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医学統計学(基本)1:母集団と標本・推定

Shuntaro Sato
February 24, 2020

 医学統計学(基本)1:母集団と標本・推定

Shuntaro Sato

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

    1
    ҩֶ౷ܭֶʢجຊʣ

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  2. 2
    0WFSWJFX
    w ฼ूஂͱඪຊ
    w ਪఆ
    w ఺ਪఆ
    w ۠ؒਪఆ
    w ඪ४ภࠩͱඪ४ޡࠩ
    w ৴པ۠ؒ

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  3. ฼ूஂͱඪຊ
    ʢ1PQVMBUJPOBOE4BNQMFʣ
    3

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

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

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

    શͯͷඪຊͷσʔλΛऔಘ͢Δ
    શ਺ௐࠪ
    େม

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

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  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

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  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

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  10. ࣭໰ͦͷ
    10
    ೔ຊͷҩֶ෦೥ੜʢ೥౓ೖֶʣͷ0ܕͷׂ߹͕஌Γ͍ͨ
    Ͳ͏͠·͔͢ʁ
    ࿈ଓई౓Ͱ͸ͳ͍

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  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

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  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

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  13. ࣭໰ͦͷ
    13
    ؔઅϦ΢Ϛνױऀͷ$31ͷฏۉ஋͕஌Γ͍ͨ
    Ͳ͏͠·͔͢ʁ
    ҩྍσʔλʹͳͬͨ

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

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  15. ແ࡞ҝநग़ͱΈͳ͢
    15
    "36පӃʹ
    ௨Ӄதͷ
    ؔઅϦ΢Ϛνױऀ
    ೔ຊશࠃͷ
    ؔઅϦ΢Ϛνױऀ
    શһ
    "36පӃʹ௨ӃதͷؔઅϦ΢Ϛνױऀͱ
    ฼ूஂͷ෼෍͕ࣅ͍ͯΔͱ͍͏ԾఆΛ͓͘
    ର৅࣬ױ΍σʔλʹΑͬͯ͸ɼ
    ͜ͷԾఆ͕ଥ౰͔Ͳ͏͔͸ॏཁ

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  16. ਪఆ
    ʢ&TUJNBUJPOʣ
    16

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  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

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  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

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  19. ఺ਪఆ
    ʢ1PJOUFTUJNBUJPOʣ
    19

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  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๏

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  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

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  22. ۠ؒਪఆ
    ʢ*OUFSWBMFTUJNBUJPOʣ
    22

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  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

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  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

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  25. ۠ؒਪఆʢ*OUFSWBMFTUJNBUJPOʣ
    25
    ฼ฏۉʢਅ஋ʣ


    ఺ਪఆͷෆ࣮֬ੑΛ۠ؒͰද͢
    ඪຊฏۉͷ͹Β͖ͭΛܭࢉ͢Ε͹Α͍ͷͰ͸ʁ
    ۠ؒਪఆʢ*OUFSWBMFTUJNBUJPOʣ
    ඪຊฏۉ

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  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

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  27. ඪ४ภࠩͱඪ४ޡࠩ
    27
    ඪຊ ฏۉ஋ ඪ४ภࠩ
    4BNQMJOH
    4BNQMJOH
    4BNQMJOH
    4BNQMJOH
    4BNQMJOH
    ඪ४ޡࠩ
    ฏۉ஋ͷ
    ඪ४ภࠩ
    ฏۉ஋ͷਫ਼౓Λද͢
    σʔλͷ͹Β͖ͭ
    Λද͢
    4&4UBOEBSEFSSPS

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  28. ඪ४ޡࠩͰ۠ؒਪఆ
    28
    ฼ฏۉʢਅ஋ʣ


    ඪຊฏۉ
    4& 4&
    ¯
    x
    ¯
    x ± SE
    ؒҧͬͯ͸͍ͳ͍͚ͲɼҰൠతͰ͸ͳ͍

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  29. ৴པ۠ؒʢ$POpEFODF*OUFSWBMʣ
    29
    ฼ฏۉʢਅ஋ʣ


    ඪຊฏۉ
    4& 4&
    ¯
    x
    ¯
    x ± SE
    4& 4&
    ¯
    x
    ¯
    x ± 1.96 ⋅ SE
    ৴པ۠ؒ

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  30. ৴པ۠ؒͷҙຯ
    30
    ฼ूஂ͔ΒLݸͷඪຊΛແ࡞ҝநग़͠ɼ
    Lݸͷ৴པ۠ؒΛࢉग़͢Δͱɼ
    ͷׂ߹ͷ৴པ۠ؒ͸ਅ஋ΛؚΉ

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

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

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  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

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