医学統計学（基本）1：母集団と標本・推定

Transcript

1. ฼ूஂͱඪຊɾਪఆ 4BUP
   !4IVOUBSPPP 1 ҩֶ౷ܭֶʢجຊʣ
   
2. 2 0WFSWJFX w ฼ूஂͱඪຊ
   w ਪఆ
   w ఺ਪఆ
   w ۠ؒਪఆ
   w ඪ४ภࠩͱඪ४ޡࠩ
   w ৴པ۠ؒ
3. ฼ूஂͱඪຊ
   ʢ1PQVMBUJPO
   BOE
   4BNQMFʣ 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࡞ҝநग़ʢ3BOEPN
   TBNQMJOHʣ 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
    ʢ1PJOU
    FTUJNBUJPOʣ 19
20. ఺ਪఆʢ1PJOU
    FTUJNBUJPOʣ 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*OUFSWBM
    FTUJNBUJPOʣ 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͸ඪຊ͝ͱʹҟͳΔ
    
    ෆ࣮֬ੑ
25. ۠ؒਪఆʢ*OUFSWBM
    FTUJNBUJPOʣ 25 ฼ฏۉʢਅ஋ʣ    ఺ਪఆͷෆ࣮֬ੑΛ۠ؒͰද͢ ඪຊฏۉͷ͹Β͖ͭΛܭࢉ͢Ε͹Α͍ͷͰ͸ʁ ۠ؒਪఆʢ*OUFSWBM
    FTUJNBUJPOʣ ඪຊฏۉ
26. ඪ४ภࠩʢ4%
    4UBOEBSE
    EFWJBUJPOʣ 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&
    4UBOEBSE
    FSSPS
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
    *OUFSWBMT
    CF
    *OUFSQSFUFE
    "N
    +
    &QJEFNJPM
    
    <DJUFE
    
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    >
    EPJ BKFLXBB
32. 5BLF
    )PNF
    NFTTBHF 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