医学統計学(基本)1:母集団と標本・推定

38e2af7f8bdad4f2087ab3d42b627e33?s=47 Shuntaro Sato
February 24, 2020

 医学統計学(基本)1:母集団と標本・推定

38e2af7f8bdad4f2087ab3d42b627e33?s=128

Shuntaro Sato

February 24, 2020
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  1. ฼ूஂͱඪຊɾਪఆ 4BUP !4IVOUBSPPP 1 ҩֶ౷ܭֶʢجຊʣ

  2. 2 0WFSWJFX w ฼ूஂͱඪຊ w ਪఆ w ఺ਪఆ w ۠ؒਪఆ

    w ඪ४ภࠩͱඪ४ޡࠩ w ৴པ۠ؒ
  3. ฼ूஂͱඪຊ ʢ1PQVMBUJPOBOE4BNQMFʣ 3

  4. ࣭໰ͦͷ 4 ೔ຊͷҩֶ෦೥ੜʢ೥౓ೖֶʣͷ਎௕ͷฏۉ஋͕஌Γ͍ͨ Ͳ͏͠·͔͢ʁ

  5. ճ౴Ҋ 5  ೔ຊͷҩֶ෦೥ੜશһͷ਎௕Λௐ΂ͯɼฏۉ஋Λܭࢉ͢Δ  ద౰ʹԿਓ͔ௐ΂ͯɼฏۉ஋Λܭࢉ͢Δ  "36େֶҩֶ෦೥ੜશһͷ਎௕Λௐ΂ͯɼฏۉ஋Λܭࢉ͢Δ

  6. શ਺ௐࠪ 6 w ೔ຊͷҩֶ෦೥ੜશһ͔Β਎௕Λௐ΂Δ w ֤େֶͷ݈߁਍அͷσʔλΛ΋Β͏ ඪຊ TBNQMF શͯͷඪຊͷσʔλΛऔಘ͢Δ શ਺ௐࠪ

    େม
  7. ແ࡞ҝநग़ʢ3BOEPNTBNQMJOHʣ 7 ೔ຊશࠃͷ ҩֶ෦೥ੜ શһ ແ࡞ҝʹநग़͞Εͨ ೔ຊશࠃͷ ҩֶ෦೥ੜ ແ࡞ҝநग़ ͜ͷͭͷूஂͷಛ௃͸

    ΄΅ಉ͡ʹͳΔ
  8. ฼ूஂͱඪຊ 8 ೔ຊશࠃͷ ҩֶ෦೥ੜ શһ ແ࡞ҝʹநग़͞Εͨ ೔ຊશࠃͷ ҩֶ෦೥ੜ ແ࡞ҝநग़ ฼ूஂʢ1PQVMBUJPOʣ

    ڵຯͷର৅Ͱ͋Δूஂͷ શू߹ ඪຊʢ4BNQMFʣ ฼ूஂͷ෦෼ू߹ ฼ूஂ͔Βແ࡞ҝநग़͞Εͨඪຊͷ෼෍͸ɼ ฼ूஂͷ෼෍ͱ਺ཧతʹҰக͢Δʢେ਺ͷ๏ଇʣ Histogram of x x Frequency 150 160 170 180 190 0 500 1000 1500 Histogram of y y Frequency 160 165 170 175 180 0 2 4 6 8 10 14
  9. Histogram of y y Frequency 160 165 170 175 180

    0 2 4 6 8 10 14 ແ࡞ҝநग़ʁ 9 ೔ຊશࠃͷ ҩֶ෦೥ੜ શһ "36େֶͷ ҩֶ෦೥ੜ ৗࣝతʹ෼෍͕ҟͳΔͱ͸ߟ͑ͮΒ͍ Histogram of x x Frequency 150 160 170 180 190 0 500 1000 1500 ඪຊ͸฼ूஂͷແ࡞ҝநग़ͱΈͳ͢
  10. ࣭໰ͦͷ 10 ೔ຊͷҩֶ෦೥ੜʢ೥౓ೖֶʣͷ0ܕͷׂ߹͕஌Γ͍ͨ Ͳ͏͠·͔͢ʁ ࿈ଓई౓Ͱ͸ͳ͍

  11. A O B AB Frequency 0 500 1500 2500 3500

    A O B AB Frequency 0 10 20 30 40 ΍ͬͺΓແ࡞ҝநग़ 11 ೔ຊશࠃͷ ҩֶ෦೥ੜ શһ ແ࡞ҝʹநग़͞Εͨ ೔ຊશࠃͷ ҩֶ෦೥ੜ ແ࡞ҝநग़ ௐ΂Δͷׂ͕߹Ͱ΋ಉ͡
  12. A O B AB Frequency 0 10 20 30 40

    A O B AB Frequency 0 500 1500 2500 3500 ແ࡞ҝநग़ͱΈͳ͢ 12 ೔ຊશࠃͷ ҩֶ෦೥ੜ શһ "36େֶͷ ҩֶ෦೥ੜ ඪຊͱ฼ूஂͷ෼෍͕ࣅ͍ͯΔͱ͍͏ ԾఆΛ͓͘
  13. ࣭໰ͦͷ 13 ؔઅϦ΢Ϛνױऀͷ$31ͷฏۉ஋͕஌Γ͍ͨ Ͳ͏͠·͔͢ʁ ҩྍσʔλʹͳͬͨ

  14. ΍ͬͺΓແ࡞ҝநग़ 14 ແ࡞ҝநग़ ແ࡞ҝʹநग़͞Εͨ ؔઅϦ΢Ϛνױऀ ೔ຊશࠃͷ ؔઅϦ΢Ϛνױऀ શһ ҩྍσʔλͰ΋ಉ͡

  15. ແ࡞ҝநग़ͱΈͳ͢ 15 "36පӃʹ ௨Ӄதͷ ؔઅϦ΢Ϛνױऀ ೔ຊશࠃͷ ؔઅϦ΢Ϛνױऀ શһ "36පӃʹ௨ӃதͷؔઅϦ΢Ϛνױऀͱ ฼ूஂͷ෼෍͕ࣅ͍ͯΔͱ͍͏ԾఆΛ͓͘

    ର৅࣬ױ΍σʔλʹΑͬͯ͸ɼ ͜ͷԾఆ͕ଥ౰͔Ͳ͏͔͸ॏཁ
  16. ਪఆ ʢ&TUJNBUJPOʣ 16

  17. ਪఆʢ&TUJNBUJPOʣ 17 ແ࡞ҝநग़ ฼ूஂ ඪຊ Histogram of x x Frequency

    150 160 170 180 190 0 500 1000 1500 Histogram of y y Frequency 160 165 170 175 180 0 2 4 6 8 10 14 w ฏۉ஋ w தԝ஋ w ඪ४ภࠩ w ࢛෼Ґ w ʜ ᶃ ຊ౰͸฼ूஂͷಛ௃ ͕஌Γ͍ͨ w ฏۉ஋ w தԝ஋ w ඪ४ภࠩ w ࢛෼Ґ w ʜ ܭࢉ ܭࢉͰ͖ͳ͍ ᶄ ඪຊͰ฼ूஂͷಛ௃Λ ਪఆ͢Δ ౷ܭֶͰ࠷΋େࣄͳߟ͑ํ 
  18. ฼਺ʢ1BSBNFUFSʣͱ෼฼ 18 ฼ूஂ Histogram of x x Frequency 150 160

    170 180 190 0 500 1000 1500 w ฏۉ஋ w தԝ஋ w ඪ४ภࠩ w ࢛෼Ґ w ʜ ܭࢉ ฼਺ʢ1BSBNFUFSʣ ฼ूஂͷಛ௃Λද͢਺஋ʢ౷ܭྔʣ w ฼ฏۉ஋ w ฼தԝ஋ w ฼ඪ४ภࠩ w ฼࢛෼Ґ w ʜ ਖ਼֬ʹ ද͢ͱ Ϋϥεͷ0ܕͷׂ߹Λܭࢉ͢Δ શମਓ 0ܕਓ 20 100 = 20 % ͜Ε͸෼฼ɽ฼਺Ͱ͸ͳ͍ɽ
  19. ఺ਪఆ ʢ1PJOUFTUJNBUJPOʣ 19

  20. ఺ਪఆʢ1PJOUFTUJNBUJPOʣ 20 ແ࡞ҝநग़ ฼ूஂ ඪຊ Histogram of x x Frequency

    150 160 170 180 190 0 500 1000 1500 Histogram of y y Frequency 160 165 170 175 180 0 2 4 6 8 10 14 ܭࢉ ඪຊฏۉ ¯ x = x1 + x2 + ⋯ + xn n ฼ฏۉ μ ఺ਪఆ ฼ूஂͷະ஌ͷ฼਺Λ ͋ΔҰͭͷ஋Ͱਪఆ͢Δํ๏
  21. ఺ਪఆ஋͸Ұ͔ͭʁ 21 ແ࡞ҝநग़ ฼ूஂ ඪຊ Histogram of x x Frequency

    150 160 170 180 190 0 500 1000 1500 Histogram of y y Frequency 160 165 170 175 180 0 2 4 6 8 10 14 ฼ूஂ͸Ұͭ ఺ਪఆ஋͸Ұ͔ͭʁ
  22. ۠ؒਪఆ ʢ*OUFSWBMFTUJNBUJPOʣ 22

  23. ඪຊ͸ແݶʹ࡞ΕΔ 23 ແ࡞ҝநग़ ฼ूஂʢҰͭʹܾ·Δʣ Histogram of x x Frequency 150

    160 170 180 190 0 500 1000 1500 ແ࡞ҝநग़ ඪຊ ແ࡞ҝநग़ͷͨͼʹɼ ҟͳΔඪຊʹͳΔ ఺ਪఆ஋͸Ұͭʹܾ·Βͳ͍ɽඪຊʹΑΓҧ͏
  24. γϛϡϨʔγϣϯ 24 Sampling: 1 169.0 Sampling: 2 171.0 Sampling: 3

    170.0 Sampling: 4 171.0 Sampling: 5 170.0 160 170 180 160 170 180 160 170 180 160 170 180 160 170 180 0 5 10 Height count 0 200 400 150 160 170 180 190 Height count ฼ूஂ ฼ฏۉ μ = 170.0 /Ͱແ࡞ҝநग़ ඪຊฏۉ͸ඪຊ͝ͱʹҟͳΔෆ࣮֬ੑ
  25. ۠ؒਪఆʢ*OUFSWBMFTUJNBUJPOʣ 25 ฼ฏۉʢਅ஋ʣ    ఺ਪఆͷෆ࣮֬ੑΛ۠ؒͰද͢ ඪຊฏۉͷ͹Β͖ͭΛܭࢉ͢Ε͹Α͍ͷͰ͸ʁ ۠ؒਪఆʢ*OUFSWBMFTUJNBUJPOʣ ඪຊฏۉ

  26. ඪ४ภࠩʢ4%4UBOEBSEEFWJBUJPOʣ 26      ฏۉ஋ = 3

    + 7 + 9 + 11 + 20 5 = 10 ඪ४ภࠩ͸ฏۉ஋͔ΒͷͣΕΛҰͭͷ਺஋Ͱද͢            ୯७ʹࠩΛ଍͢ͱʹͳΔͷͰʜ ඪ४ภࠩ = (−7)2 + (−3)2 + (−1)2 + 12 + 102 5 − 1 = 6.3
  27. ඪ४ภࠩͱඪ४ޡࠩ 27 ඪຊ ฏۉ஋ ඪ४ภࠩ 4BNQMJOH   4BNQMJOH 

     4BNQMJOH   4BNQMJOH   4BNQMJOH   ඪ४ޡࠩ ฏۉ஋ͷ ඪ४ภࠩ ฏۉ஋ͷਫ਼౓Λද͢ σʔλͷ͹Β͖ͭ Λද͢ 4&4UBOEBSEFSSPS
  28. ඪ४ޡࠩͰ۠ؒਪఆ 28 ฼ฏۉʢਅ஋ʣ    ඪຊฏۉ 4& 4& ¯

    x ¯ x ± SE ؒҧͬͯ͸͍ͳ͍͚ͲɼҰൠతͰ͸ͳ͍
  29. ৴པ۠ؒʢ$POpEFODF*OUFSWBMʣ 29 ฼ฏۉʢਅ஋ʣ    ඪຊฏۉ 4& 4& ¯

    x ¯ x ± SE 4& 4& ¯ x ¯ x ± 1.96 ⋅ SE ৴པ۠ؒ
  30. ৴པ۠ؒͷҙຯ 30 ฼ूஂ͔ΒLݸͷඪຊΛແ࡞ҝநग़͠ɼ Lݸͷ৴པ۠ؒΛࢉग़͢Δͱɼ ͷׂ߹ͷ৴པ۠ؒ͸ਅ஋ΛؚΉ

  31. ৴པ۠ؒͷҙຯ 31 IUUQTSQTZDIPMPHJTUDPNE$* ఺ਪఆ஋ͷਫ਼౓Λද͢ɼͱߟ͑Δͷ͕ྑ͍ ৴པ۠ؒͷதʹਅ஋͕ଘࡏ͢Δ֬཰͸ ৴པ۠ؒͷதʹਅ஋͕ଘࡏ͢Δ֬཰͸͔ /BJNJ"* 8IJUDPNC#8$BO$POpEFODF*OUFSWBMTCF*OUFSQSFUFE "N+&QJEFNJPM<DJUFE+BO>EPJ BKFLXBB

  32. 5BLF)PNFNFTTBHF 32 w ฼ूஂͷύϥϝʔλ͸෼͔Βͳ͍ w ฼ूஂͷύϥϝʔλΛඪຊͰਪఆ͢Δ w ඪຊ͝ͱʹ఺ਪఆ஋͸ҟͳΔ w ৴པ۠ؒͰ఺ਪఆ஋ͷਫ਼౓Λදݱ͢Δ

  33. ࢀߟจݙͱҾ༻จݙ  ୮ޙढ़࿠  ҩֶ΁ͷ౷ܭֶ<ୈ൛>ே૔ॻళ w গ͠ݹ͍͕ɼ಺༰͸·ͱ·͍ͬͯΔ w ਺ࣜࠞ͡Γ 

    ౦ژେֶڭཆֶ෦౷ܭֶڭࣨ  ౷ܭֶೖ໳౦ژେֶग़൛ձ w গ͠ݹ͍͕ɼ಺༰͸·ͱ·͍ͬͯΔ 33