo7SpdRMqZEVgAHewAAmsGAnMCgQ0CgUXQwQ4gsGbMeSfYadIp3gWGwHSknBmBBdDB9kwvunZJpxDYnJX9QmANx+kFApORcmYEFkAH2zO9GNkljcCMSCOw4zDtKl1EypkRWAAdbA8Ca8iMc4gnSec4g5hEYFsENgYEFkEHmxMsuXZJ5xDYjKX9XGBNx+kEApORcmYEFkAHmxOsRSQ9j3UIzCDoEk73s1RaBQKLoIPNQWBNQWBOILAhILAIOtgcBNaUZQLL4i+DoItAYENAYBF0sDkIrC3VBkNg/UBgQ0BgEXSwNdF6S9IzQWBOHAdKpVUgsAg62BoE1hgE5gQCGwECi6CDrUFgjVkisCTvAttaBF0EAhsBAougg40J33hL0jNZKLDW43TCIOgiENgIEFgEHWxMuNyS9FxqDYbAOnK8p6XSKhBYBB1sDAJrznyB5TmDaBF0EQhsAAgsgg62Jb50H0nPZZHA2o/TB4egi0BgA0BgEXSwLfFiS9JzQWBOHO1qqbQKBBZBB9uSSGBJLuZbf0H6jAJLcjHfHQhMDwKLoINtQWAdmCuwPP5CYDpSzozAAuhgWxBYBxCYEwhMDwKLoINNubIO2SWdSmA1xxkC68tLrHaVLiLlzAgsgA42BYF1AYE5gcDkILAIOtgUBNaFeQJL9C4wBKYj5cwILIAOtuTauS67pNcgsD7jdCCZwA7B2lW6iJQzI7AAOtiSa8uQXdKJBFa3viOwziAwNQgsgg62BIF1Yo7AMp1BRGA6Us6MwALoYEOuvlrOLukVCKzXOO3JJrB9tHaVLiLlzAgsgA425OoqZJd0MoGVH2kIrDcITAwCi6CDDUFg3UBgTiAwMQgsgg42JJfAinCZuV5gqfzlE3QRCEwMAougg+24vsiS9BJqziEisN4gMDEILIIOtgOBdQSBOXEIl0qrQGARdLAdCKwjCMwJBKYFgUXQwXYgsI4gMCcQmBYEFkEHm3HjaRqSXka5wfZJJ/OXUdAlIDAtCCyCDjbjxgpL0stAYEYgMC0ILIIONgOBdQWBObGPl0qrQGARdLAVt17oTdLLKH8h/S7pVBdC3OETdBEITAoCi6CDrbi1vpL0QmoF1nea1hgFXQICk4LAIuhgKxBYZxCYEfsdLpVWgcAi6GArEFhnis8hPiad7gyiU9BFIDAlCCyCDjbi5upql3Sqi/nuqBNY52Eak+tivlsEpgWBRdDBRiCw7iAwI3Z7XLtKF5FyZgQWQAcbgcC6g8CcQGBCEFgEHWwEAutP4Sqf0F8ITEfKmRFYAB1sBALrDwIzAoEJQWARdLANtxcgu6QRmBH5BHYw2OghZpByZgQWYLesFuE3MwITUPhC+oQvokdgOlLOjMAC7JbVIvxmRmAKygXWfZTGIDAZKWdGYAF2y2oRdjMX7A3skkZgRuQU2BuvepSRcmYEFmC3rBZhN3PB+mOXdE6BFcyc8AxiRoFtEZgMBBZht6wWYTczAtNQKrD+kzQGgclIOTMCC7BbVotwm7lkZ2CXNAIzIqnA8gVtV+kiEFiE3bJahNvMJcsPSTfgbgXmFnQRKYNOmTQCi2BZbQECU1GQdM4zWwlHRmAyEFgEy2oLEJgKBGZEznOIGZNGYBEsqw0oezaJpBuAwIzI+H6FpEkjsACW1QYgMBm3o0769qSEIyMwGQgsgmW1AQhMRpHAMiadcOSU1+xKmjQCC2BZXU7Z22tJugk3s0ZgMjJeNTlr0ghsGpbV5RRe4IikW3Ar7DcITAYCU4HAIlhWF1N6jXSSbkGBwFImnXDkg8DSGSxn0ghsmpQHu1cHi/9KldXUhdjNfOvhAgLT8TblFixp0k1uB4F5YDUzApOCwGxAYCoQWETKg92rgwhMyvW4dwtqyqQTjozAZCCwiJQHu1UHSy/Dapd0xov5bm+dQ8wqsIwX890Hnc9g+cqBwGIyHuxeHURgYhCYCwhMBQKLyHiwe3UQgYm5NvcbBCYEgalAYBEZD3arDha+iN4w6cQCCwffL6d2SReQWWDJDJavHAgsJuPBbtXB4pXHLumsArsy+BsEpmQfNAITgMAiMh7sVh1EYHKuCmxrmHQBCExGvnIgsJiMB7tTB4vPIPolnVlgweQITMqzwHIZLF85EFhMxoPdqYPlC49d0mkFFk+OwKQcgkZg/UFgERkPdqcOIrABRJM/LaV2SReAwGTkKwcCi8l4sBt1sPwMol/SqQU2OToC0/IisFQGy1cOBBaT8WA36mDFumOXdF6BRaMjMC1PQSOw7iCwiIwHu1EHEdgQEJgFCEwFAovIeLD7dLDiDCJJN+T+BGYa9HUQmAoEFpHyYLfpYM3jZpJuyGTwzwtpyqQTjozAZCCwiJQHu00HEdggEJgDz0HnMljmpJeCwDwwmbnmDCJJtwSBOYDAVCCwiJQHu0sHq555J+mGTD10eIPAxCAwFQgsIuXB7tJBBDaMaYEd/pEy6YQjHwsskcEyJ70UBOaBx8xVZxBJuimX2b9BYGpegkZgnUFgESkPdpMO1r13h6SbMiWwp3+lTDrhyCcCy2Ow1EkvBIF54DEzAhsIAhvPa9AIrC8ILCLlwe7RwboziCTdlvP03yAwOQhMBQKLSHmwe3Sw8uo/JN2WS4E9/zNl0glHRmAyEFhEyoPdo4MIbCgIbDhHQScyWPKkF4HAPHCYufIMol/SiS/mu+M0/zfJBZb5Yr47EFhXEFhExoPdo4O1S45d0skFtj0X2Mu/7ZIuAIHJyFcOBBaT8WD36CACGwwCG82pwLIYiN0LNAAAIABJREFULF85EFhMxoPdooO1ZxD9kr4Dgb3cgTcIbADHQSOwniCwiIwHu0UHq1ccu6SzC2x7KrDXj9slXcA9CCyJwfKVA4HFZDzYLTqIwIaDwAZzEjQC6wgCi8h4sFt0EIEN5/Uc4hsENgIEpgKBRWQ82B06WP0UmF/S6QW2PRbY0Yftki7gLgSWw2D5yoHAYjIe7A4drF9w7JJGYEbkF1iaLVi+ciCwmIwHu0MHEZgBz9vgNwhsCAhMBQKLyHiwG3Sw/gyiX9L5BbZ9FdjxR+2SLuA+BJbCYPnKgcBiMh7sBh2csd7YJX0fAttcrpx2SRdwBwLLsgXLVw4EFpPxYB/fwRkbMJLuwbPATj6YMumEI08ILIPB7iDp2SAwD0bPPOfxMkl3AIGN5DxoBNYLBBaR8mAf3kEEZsJuK3zxwD9l0glHRmAyEFhEyoN9dAfnnEEk6S4cBHb6sZRJJxx5SmAJDHYPSc8FgXkwXmD130TSPUBgA7kIGoF1AoFFpDzYR3cQgdmAwAaCwFQgsIiUB/vgDs46g0jSXdg/CXb2sZRJJxx5UmD+BruLpGdiJbC3MIbHNXP0CPDMTmCjZ4BnHgU2egS4gpXAmtzM24yPVsc+iJq3ASPpPkz8MlImnXDkiaAzbMHuI+l5IDAPRgtszreRdBcmHk6kTDrhyFNBI7AuILCIlAc7ApPhPvObNwhsGAhMBQKLSHmwD+3gzDOIJN2FvcDOfh8pk044ciAwd4PdSdKzQGAeDBbYrO+zS/oOLua7XzDvQmD3cDHfPQisBwgsIuPBjsCagMCMQGAy8pUDgcVkPNiHdnDuGUS/pO9BYG/eTJxDtEu6AAQmI185EFhMxoN9tMDmfaNd0ncisMs7Ypd0AfckMHOD5SsHAovJeLCP7ODsDZhf0gjMiLsRmP8WLF85EFhMxoN9sMBmfqdd0ncgsDfPAju5J3ZJF4DAZOQrBwKLyXiwI7Am3IfAdv+HwMYQCczbYPnKgcBiMh7sAzs4/wyiX9L5BfbmVWDHd8Uu6QLuR2D2W7B85UBgMRkP9rECm/utdknfhcAO/0BgQwgFZm2wfOVAYDEZD3YE1gQEZsQdCcx9C5avHAgsJuPBPq6DC84g+iWdXmBvjgV2dF/ski4AgcnIVw4EFpPxYB8qsNnfa5f0PQjs+Z8IbASxwJwNlq8cCCwm48E+rINLNmAk3Zx7EthU0P/vr242v/n8Hz/abP7y7ygHKiAKGoG1BoFFpDzYBwps/jeTdGPenArs9VeTMmkEpiJhORBYSMqDHYHJMJ75ZJk8NljKpO9MYMYGS1gOBBaS8mAf1MFFZxD7Jt1trfNtx9kqicD0hEFbGyxhORBYSMqDfZzAFnw3AmvL2RqJwPTEQSOwtiCwiJQHOwI7Z30CO3+Qf7Q9TtlpBKYiYTkQWEjKg31MB5edQURgbblYIhGYnKsCszVYwnIgsJCUB/swgS35dgTWFAQ2nitBI7CmILCIlAc7AjtndQK7fIj/ukFO2WkEpiJhORBYSMqDfUgHF55BRGBNmVggEZia6wJzNVjCciCwkJQH+yiBLfp+BNaQqfXx5RFGyk7fmcCMt2AJy4HAQlIe7CM6uHQDhsBaMrk8IjAxNwRmarCE5UBgISkP9kECW3YDdgJLfDHf6dUxs8CmfhmpBea7BctXDgQWk/FgH9HBxRswBNaQ6cXx+XeUsdPlAvvZX9388rdfvuA3L75LCAJTgcAiMh7sgwS28BYQWDuCxfEOBfZrz//xtzebv/SfbH/xH/3O9hu7f+z51uBN2S2BeRosXzkQWEzGgx2BXTAtsJd//OJvHC2Fz+QVWLQ23qHAnlz1L//D/3iz+w3/7N/69u63evhdPv5WPyMd8pzrQSOwdiCwiIwH+4AOLj+DOGQH9o3NYYn71ubltNMrqQU2+fGn31LGTkcC2/yl39hu/4u/ufnN3X985tvf+szeW4df5o82Y88g3haYpcHylQOBxWQ82McIbOlNdBfYxNmmn/3V/UP4x88+n3U6Iq3A4pXxDgV24Dd2v8rN5mCsbz39Nr8x+mUdN4JGYM1AYBEZD3Z9BxtswPoLbOJs0+5B+i9/e/IEYm6BBZ+5N4H90kFh/9ruN/ut3b/2W6/HX/bu1/motLFnEAsE5miwfOVAYDEZD/YhAlt8G90FNnG2aX8S8dcmTyDmFdiVdXHz4e4+Zez0tMA+8y//5mbzS7/x7f1//p1f3fzr+389nUMcfgbxZtAIrBUILCLjwS7vYIsNmEBgE2ebdv/+pckTiKkFFn7uw53BMnZ66pfxo2iH9aP9L3T4GUQEJgOBRWQ82EcIbPmNdBbY9Nmm/eP0yROI9ymwd/clsKmN83b/qOTXDM4glgjM0GD5yoHAYjIe7Ajsguhs03Z/EnF6HUwqsKur4rvHLVjKTk/9Mr4VCezxd/rL3x5/BvF20AisEQgsIuPBru7gZvOhu8DCs03784mTZxCTCuz6o/qdwDYZOz31y4jPEe7OIY4/g1gkMD+D5SsHAovJeLCLO/jorw8b3ExngcUP1jfRFqwEu3ZcXxLfvUsqsImgn94DMcXjp/6NvzF9YljJ7aAdDZawHAgsJOXBLhbYhx++a3AzXZMOzzb9aLP5zN8JngQrwa4dNwW2N5hsnGZcjvyjTXyS8FubX/rVyG46CiqNwJqAwCIQ2C02GQQWnU96fKj+l3/nykP5m7i148ZD+ndPWzDZPM2YFlj0wGP3qtP52+pWIDAVCCwCgd3iUWDv3AUWKuob+zXwR5vZL1hza8eNBfHd0xZMNU47Lkc+uTzYGcF708WUCczNYAnLgcBCENgtdhswd4FFZ5t+dHicvlvuZr5iza0dtwX27l4Etv3bm78Sfvm35m+q21FSaQTWAgQWgcBusMkisIkH5C8bs8cH8zNfsmbWjlsP6N8dtmBmU5dQN/LRHwUbCAJTgcAiENgN9v5yF1hwtukbL1r71tyTiGbtuLUcPgls2FE5n7qgf+RwBrFUYGYGM6t0EQgsAoFdZ5NCYFfPNi3CrB0lAnt3/wL7u7N31E0pqjQCawACi0Bg1zn4y15g3fCa+ebD+Xdpt2DlQe8vDuawAUNgMhBYBMvqVTYIzIjbp6P2AvvDjAYrD3p/4WaDZ8DKBeZlMKtKF4LAIlhWr7J/DT0CM+H2UngQ2B/etcB+9m9uNn/l2/0mKaes0m4Gs6p0IQgsgmX1Kk8bMATmQMFK+CywFhev1OIUdCmFlUZgi0FgESyr19jcs8DSXcy3YCF8FVgygzX5gwdqEJgKBBZht6wWIRTYOwTmQrnA8p1DvHOBORnMqdKlILAIu2W1CJnAPkRgNpSsgy8Cy2awexaY2RbMqNLFILAIu2W1CNHMGwTmM3PR4/hngaV7Kf29C8zIYD6VLgeBRdgtq0VoZn71FwIbT9Ei+CKwbO9mvmuBeRnMp9LlILAIu2W1CJHAXvyFwIZTtgYeCSzXCxHvW2BWJxFtKl0BAouwW1aLkMy8QWBGR3vZEngisExKQGAybCpdAQKLsFtWi1AJ7B0C6z9HGbUCS3YO8f4FZmMwm0pXgMAi7JbVIhQzH2/AENhoClfAY4GlOod45wJz2oK5VLoGBBZht6wWIZj5xF8IbDClj+BPBZbICSsQmIvBTCpdBQKLsFtWi1AI7NhfCGwwpcvfkcBynUO8d4EZGcyk0lUgsAi7ZbWI/jNvENgej5mLV78TgWUy2N0LzOckokel60BgEXbLahESgb27c4EV4TFz8eJ3LLBcBvMIuo5agXkY7O6TvgIC80AgsA8R2A6LmcvXvhOBpXodh0XQldRVGoHNB4FFsKxOskFgBxxmrnjsfiGwNAZzCLqWaoFZGOz+k45BYB70nvncXwhsJBUL36nAMr2OwyHoWiorbWKwFSQdgsA86C6wM38hsIHUrHvnAstjMIOgq6mtNAKbCwKLYFmd4GIDhsAGUrPsnQkskcEMgq4GgalAYBEsqxOcvQQRgQ1licDynEQ0CLqaGQIzMNgako5AYB70nflyA4bAxlG16l0KLIvBxgddT3WlEdhMEFgEy+oFE/5CYOOoWvQuBJZmCzY+6HrmCGy8wVaRdAAC86CvwC79hcCGUbfmTQgsicGGBz2D+kojsHkgsAiW1XOmNmAIbBSVj9kvBZbFYKODnsMsgQ032DqSngaBedBZYBf+QmCjqFzwJgSW5CTi6KDnMKPSBgZbSdKTIDAPOs48uQG7S4FluJhv7Xo3KbAMF5S6/4v5PoHA5oDAIuyW1SL6zTztLwQ2iNrlLhCYvxzWJLDBBjM7DItAYBF2y2oRHQU26S8ENobq1W5KYCnOIa5GYOO3YGaHYREILMJuWS2i28zBBgyBDaH+0fq0wBIYbFUCG2sws8OwCAQWYbesFtFTYFP+QmBDqF/qJgWWwWDrEdhwg5kdhkUgsAi7ZbWIfgKb3oAhsBHMWOmmBZbAYCsS2OiTiGaHYREILMJuWS2i18zRGUQENoIZC10gMP+nwVYmsJEGMzsMi0BgEXbLahGdZg79hcAGMGedCwXmbrA1CWzwFszsMCwCgUXYLatF9Jk59hcC0zPrcXokMHuDrU1gAw1mdhgWgcAi7JbVIjoJLPQXAtMza5ELBeZ+EnFVAhtrMLPDsAgEFmG3rBbRZeYrGzAEJmfeGndFYN4GW5fAhp5ENDsMi0BgEXbL6o5f/Pn/9Mknn/yDP/m/Lj/zp5+88L3Dh/6fP/7kk3/0+pU/+OR/nPlTo5fQI7ABzHyMHgts5hZMVcX1CWyYwcwOwyIQWITdsvrIX/yT54XhYgH4iz8+XzW+v//3d7/38gV///+e91OvbcDuUmBFDJp57gJ3TWBzDKarYspyzK80AqsCgUUYLqvHK8P5svHjT85WjccP/A8//Fd/+snzWvH9uRuwq/5CYGLmrm9XBDZnCyasYspyLBLYKIOtLOkTEJiAxwey3/2nP9xu//njo9/v/tnp535wWCzeHn3xf/vD/UJzWCwWbMCu+QuBaZm9vF0VWL3BCqp4/MVLqpiyHAsqPc5ga0v6GATWn8cV4O8fnkfYPcvwR6ef/P5hHXmZ+Wf/eL9cPH7lHz19/nvzfur1DRgC0zJ7cbsmsHqDlVTxhYVVTFmOJZUeZrDVJX0EAuvPD17P1jwuILsHta88rg77D7zM/Px49/Do9/E/T7++mBv+QmBa+gis+iRiSRVfWFjFlOVYVGkEVg4Ci/BbVr//emrm8UHt6WmYx0Vi//D2WGDfO3zTbrl4XFS+t53DLX8hMCnzH5zfEFilwUqqePyB7x2+aVYVU5ZjqcCGGGx9Sb+CwKQ8rhqnD2N//PSQONiB/fiTuRuwG/5CYEoWrGzXBbbg3cxhFV9YWMWU5VhWaQRWDAKLsF5Wf3z+xMMPPvnun/3z3Rtz/tH/fvjAyRMP/TZgCEzIkkfmtwQ222Ddq5iyHIsFNsJgK0z6BQQm5fvnj3K//8l3/+enVy7/yQ+fPvL60q+5G7Db/kJgQpYsazcENt9g3auYshwLKz3GYGtM+hkEpuTxUe/p8w7HFz94WiGO3nzziz89f6VzGQX+QmA6Fq1qtwQ212D9q5iyHEsrPcRgq0z6CQQmZPcu0u9dfORP/s/Hf/xX/9vLO0v/j8PlD/5sd1Jnd5Lnn/13n3zyD6tWjwJ/ITAZy9a0mwKb9zTYlSr+q0ZVTFmOxZVGYGUgsAjfZXW3RPxR8Lm3u1c4Pz0k3i0TuwvQ/ewfH5aO6Qv/xJRswBCYioWPyQsENvOCHFEVt42qmLIcLQQmN9g6kz6AwGRcXTTe7k/hfO/kY/tHvbsXN//wF+fvMb1Kib/uUmCWF/NduKDdFtgMg133V5sqruxivi8MMJjZYVgEAouwW1af+Ge7RSN8HvztyZtM9xwe9X5//2D46QVhRRRtwBCYiKXrWYHAqg12vYrbNlVcq8AGGMzsMCwCgUXYLasHdqdf/vv4028v34ez/9sVz9fx+X7xi8DK/IXANCxezUoEVvk02I0qbttUcbUC0z8NZnYYFoHAIuyW1R2/+P6N5w4uBXa4dOrz493vf1J4IdVCfyEwCcsfjZcJrMJgN6u4bVPFVQtMazCzw7AIBBZht6xuD4vGd//pxCdeztW8vbgY+OFvVzyvGj8oFliZvxCYggZLWZHAKgx2u4rbNlVcr8DkBjM7DItAYBF2y+r28EcsJp/5/vHzW27e7taH4695+tsVtTuw0g0YAhPQYiErE1i5wW5XcdumiisWmNpgZodhEQgswm5ZPbws+fIvuO94XBQ+2T8cfrt7ZHz83MLTHw+sfuKh0F8IrD9NlrFCgZUarKCK21ZVXK/AxE+DmR2GRSCwCLtl9fwB7Qn7J9T/xXb7X5/9gcGXK/dUvfSr3F8IrD9NVrFSgZW9kKOkiud/63JeFVcvMKHBzA7DIhBYhN2y+vz+zyf2a8Nf/PHTGnF8AZ+jdeH10qlVb74p9xcC606bRaxcYCUG01Vx3QLTGszsMCwCgUXYLasnF5k7XzVeP/vd//Xoe44unfq05nyv4CdVbMAQWG8aLWHFAisxmK6KaxeY1GBmh2ERCCzCblndPbkQrxrb7Z/v/oTFf/O//Iujbzn52xV//k8++eQfTj9vcUqNvxBYZ1otYOUCKzBYURX/QYMqblcvMKXBzA7DIhBYhN2yWkSDmR/1Ve4vBNaXZstXhcB2T4P5SMNplmJaVhqBXQOBRdgtq0Usn7lq/3WfAitCJrA2N1QjsAV/3rIDKcvRVmAig605aQTmweKZK/2FwLrSbvGqEpiVwVKWo2WlZQZbc9IIzIOlM9edP0RgfWm4dNUJbN4fB+tDynI0rbTKYGtOGoF5sHDm2v0XAutJy4WrVmA+BktZjraVFhlszUkjMA+WCqzWXwisH02XrUqBGRksZTkaV1pjsDUnjcA8WDZz/QYMgXWj7aJVKzAfg6UsR+tKSwy25qQRmAdLZt7M8BcC60XjJataYDYGS1mO5pVWGGzNSSMwDxbMvKl+AQcC60frBateYC4GS1mO9pUWGGzNSSMwD+bPPM9fCKwPzZerGQIzMVjKcnSodH+DrTlpBObB7JnnnD5EYL1ov1jNEZiHwVKWo0eluxtszUkjMA/mzjzXXwisBx2WqlkCszBYynJ0qXRvg605aQTmwcyZZ/sLgXWgx0I1T2AOBktZjj6V7mywNSeNwDyYN/N8f92lwAZfzLfLMjVTYOMNtvqL+R7T12Bmh2ERCCzCblktYtbMC/yFwJrTZ5GaK7DhBkNgx3Q1mNlhWAQCi7BbVouYMfOst38hsF4zd1qiZgtsb7CBDkFgJ7zpqDCzw7AIBBZht6wWUT/zzJfPI7AuP7rb+jRfYIMNhsBO6Wgws8OwCAQWYbesFlE980J/IbCm9FudFgjs0WADFYbAzujXEbPDsAgEFmG3rBZRO/Oi04cIrDEdH10vEdjQTRgCu6BXS8wOwyIQWITdslpE5cyL/YXAGtLzGfplAjtswnrNdhUEdkmnopgdhkUgsAi7ZbWIupmX+wuBtaPrK8wWCmzcqxER2AR9tupmh2ERCCzCblktombmZS8/RGBt6fnysm0Dgb0bdBYRgU3RpS1mh2ERCCzCblktomLmpS/fQGAt6eyvFgIbYzAENsmbDoUxOwyLQGARdstqEcUzb9r4C4E1ocdydMpygQ16MSICC2hfGbPDsAgEFmG3rBZROnMjfSGwJnTXVxOBjdmEIbCI5q0xOwyLQGARdstqEWUzt9p+vbtPgRXRcGaBv9oIbMgmLGU5NJVuXJw1J43APCiauZ2+ENhyFPpqJbARm7CU5RBVum131pw0AvOgYOaG2693CGwhb/o/+3Vg/8tqILCnTZjw6E5ZDlWlm9ZnzUkjMA9uz9xUXwhsGTJ/tRPYXmHKbVjKcugq3bBAa04agXlwY+ZN2+3XOwS2BJ2+mgpMbLCU5RBWul2L1pw0AvPg+sx7e7XUFwJbgM5e27YCeye9tFTKckgr3Upha04agXlwbeZNB38hsLkId1879r+sdgITvpojZTm0lW5ksDUnjcA8CGduf/LwQIuZ7yvpIsT66iCwg8EEDktZDnmlWzhszUkjMA+imQ+br/b+QmBzUD759cT+l9VUYKqnwlKWY0Cll3dqzUkjMA+mZ+5y8vBAi5nvKOkC3gzQVxeBvSis76GeshwjKr24V2tOGoF5MDVzp5OHB1rMfDdJlzBEX50E9k6xDUtZjkGVXlauNSeNwDy4mHnTcfe1o8XM95F0CWN2Xzv2v6wOAuu/C0tZjlGVfrOkYWtOGoF5cDbzpttzX8+0mNkt6U4X8x1nr21Hgb3r7DAu5lvHgpaZHYZFILAIu2W1iOOZN/31hcCKWfTYeDn7X1YngR0U1slhCKyauU0zOwyLQGARdstqES8zS+z1DoEVMtZe294Ce1JYj2fDENgcZvXN7DAsAoFFDO/gLJ5mfrZXb30hsNu8Gbz3OrD/ZXUU2LvXM4ltjYPAZjGndaNnngMCixjfwTm83R6WEI293iGwG7zx0JdEYO+O9mHtjn4ENpfq7hnMXA0Ci7DoYC0v7tLY6x0Cu8YbG32pBHassEYLAAJbQF0BPWauA4FFuHSwmM2RvVT6QmARRu7as/9lCQS248OWJxMR2DIqHkXZzFwBAosw6uBtNvqt1xMNhrdLeqnAnHZez+x/WSKBvXveiLWwGAJbzpuyRlrNXIipwL7zWw8Pn//q1Q9Ofsn0KLMw62DI5mTnpVqgXmhwD+ySni+wN28K1wo5+1+WTmDvXhz2JLHZywECa0JJMd1mLsFTYB897PnilQ9Ofkkwyiz8OnjO5tRd+60XAmvAPIH5ymvH/pclFdiOl27O34shsGa8uVFRx5lvYSmwjx8++9Xt+997ePhS+MHJL4lGmYVnB/dsztX1et4QgTWgTmDny4KfvHYc2qEW2J4ziVUaCYG15UpbbWe+gqPAfv7lZ0l97veDD05+STjKLBw7OGGus+e8EFgDygQ2IS5LdR04tGOIwPYcFXazqTEZAmtPUF3rmQMcBfbpk5UeLfW14IOTXxKOMguXDm6O+TBW1wEE1pnJY99cXjsO7RgnsD2n9T022ZXVIlE5XkhR6axVPsFRYB+/Ps/1peCDk18SjjKLcR3cbK5I68YLDRFYa64c5pmO9kM7BgvsictCn1X+ZO1wLkeEd6VPyV1wR4F99GqnLwYfnPyScJRZdO3g+QF7U1k3zfUEAqvn9hGc77i+4NAOD4G9ENX8+uGR4Jzi6ErPIOlRYCiw919/3lV9/PDrfzD5wckv+ZUX3jbh1lG0iNhRF/x71sztfVralEvOH3pTcTzc1BusiUbHBwJryOg1Go5p0yaoYNyhB9loVDkEVsfoVRmOaNMXUNH1yIRcNOqUgcCeyfAcWDdSzkzSIlImnXDknEGvOmkE5kHKmUlaRMqkE46cM+hVJ932VYhfev7HF4MPTn5JOMos6KAKklaRMumEI+cMetVJ8z4wD1LOTNIiUiadcOScQa86aa7E4UHKmUlaRMqkE46cM+hVJ821ED1IOTNJi0iZdMKRcwa96qQbX43+Yepq9A8nV6Of+JJolFnQQRV2SW8a/EVmS+ySLqDol+FGxqDXXemmAnt//Me+3n/98ELDkw+e/deNUWZBB1XYJY3AjEBgMlLO7Ciwkz+3/Cww/iJzCSlndksagRmBwGSknNlTYEtAYMmwSxqBGYHAZKScGYEF0EEVdkkjMCMQmIyUMyOwADqowi5pBGYEApORcmYEFkAHVdgljcCMQGAyUs6MwALooAq7pBGYEQhMRsqZEVgAHVRhlzQCMwKByUg5MwILoIMq7JJGYEYgMBkpZ0ZgAXRQhV3SCMwIBCYj5cwILIAOqrBLGoEZgcBkpJwZgQXQQRUkrSJl0glHzhn0qpNGYB6knJmkRaRMOuHIOYNeddIIzIOUM5O0iJRJJxw5Z9CrThqBeZByZpIWkTLphCPnDHrVSSMwD1LOTNIiUiadcOScQa86aQTmQcqZSVpEyqQTjpwz6FUnjcA8SDkzSYtImXTCkXMGveqkEZgHKWcmaREpk044cs6gV500AvMg5cwkLSJl0glHzhn0qpNGYB6knJmkRaRMOuHIOYNeddIIzIOUM5O0iJRJJxw5Z9CrThqBeZByZpIWkTLphCPnDHrVSSMwD1LO7JY0F/M1gov5ykg5MwILoIMq7JJGYEYgMBkpZ0ZgAXRQhV3SCMwIBCYj5cwILIAOqrBLGoEZgcBkpJwZgQXQQRV2SSMwIxCYjJQzI7AAOqjCLmkEZgQCk5FyZgQWQAdV2CWNwIxAYDJSzozAAuigCrukEZgRCExGypkRWAAdVGGXNAIzAoHJSDkzAguggyrskkZgRiAwGSlnRmABdFCFXdIIzAgEJiPlzPcoMAAAgHLOPYLAAAAgBeceSbjxP2HiLkEXSFoFSYsgaBX9kkZgUAZJqyBpEQStAoFF0EEVJK2CpEUQtAoEFkEHVZC0CpIWQdAqEFgEHVRB0ipIWgRBq0BgEXRQBUmrIGkRBK0CgUXQQRUkrYKkRRC0CgQGAABwAgIDAICUIDAAAEgJAgMAgJQgMAAASAkCAwCAlCAwAABICQIDAICUIDAAAEhJboF9+vCl539+57ceHj7/1ZHD3DXEq4A+C/jp3/pgF+0fPP0nQXfj/e8+Jv3v/OfP/9kl6dQC+/mXXw74jx72fHHoPPcL8SqgzwI+PiT78OsHgxF0N3765UO2T53uk3Rmgf38Ky/hfPzw2a9u3//ew+sjWGgI8SqgzwI+fXj4d//L7fu/98FhJSXobrz/+sMXvrnP9mu7/+yUdGKB/eSDF7s/P3T9+OFzvz90pvuEeBXQZwUfPW0BHtfT3ybonny6T/g58V5JpxXY+999ePjCV54O+E+fUnlM6WtDp7pPiLc/9FnCS6KHfxB0P14fKuzO1vZKOq3JUSTfAAADCUlEQVTAfvLBZ//64yb1cMB//Hxm9SNOBXSAePtDn7UcFlKC7s9BYL2Sziuwv/bN7csB/9FrOjwb2x7i7Q991vKTD3YCI+juPJZ6F22vpNMKbMfzAf9y4D/ZHppCvCLos479czEE3Z2ffn1/7rBb0ggMbkG8IuizjMcN2JcIujuf7t6vsHvuC4FNwQEvgXhF0GcVP//KPliC7synn/+3Hx6+8NsIbBoOeAnEK4I+i3gMeP8Sb4Luz/uPdlkjsD37t8o8PDy/EJMDXgLxiqDPGh73X4e3KBG0gP2rOBDYnkBgry/N5MVEPSBeDfRZwk+//OQvgpawV1avpHMJ7AzeN6OBeDXQZwWPj4I/982nfxO0gL3AeB/YBC8HPG+o7wrxaqDPAh799YWXixkRdDdeTxru91xciWOCl4y4pFlXiFcDfe7PY7RHz8EQdD+eMz28Y4FrIU5w/MzgAxeV7gfxSqDP/TlbQAm6G4/K+sI3t9vvfHB4xNAp6TsR2Hv+rE9PiFcCfe7Oz5/+RtXz36ki6H48v+TucMa2U9J3IjD+sGpniFcAfe7O86L6+ocWCbob/9/v9v/b16kFBgAA6wWBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApASBAQBAShAYAACkBIEBAEBKEBgAAKQEgQEAQEoQGAAApOT/B4CkvS/c1ph5AAAAAElFTkSuQmCC" width="576" /> ] --- <footer></footer> # Hypothesis Testing ### Review Directional Hypothesis: `\(H_1\)`: `\(\mu_x < \mu_y\)` .smaller[ `\(\alpha = 0.05\)` ] .center[ <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Hypothesis Testing ### Review `\(\alpha\)`, `\(\beta\)`, and `\(\pi\)` .center[ <img src="data:image/png;base64,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" width="576" /> ] --- <footer></footer> # Hypothesis Testing ### Review Type I and Type II errors | | | Null hypothesis `\(H_0\)` is ... | | |--------------------------- |-------------- |--------------------------------------- |---------------------------------------- | | | | _True_ | _False_ | | __Decision about `\(H_0\)` ...__ | _Don't reject_ | Correct inference | Type II error <br> (false negative) <br> `\(\beta\)` | | | _Reject_ | Type I error <br> (false positive) <br> `\(\alpha\)` | Correct inference | --- <footer></footer> # Power Analysis A test’s statistical power depends on the following factors: - the significance criterion ( `\(\alpha \uparrow \rightarrow \pi \uparrow\)` ) - the sample size used to detect the effect ( `\(n \uparrow \rightarrow \pi \uparrow\)` ) - the magnitude of the effect, i.e. the effect size ( `\(d \uparrow \rightarrow \pi \uparrow\)` ) --- <footer></footer> # Power Analysis Several scenarios: - Calculate the required _sample size_ for a given power: - given: power, effect size (Cohen's `\(d\)` ), significance level ( `\(\alpha\)` ), type of test - Calculate the effect size you are able to detect for a given power and sample size: - given: power, number of observations (sample size `\(n\)` ), significance level ( `\(\alpha\)` ), type of test -- Be careful: true power `\(\neq\)` observed power <br> `\(\rightarrow\)` do not use post-hoc power analyses! --- <footer></footer> # Power Analysis ### Software packages R: ```r require("pwr") library(pwr) ``` `power.*` or `pwr.*` commands <br> Stata: `power` command (see `help power`) --- <footer></footer> # Power Analysis ### Example 1 .smaller[ Kirchler, M., Palan, S. (2018) Immaterial and monetary gifts in economic transactions: evidence from the field. Experimental Economics 21. [Link](https://doi.org/10.1007/s10683-017-9536-1) From Table 1, we see: `\(\bar{x}_{NORMAL} = 106.03, s_{NORMAL} = 18.78, n_{NORMAL} = 36\)` `\(\bar{x}_{COMPLIMENT} = 117.20, s_{COMPLIMENT} = 20.55, n_{COMPLIMENT} = 36\)` ] -- <br> .smaller[ Do <u>not</u> use this data for post-hoc power analysis (see [here](http://daniellakens.blogspot.com/2014/12/observed-power-and-what-to-do-if-your.html)), but, e.g. for _calculating the required sample size_ or _calculating the targeted power_ for a new analysis. ] --- <footer></footer> # Power Analysis ### Example 1 .smaller[ Calculate `\(d\)`: `\(d = \frac{\bar{x}_{NORMAL} - \bar{x}_{COMPLIMENT}}{\sqrt{s_{NORMAL}^2 + s_{COMPLIMENT}^2/2}}\)` ```r d = (106.03 - 117.20)/(((18.78^2 + 20.55^2)/2)^(1/2)) print(d) ``` ``` ## [1] -0.5674399 ``` .left-column-reverse[ Calculate power for `\(n = 80\)`: ```r pwr.t.test(n = 80, d = -0.5674399, sig.level = 0.05) ``` ``` ## ## Two-sample t test power calculation ## ## n = 80 ## d = 0.5674399 ## sig.level = 0.05 ## power = 0.9459666 ## alternative = two.sided ## ## NOTE: n is number in *each* group ``` ] ] --- <footer></footer> # Power Analysis ### Example 2 .smaller[ What sample size do you need to detect a medium effect size of `\(d = 0.5\)` with 90% power if you use `\(\alpha = 0.05\)`? (using a two-sided `\(t\)`-test) ```r pwr.t.test(d = 0.5, sig.level = 0.05, power = 0.9, type = c("two.sample")) ``` ``` ## ## Two-sample t test power calculation ## ## n = 85.03128 ## d = 0.5 ## sig.level = 0.05 ## power = 0.9 ## alternative = two.sided ## ## NOTE: n is number in *each* group ``` ] --- <footer></footer> # Power Analysis ### What's an appropriate power? - most fields use `\(\pi = 0.80\)` as a the conventional/standard power - this implies a probability of a Type II error (false negative) of `\(\beta = 1 - \pi = 0.2\)` and therefore, with a conventional `\(\alpha = 0.05\)` a 4-to-1 trade-off between `\(\beta\)`- and `\(\alpha\)`-risk - however, depending on the field and research question, this might be inappropriate `\(\rightarrow\)` depending on field and research question, think about: _what is more important - avoiding false positives or false_ _negatives?_ --- <footer></footer> # _p_-values .smaller[ Suppose you have an hypothesis that U.S. public companies with small boards of directors outperform companies with large boards. You create two value-weighted portfolios and test for differences in mean returns. The key parameter of interest, the mean performance difference, is significant with `\(p = 0.01\)`. Consider the following six statements (true/false): ] -- .left-column-reverse[ .smaller[ - (i) You have disproved the null hypothesis (no difference in mean performance). ] ] -- .left-column-reverse[ .smaller[ - (ii) You have found the probability of the null hypothesis being true. ] ] -- .left-column-reverse[ .smaller[ - (iii) You have proved the hypothesis that firms with small boards outperform firms with large boards. ] ] -- .left-column-reverse[ .smaller[ - (iv) You can deduce the probability of your hypothesis (small better than large) being true. ] ] -- .left-column-reverse[ .smaller[ - (v) If you reject the null hypothesis (no difference), you know the probability that you are making a mistake. ] ] -- .left-column-reverse[ .smaller[ - (vi) You have a reliable finding in the sense that if, hypothetically, the experiment were repeated a large number of times, you would obtain a significant result 99% of the time. ] ] -- .right-column-reverse[ .larger[ .emph[ __All of them are false!__ ] ] ] --- <footer></footer> # _p_-values ### Definition > A `\(p\)`-value is the probability of the observed data (or of more extreme > data points), _given that the null hypothesis `\(H_0\)` is true_. -- > The `\(p\)`-value indicates the probability of observing an effect, `\(D\)`, (or greater) > given the null hypothesis `\(H_0\)` is true, that is, `$$p(D|H_0)$$` -- .emph[ `$$\underline{\text{not}}\; p(H_0|D)\; !$$` ] --- <footer></footer> # Multiple Hypothesis Testing ### A comical illustration .center[![](figures/significant1.png)] .smaller[ From [https://xkcd.com/882/](https://xkcd.com/882/) ] --- <footer></footer> # Multiple Hypothesis Testing ### A comical illustration .center[![](figures/significant2.png)] .smaller[ From [https://xkcd.com/882/](https://xkcd.com/882/) ] --- <footer></footer> # Multiple Hypothesis Testing ### A comical illustration .center[![](figures/significant3.png)] .smaller[ From [https://xkcd.com/882/](https://xkcd.com/882/) ] --- <footer></footer> # Multiple Hypothesis Testing `\(\rightarrow\)` testing multiple hypotheses simultaneously can be a problem .smaller[ `\(Pr(\text{making a type I error}) = \alpha\)` ] -- .smaller[ `\(Pr(\text{not making a type I error}) = 1 - \alpha\)` ] -- .smaller[ `\(Pr(\text{not making a type I error }\textbf{in m tests}) = (1 - \alpha)^\textbf{m}\)` ] -- <br> .smaller[ Thus, with `\(\alpha = 0.05\)` and 20 hypotheses, we get a _family-wise error rate (FWER)_ `\(FWER = 1 - (1 - 0.05)^{20} = 0.642\)`, i.e. the probability of at least 1 type I error is 64.2%! ] --- <footer></footer> # Multiple Hypothesis Testing ### Definitions <br> Family-wise error rate (FWER) > _probability_ of false discoveries > ... <br> False-discovery rate (FDR) > _proportion_ of false discoveries > ... --- <footer></footer> # Multiple Hypothesis Testing ### Possible solutions: `\(p\)`-value corrections .smaller[ - Bonferroni correction - controls FWER - set significance cut-off at `\(\alpha / m\)` ( `\(m\)` ... number of tests) - applied to example above: `\(\alpha / m = \frac{0.05}{20} = 0.0025\)`, `\(\textit{FWER} = 1 - (1 - 0.0025)^{20} = 0.049\)` - very conservative ] -- .smaller[ ```r pvalues <- runif(20)/10 # 20 random p-values sort(pvalues) ``` ``` ## [1] 0.0008945796 0.0073144469 0.0100053522 0.0260427771 0.0277374958 ## [6] 0.0286000621 0.0293739612 0.0415607119 0.0455102418 0.0583987980 ## [11] 0.0585800305 0.0724405893 0.0754675027 0.0761702403 0.0813574215 ## [16] 0.0906092151 0.0949040221 0.0954068775 0.0962204624 0.0971055656 ``` ```r p.adjust(sort(pvalues), method = "bonferroni") ``` ``` ## [1] 0.01789159 0.14628894 0.20010704 0.52085554 0.55474992 0.57200124 ## [7] 0.58747922 0.83121424 0.91020484 1.00000000 1.00000000 1.00000000 ## [13] 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 1.00000000 ## [19] 1.00000000 1.00000000 ``` ] --- <footer></footer> # Multiple Hypothesis Testing ### Possible solutions: `\(p\)`-value corrections .smaller[ - Bonferroni correction - Holm–Bonferroni correction - controls FWER - order the `\(p\)`-values from lowest to highest: `\(p_1 \leq p_2 \leq ... \leq p_k\)` - set significance cut-off at `\(\frac{\alpha}{m + 1 - k}\)` (with `\(k\)` being the rank of the respective `\(p\)`-value) - applied to example above: `\(\frac{\alpha}{m + 1 - k} = \frac{0.05}{20 + 1 - 1} = 0.0025\)` for the smallest `\(p\)` ( `\(k=1\)` ), `\(\frac{\alpha}{m + 1 - k} = \frac{0.05}{20 + 1 - 2} = 0.00263\)` for the second-smallest `\(p\)` ( `\(k=2\)` ), and so on until `\(\frac{\alpha}{m + 1 - k} = \frac{0.05}{20 + 1 - 20} = 0.05\)` for the largest `\(p\)` ( `\(k=20\)` ) ] -- .smaller[ ```r p.adjust(sort(pvalues), method = "holm") ``` ``` ## [1] 0.01789159 0.13897449 0.18009634 0.44272721 0.44379993 0.44379993 ## [7] 0.44379993 0.54028925 0.54612290 0.64238678 0.64238678 0.65196530 ## [13] 0.65196530 0.65196530 0.65196530 0.65196530 0.65196530 0.65196530 ## [19] 0.65196530 0.65196530 ``` ] --- <footer></footer> # Multiple Hypothesis Testing ### Possible solutions: `\(p\)`-value corrections .smaller[ - Bonferroni correction - Holm–Bonferroni correction - Benjamini, Hochberg, and Yekutieli correction - controls FDR - order the `\(p\)`-values from lowest to highest: `\(p_1 \leq p_2 \leq ... \leq p_k\)` - starting from `\(k\)`, identify the first `\(i\)` such that `\(p_i < \frac{i}{k} \alpha\)` - declare all tests `\(1, ..., i\)` significant, tests `\(i + 1, ..., k\)` not significant ] -- .smaller[ ```r p.adjust(sort(pvalues), method = "BH") ``` ``` ## [1] 0.01789159 0.06670235 0.06670235 0.08392560 0.08392560 0.08392560 ## [7] 0.08392560 0.09710557 0.09710557 0.09710557 0.09710557 0.09710557 ## [13] 0.09710557 0.09710557 0.09710557 0.09710557 0.09710557 0.09710557 ## [19] 0.09710557 0.09710557 ``` ] -- .smaller[ - Several other correction procedures ] --- <footer></footer> # Related Literature .smaller[ - Hoenig, J. M., & Heisey, D. M. (2001). The Abuse of Power. The American Statistician, 55(1), 19–24. - Benjamin, D. J., Berger, J. O., Johannesson, M., Nosek, B. A., Wagenmakers, E.-J., Berk, R., … Johnson, V. E. (2018). Redefine statistical significance. Nature Human Behaviour, 2(1), 6–10. - Harvey, C. R., Liu, Y., & Zhu, H. (2016). ... and the Cross-Section of Expected Returns. Review of Financial Studies, 29(1), 5–68. - Harvey, C. R. (2017). The Scientific Outlook in Financial Economics. The Journal of Finance, 72(4), 1399–1440. ] --- class: middle, inverse # Your turn - Load the data in `sp500_data.csv` again - Think about interesting questions and formulate hypotheses you could test with these data - Test your hypothesis(-es) using appropriate tests - Can you reject the `\(H_0\)`? - Comment on upcoming issues regarding the statistical power, multiple hyptheses, etc.