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統計検定について/studying statistical test
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Chisa Murata
August 07, 2020
Design
0
300
統計検定について/studying statistical test
統計検定について、会社の制作チームメンバーに向けて勉強会をやりました!
Chisa Murata
August 07, 2020
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Transcript
ूܭϋϯζΦϯ ʙݕఆฤʙ Chisa Murata
ࠓͷςʔϚ ʮ౷ܭݕఆʯͰ͢ʂʢจܥઢͰղઆʣ
౷ܭֶͬͯʁʁ Έͳ͞ΜͷΠϝʔδɺ ͍ͬͯΔ͜ͱΛڭ͍͑ͯͩ͘͞
࠷ॳͷ౷ܭֶͷΠϝʔδ ʢࢲͷ߹ʣ p ͳΜ͔ͦ͠͏ʢ5)&ɾཧܥʣ p ͱΓ͋͑ͣ౷ܭʹج͍͓͚ͮͯͬͯ৴པ ͯ͠Β͑Δຐ๏ p ֶͷͷ͕୯ҐΛམͱ͢ڪාՊ
େֶଔۀ࣌ͷ౷ܭֶͷΠϝʔδ p ͳΜ͔ͦ͠͏ʢ5)&ɾཧܥʣ ˣ p ͱΓ͋͑ͣجຊͱπʔϧ͕Θ͔Εࣈग़ͤΔ p ΈͷʹͳΔͱͬͺ͍͠ʢ5)&ɾཧܥʣ
େֶଔۀ࣌ͷ౷ܭֶͷΠϝʔδ p ͱΓ͋͑ͣ౷ܭʹج͍͓͚ͮͯͬͯ৴པͯ͠ Β͑Δຐ๏ ˣ p ͍͍ͩͨ֬ͱมΘΒͳͯ͘ɺͲͷ͙Β͍ۮવΛڐ ༰͢Δ͔݁ہਓ͕ܾؒΊΔ p Γ͍ͨ͜ͱʹΑͬͯݕఆ݁ՌมΘΔ
ࠓͷΰʔϧ ౷ܭֶʹର͢ΔΠϝʔδΛ Ξοϓσʔτͯ͠Β͏ɻ ࣮ࡍʹ͑ΔΑ͏ʹ͢Δɻ
શ෦Θ͔Βͳ͍͍ͯ͘ͷͰɺ ʮΘ͔Δͱ͜ΖɺΘ͔Γͦ͏ͳͱ͜Ζʯ Λେʹ͍ͯͩ͘͠͞
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " #
ඞͣͭʮԾઆʯΛཱͯ·͢ " #
ؼແԾઆʢ)ʣɺରཱԾઆʢ)ʣ " #
ؼແԾઆɿ"#ΑΓ$53͕ߴ͍ ରཱԾઆɿ"#ΑΓ$53͕ߴ͘ͳ͍ " #
ؼແԾઆɿ"#ΑΓ$53͕ߴ͍ ରཱԾઆɿ"#ΑΓ$53͕ߴ͘ͳ͍ " # ඞͣ૬͢ΔΑ͏ʹ͢Δ
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5 #όφʔͷ΄͏͕ ΫϦοΫ͞Ε·͢ʂʂ
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5 #όφʔͷ΄͏͕ ΫϦοΫ͞Ε·͢ʂʂ
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5 ۮવͪΐͬͱΑ͔ͬͨ ͚ͩ͡Όͳ͍ͷʁ ݴ͏΄Ͳࠩͳ͍ΑͶʁ
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5 ۮવͪΐͬͱΑ͔ͬͨ ͚ͩ͡Όͳ͍ͷʁ ݴ͏΄Ͳࠩͳ͍ΑͶʁ ݕఆͯ͠ΈΑ͏
ؼແԾઆʢ)ʣɺରཱԾઆʢ)ʣ " #
ؼແԾઆɿ"ͱ#ͷ$53͍͠ ରཱԾઆɿ"ͱ#ͷ$53͘͠ͳ͍ " #
͜ΕΛݕূ͢ΔͨΊʹ ʮൺͷࠩͷݕఆʯͱ͍͏ͷΛΓ·͢ɻ ʢ౷ܭքͰಠཱੑͷݕఆɺРݕఆͳͲͱ͍͏ݺͼํ͕ϙϐϡϥʔʣ ࣜҎԼͷ௨ΓΒ͍͠Ͱ͢ɻ͋ͬͯ͞ΈΑ͏ લఏ ࣜ
͜ΕΛݕূ͢ΔͨΊʹ ʮൺͷࠩͷݕఆʯͱ͍͏ͷΛΓ·͢ɻ ʢ౷ܭքͰಠཱੑͷݕఆɺРݕఆͳͲͱ͍͏ݺͼํ͕ϙϐϡϥʔʣ ࣜҎԼͷ௨ΓΒ͍͠Ͱ͢ɻ͋ͬͯ͞ΈΑ͏ લఏ ࣜ ҙຯෆ໌ʢগͳ͘ͱࢲʹʣ ɻ πʔϧͰΘ͔Γ·͢ https://keisan.casio.jp/exec/user/1491916580
γϯΩϯάλΠϜɿೖྗͯ͠ΈΑ͏ʢʣ ΫϦοΫͲͪΒͱಉ͡ʁ ώϯτɿඪຊ ඪຊͱ͍͏ͷ ࠩΛݟ͍ͨσʔλͷάϧʔϓͷ͜ͱͰ͢ɻ ࠓճͳʹͱͳʹͷࠩΛݟ͍ͨͷͰ͠ΐ͏͔ʁ " # 17ͲͪΒ $5
$5
͑ " # 17ͲͪΒ $5 $5
ʮܭࢉʯΛԡͯ͠ΈΑ͏
ҙຯෆ໌ͩͱࢥ͍·͕͢આ໌͠·͢ɻ
ʮغ٫͞ΕΔʯʹͳ͍ͬͯͨΒ ʮ"ͱ#ͷ$53͕͍͠ͱ͍͑ͳ͍ʯʹͳΓ·͢ʂ
ؼແԾઆɿ"ͱ#ͷ$53͍͠ ˠ ͜ͷԾઆ͕ࣺͯΒΕΔ غ٫͞ΕΔ ରཱԾઆɿ"ͱ#ͷ$53͘͠ͳ͍ ˠ ࠾༻ " #
ʮ"ͱ#ͷ$53͘͠ͳ͍ͱ͍͑Δʯ " # 17ͲͪΒ $5 $5 ׂ߹Ͱݟͯ#ͷ΄͏͕$5͕ଟ͍ͷͰɺ #͕$5͕ߴ͍ͱ͍ͬͯ0,ͱ͍͏͜ͱʹͳΔɻ
༗ҙਫ४ΛܾΊΔ ʢͲͷ͙Β͍·ͰۮવΛڐ༰͢Δ͔ܾΊΔʣ غ٫ҬΛܾΊΔͱݴ͏
σʔλΛੳ͢Δࡍʹͱͯා͍ͷ͕ ʮͨ·ͨ·ͦ͏ͳͬͨʯͱ͍͏ʮۮવʯɻ p ʮͨ·ͨ·ʯ"ͷ੨͕ݏ͍ͳਓ͕ඃݧऀͷதʹଟ͔ͬͨ p ʮͨ·ͨ·ʯ#ͷΦϨϯδ͕͖ͳਓ͚͕ͩू·͍ͬͯͨ ͱ͍͏Α͏ͳՄೳੑͳ͘ͳ͍ " #
ݕఆͰɺͦΜͳ ʮͨ·ͨ·ɺ͕ࠩग़ͯ͠·͏ۮવͷ֬ʯ ΛٻΊ͍͖ͯ·͢ɻ ʢࠓͽΜͱ͜ͳ͍͔͠Εͳ͍ͷͰ͋ͱͰ͏ͪΐͬͱৄ͘͠આ໌͠·͢ʣ ۮવඞͣଘࡏ͠·͢ɻ ʮͨ·ͨ·͕ࠩग़ͯ͠·͕ͬͨ֬ Կˋ͙Β͍ͳΒڐͤΔͷ͔ʁʯΛఆΊΔͷ͕ ༗ҙਫ४Ͱ͢
Ͳ͏ܾͬͯΊͨΒ͍͍ͷʁ
ͱΓ͋͑ͣͰ0,Ͱ͢ɻ ʢ͍͍ͩͨճʹճ͙Β͍அޡΔͳΒ͍͍ͩΖ͏ͱ͍͏ײ͡ʣ ϏδωεͳΒͱ͔Ͱ͍͍ͩΖ͏ɺ ͱ͍͏આ͋Γ·͢ɻ ݫ͘͠ݟΔͳΒͰ͢ɻ ʢҩֶܥͱ͔ͩͱ͜Εʣ
ؼແԾઆɿ"ͱ#ͷ$53͍͠ ˠ ͜ͷԾઆ͕ࣺͯΒΕΔ غ٫͞ΕΔ ରཱԾઆɿ"ͱ#ͷ$53͘͠ͳ͍ ˠ ࠾༻ " #
ؼແԾઆɿ"ͱ#ͷ$53͍͠ ˠ ͜ͷԾઆ͕ࣺͯΒΕΔ غ٫͞ΕΔ ରཱԾઆɿ"ͱ#ͷ$53͘͠ͳ͍ ˠ ࠾༻ " # ̋ʮ"ͱ#ͷ$53͘͠ͳ͍ͱ͍͑Δʯ
ʷʮ"ͱ#ͷ$53͘͠ͳ͍ʯ ͬͯײ͡ɻ ͜͜ͰͷϙΠϯτ ʮରཱԾઆ͕֬ఆ͢ΔʯΘ͚Ͱͳ͍ ͜ͱ ʢͩͬͯ֬ͷΛͯ͠Δ͔Βʣ ౷ܭతʹʮରཱԾઆΛ࠾༻͢Δʯͱݴ͍·͢ɻ
͜ΕͰݕఆͰ͖ΔΑ͏ʹͳͬͨ
֬ͱ౷ܭࣅͯΔ ͓·͚
֬ લఏ͕ͱʹͳΔ ͋ΔαΠίϩɺ֤ͷग़Δ֬͘͠ ɻ ͜ͷαΠίϩΛԿ͔͛ͨͱ͖ͷظฏۉͳͲ ΛٻΊΔɻ
֬ લఏ͕ͱʹͳΔ ͋ΔαΠίϩɺ֤ͷग़Δ֬͘͠ ɻ ͜ͷαΠίϩΛԿ͔͛ͨͱ͖ͷظฏۉͳͲ ΛٻΊΔɻ ౷ܭֶ ࣮ࡍͷσʔλ͕ͱʹͳΔ
͋ΔαΠίϩɺͲͷ͘Β͍ͷ֬Ͱ֤ࣗͷ͕ग़Δ͔ Θ͔Βͳ͍ɻ ͱΓ͋͑ͣԿ͛ͯΈͯɺͦΕͧΕͷͷग़Δ֬ Λ༧͢Δɻ
౷ܭֶ ࣮ࡍͷσʔλ͕ͱʹͳΔ ͋ΔαΠίϩɺͲͷ͘Β͍ͷ֬Ͱ֤ࣗͷ͕ग़Δ͔ Θ͔Βͳ͍ɻ ͱΓ͋͑ͣԿ͛ͯΈͯɺͦΕͧΕͷͷग़Δ֬ Λ༧͢Δɻ ूஂ ͛ଓ͚ͨͱ͖ʹ ͳΜͷ͕Կճग़
͔ͨ ඪຊ Oճ͛ͨͱ͖ʹ ͳΜͷ͕Կճग़ ͔ͨ நग़ ʢԿճ͔͛Δʣ ਪଌ
͖ͬ͞ͷ݁Ռʹ͍ͭͯ
͜ͷΜͳʹʁ
྆όφʔͷΫϦοΫಉ͡ʁ " # 17ͲͪΒ $5 $5
ൺͷࠩͷݕఆΔ͜ͱϦετ ᶃ ྆όφʔͷΫϦοΫʹ͕ࠩͳ͍߹ɺ Ͳ͏͍͏ʹͳΔ͔ظΛܭࢉ͢Δ ʢظɺظ֬Λܭࢉ͢Δʣ ᶄ ࣮ࡍͷଌఆσʔλͱᶃΛൺɺ Ͳͷ͙Β͍ဃ͕͋Δ͔Λܭࢉ͢Δ ʢРΛٻΊΔʣ ᶅ
ͦͷဃ͕Ͳͷ͙Β͍ۮવͰى͖Δ͔ܭࢉ͢Δ ʢР͔ΒQΛٻΊΔʣ
ൺͷࠩͷݕఆΔ͜ͱϦετ ᶃ ྆όφʔͷΫϦοΫʹ͕ࠩͳ͍߹ɺ Ͳ͏͍͏ʹͳΔ͔ظΛܭࢉ͢Δ ʢظɺظ֬Λܭࢉ͢Δʣ ᶄ ࣮ࡍͷଌఆσʔλͱᶃΛൺɺ Ͳͷ͙Β͍ဃ͕͋Δ͔Λܭࢉ͢Δ ʢРΛٻΊΔʣ ᶅ
ͦͷဃ͕Ͳͷ͙Β͍ۮવͰى͖Δ͔ܭࢉ͢Δ ʢР͔ΒQΛٻΊΔʣ
྆όφʔͷΫϦοΫಉ͡ʁ
྆όφʔͷΫϦοΫಉ͡ʁ
྆όφʔͷΫϦοΫಉ͡ʁ
͠ύλʔϯͱΫϦοΫʹ ͕ؔͳ͍ͷͩͱͨ͠Β ʸ ʢશମʣ ͷׂ߹Ͱόφʔ͕ΫϦοΫ͞ΕΔͣɻ
None
͠ύλʔϯͱΫϦοΫʹ ͕ؔͳ͍ͷͩͱͨ͠Β ʸ ʢશମʣ ͷׂ߹Ͱόφʔ͕ΫϦοΫ͞ΕΔͣɻ "ύλʔϯΛΫϦοΫ͢Δਓͷɺ 17 ʹ
ʹͳΔͣɻ
ظ ʢύλʔϯͱΫϦοΫؔͳ͍ͳΒ͜͏ͳΔͣʣ ࣮ଌ
ൺͷࠩͷݕఆΔ͜ͱϦετ ᶃ ྆όφʔͷΫϦοΫʹ͕ࠩͳ͍߹ɺ Ͳ͏͍͏ʹͳΔ͔ظΛܭࢉ͢Δ ʢظɺظ֬Λܭࢉ͢Δʣ ᶄ ࣮ࡍͷଌఆσʔλͱᶃΛൺɺ Ͳͷ͙Β͍ဃ͕͋Δ͔Λܭࢉ͢Δ ʢРΛٻΊΔʣ ᶅ
ͦͷဃ͕Ͳͷ͙Β͍ۮવͰى͖Δ͔ܭࢉ͢Δ ʢР͔ΒQΛٻΊΔʣ
ظ ʢύλʔϯͱΫϦοΫؔͳ͍ͳΒ͜͏ͳΔͣʣ ࣮ଌ
ظ ʢύλʔϯͱΫϦοΫؔͳ͍ͳΒ͜͏ͳΔͣʣ ࣮ଌ
ظͱ࣮ଌͷࠩ
Р ɾͲͷ͙Β͍ظͱ࣮ଌ͕ဃ͍͔ͯͨ͠ͷࢦඪ ɾ͕େ͖͍ ʹ ဃ͕େ͖͍ ʢˣࠩΛग़ͯ͠ܭࢉͯ͠ΔͷͰʣ
Р
ൺͷࠩͷݕఆΔ͜ͱϦετ ᶃ ྆όφʔͷΫϦοΫʹ͕ࠩͳ͍߹ɺ Ͳ͏͍͏ʹͳΔ͔ظΛܭࢉ͢Δ ʢظɺظ֬Λܭࢉ͢Δʣ ᶄ ࣮ࡍͷଌఆσʔλͱᶃΛൺɺ Ͳͷ͙Β͍ဃ͕͋Δ͔Λܭࢉ͢Δ ʢРΛٻΊΔʣ ᶅ
ͦͷဃ͕Ͳͷ͙Β͍ۮવͰى͖Δ͔ܭࢉ͢Δ ʢР͔ΒQΛٻΊΔʣ
গ͠લʹݴͬͨΑ͏ʹɺ ʮۮવʯ͜ͷဃ͕ ىͬͨ͜Մೳੑ͕͋Γ·͢ɻ
σʔλΛੳ͢Δࡍʹͱͯා͍ͷ͕ ʮͨ·ͨ·ͦ͏ͳͬͨʯͱ͍͏ʮۮવʯɻ p ʮͨ·ͨ·ʯ"ͷ੨͕ݏ͍ͳਓ͕ඃݧऀͷதʹଟ͔ͬͨ p ʮͨ·ͨ·ʯ#ͷΦϨϯδ͕͖ͳਓ͚͕ͩू·͍ͬͯͨ ͱ͍͏Α͏ͳՄೳੑͳ͘ͳ͍ " #
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5 ۮવͪΐͬͱΑ͔ͬͨ ͚ͩ͡Όͳ͍ͷʁ ݴ͏΄Ͳࠩͳ͍ΑͶʁ
Ͳͬͪͷόφʔ͕ΫϦοΫ͕͍͍ʁ " # 17ͲͪΒ $5 $5 ۮવͪΐͬͱΑ͔ͬͨ ͚ͩ͡Όͳ͍ͷʁ ݴ͏΄Ͳࠩͳ͍ΑͶʁ ۮવ͔ͩͬͨΛ
ఆ͢Δͷ͕ݕఆ
Р ͔ΒQʢࠓճͷ݁Ռ͕ۮવग़ͨ֬ʣΛٻΊΔɻ
ܭࢉ͕ࣜ͢Ͱʹ͋ΔͷͰɺΛٻΊΔ͚ͩʂ ΤΫηϧͰܭࢉͰ͖·͢ɻ $)*42%*4535 Р ࣗ༝ ࣗ༝ ύλʔϯ ʷ ύλʔϯʹର͢ΔΞΫγϣϯ ͰٻΊ·͢ɻ
ݫີʹύλʔϯΞΫγϣϯͱ͍͏ΑΓɺදͷߦͱྻͷ߲Ͱ͢ɻ
Q ͭ·Γͷ֬Ͱࠓճͷ݁Ռ͕ۮવग़Δ ʢͷ֬Ͱɺ"ͱ#ύλʔϯʹ͕ࠩͳ࣮ͯ͘ଌΛಘ͏Δʣ
༗ҙਫ४ʢۮવΛڐ༰͢Δਫ४ʣͰͨ͠ɻ ͷ֬ͰۮવͰɺ༨༟ͰҎԼͰ͢ɻ ʮ$53͕ಉ͡ʯͱ͍͏આغ٫͞Ε·͢ɻ
ཧղΛਂΊΔۃͳ͏͔ͬΓྫ ʢઈରʹਅࣅ͍͚ͯ͠·ͤΜʣ ͏͔ͬΓͯ͠ɺ"PS#ύλʔϯͷ ϩά͕མͪͯͳ͔ͬͨʙʂʂ ࣾʹใࠂ͠ͳ͖Ό͍͚ͳ͍ͷʹϐϯνʜʜʂ
ཧղΛਂΊΔۃͳ͏͔ͬΓྫ ʢઈରʹਅࣅ͍͚ͯ͠·ͤΜʣ ͱΓ͋͑ͣΫϦοΫͨ͠ʗ͠ͳ͔ͬͨ ϢʔβʔͷσʔλམͪͯΔ͔Βɺ ΫϦοΫͨ͠ʗ͠ͳ͔ͬͨ σʔλʹϥϯμϜʹ "PS#ΛׂΓͯͱ͜͏͔ͳʜʜɻ
ϥϯμϜʢແ࡞ҝʣʹΔͳΒɺ جຊతʹʮ"ͱ#ͷҧ͍ʯ͕ग़ͯ͘Δ͕ͣͳ͍ɻ Ͱɺʮͨ·ͨ·ɺ·͙ΕͰʯ ظΑΓେ͖͘ဃ͢Δ͜ͱ͋Γ͑Δɻ ͡Ό͋ͦͷ֬ͲΕ΄Ͳͳͷ͔ʁʁ
ͦΕΛ͋ΒΘ͢ͷ͕ɺQɻ ࠓճͷσʔλͰ͍͏ͱɺQ ͷ֬ɺͱ͍͏͜ͱͰ͢ɻ ʢࢲ͜ͷఔͷཧղͰ͕͢ɺ͜Εͬ͘͟Γͨ͠આ໌ ͷΑ͏ͳͷͰɺڵຯ͕͋Δํਂ۷ͬͯΈͯͶʣ
ೋ߲ݕఆ ಛఆͷύλʔϯ͚ͩͷଟ͞ɾগͳ͕͞ ۮવʹΑΔͷ͔Ͳ͏͔ΛΈ͍ͨ Рݕఆ ʢࠓճ͜Εʣ શମͷ݁Ռ͕ۮવʹΑΔͷ͔Λݟ͍ͨ ʢ͋Δఔσʔλ͕ඞཁʣ Uݕఆ ച্ɺԠ࣌ؒͳͲͷฏۉͷ͕ࠩ ۮવʹΑΔͷ͔Ͳ͏͔ΛΈ͍ͨ
ۀʹ͑ͦ͏ͳ͞·͟·ͳݕఆ ͦΕͧΕπʔϧ͕͋Γ·͢͠ɺ 3ͱ͍͏౷ܭιϑτͰ͍ΖΜͳݕఆ͕Ͱ͖·͢ https://cran.r-project.org/
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ࢀߟจݙɾαΠτ Θ͔Γ͍͢ॱ • খྛ ࠀ ϚϯΨͰΘ͔Δ ͍͞͠౷ܭֶ 1)1ݚڀॴ •
େଜ ฏ ࠓ͔Β͑Δ౷ܭղੳ ߨஊࣾ • "#ςετʹ༻͍ΒΕΔ౷ܭతݕఆख๏ʢϩδοΫʣͷ·ͱΊˍൺֱ • IUUQTXXXSDPSFDSVJUDPKQDBSFFSFOHJOFFSCMPHBCUFTU MPHJD • ܙାʮ౷ܭͱ֬ͷҧ͍ʯ • IUUQTEFUBJMDIJFCVLVSPZBIPPDPKQRBRVFTUJPO@EFUBJMR • ΧΠೋݕఆ • IUUQTMPHJDTPGCMVFDPNDIJTRVBSFEUFTU • ΧΠ̎ͱΧΠ̎ • IUUQLPHPMBCDIJMMPVUKQFMFBSOIBNCVSHFSDIBQTFDIUNM
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