量的データを扱うときに知っておきたいこと —データの分布、有意性、効果量、信頼区間—

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ྔతσʔλΛѻ͏ͱ͖ʹ ஌͓͖͍ͬͯͨ͜ͱ —σʔλͷ෼෍ɺ༗ҙੑɺޮՌྔɺ৴པ۠ؒ— Ӝ໺ ݚʢ๺ւֶԂେֶʣ email: urano@hgu.jp ֎ࠃޠڭҭϝσΟΞֶձୈ56ճશࠃݚڀେձ ˏૣҴాେֶ ɹɹ2016. 8. 7. ຊ೔ͷࢿྉ http://bit.ly/let2016ws

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Έͳ͞Μʹ࣭໰

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• ࿦จ౳ͰޮՌྔΛใࠂͨ͜͠ͱ͸͋Γ·͔͢ • ৴པ۠ؒΛใࠂͨ͜͠ͱ͸͋Γ·͔͢ • ޮՌྔ d ΍ η2 ͷܭࢉํ๏Λ஌͍ͬͯ·͔͢ • ඪ४ภࠩͷܭࢉํ๏Λ஌͍ͬͯ·͔͢ Έͳ͞Μʹ࣭໰

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ՍۭͷσʔλΛ ༻ҙ͠·ͨ͠

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Name* Test A খ૔ ರ 70 Տ੢ େޒ࿠ 38 খਿ Ꮺ 58 ௶Ҫ ج༞ 48 ӬҪ ج༞ 28 ڮޱ ๏࢚ 54 ݪ ཽ໵ 58 ޿੉ ༎ 38 ౻ా ࢰಐ 42 ຊؒ խ඙ 47 ٶ࡚ ৎ༤ 78 ଜҪ ࿣࿠ 68 ࢁ࡚ ޹ଠ࿠ 40 ԣҪ ޛࢤ 50 ґా ༸հ 68 एࢁ ప 57 ༗അ Ղ೫ 64 ࿨ઘ ګࢠ 76 ؠҪ ඒՂ 43 ߐ઒ ༝Ӊ 90 ਆ୩ ࣿق 58 ๺઒ ઍՂࢠ 38 ࡔా Ѫࡊ 38 ਿా ඒՂ 43 ⁋ຊ ᜫ 58 ౔୩ ே߳ 60 Ӭ੉ ͘ΔΈ 48 দ໦ ಹಸ 45 ଜҪ ݁ࢠ 24 ए௬ ·Έ 36 *ʮͳΜͪΌͬͯݸਓ৘ใʯͰੜ੒ http://kazina.com/dummy/

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Group A Test A খ૔ ರ 70 Տ੢ େޒ࿠ 38 খਿ Ꮺ 58 ௶Ҫ ج༞ 48 ӬҪ ج༞ 28 ڮޱ ๏࢚ 54 ݪ ཽ໵ 58 ޿੉ ༎ 38 ౻ా ࢰಐ 42 ຊؒ խ඙ 47 ٶ࡚ ৎ༤ 78 ଜҪ ࿣࿠ 68 ࢁ࡚ ޹ଠ࿠ 40 ԣҪ ޛࢤ 50 ґా ༸հ 68 एࢁ ప 57 ༗അ Ղ೫ 64 ࿨ઘ ګࢠ 76 ؠҪ ඒՂ 43 ߐ઒ ༝Ӊ 90 ਆ୩ ࣿق 58 ๺઒ ઍՂࢠ 38 ࡔా Ѫࡊ 38 ਿా ඒՂ 43 ⁋ຊ ᜫ 58 ౔୩ ே߳ 60 Ӭ੉ ͘ΔΈ 48 দ໦ ಹಸ 45 ଜҪ ݁ࢠ 24 ए௬ ·Έ 36 Group B Test A ؠӬ ࿡࿠ 52 ২໦ ҭೋ 59 ย੉ ཽ໵ 61 ࡔݩ ᠳଠ 76 ౡଜ ༏ 45 ৓ా ௕ར 68 ௕୔ ஌࢙ 63 দҪ Ұಙ 69 ࡾݪ ༟࣍࿠ 43 क԰ ཽ࣍ 51 ੨໺ Έ͋ 36 ஑୩ ༏ 51 ؠ୩ ౧ࢠ 39 ্ݪ ܠࢠ 71 ߐޱ Ί͙Έ 26 ٴ઒ ͳͭΈ 79 େ௩ ·͞Έ 55 Ԭ໺ ࿏ࢠ 61 ֯ా ౧ࢠ 89 ઒୺ ݁ҥ 51 ਆށ ࡊʑඒ 71 ֎ࢁ Έ͋ 63 রҪ Έ͖ 41 ࠜ؛ ༏ 41 ࠜ؛ ྱࢠ 83 Ӌా ѥر 93 ෱࢜ ΈΏ͖ 47 ෍ࢪ ༑߳ 37 ଜా จੈ 52 ٢Ӭ ܙས߳ 41

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ൺ΂ͯΈΑ͏ σʔλͷཁ໿

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ൺ΂ͯΈΑ͏ Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ 15.1 16.4

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ൺ΂ͯΈΑ͏ Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ 15.1 16.4 ෼෍ͷ޿͕Γ σʔλͷத৺

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ൺ΂ͯΈΑ͏ Group A Group B 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030

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ൺ΂ͯΈΑ͏ Group A Group B 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030

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ൺ΂ͯΈΑ͏ ฏۉ஋ͷࠩ Group A Group B Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ 15.1 16.4 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030 ෼෍ͷҧ͍

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ඪ४ภࠩ

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ඪ४ภࠩ ෼෍ͷ޿͕Γʢ͹Β͖ͭʣ

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• ݸʑͷ਺஋ͱฏۉ஋ͱͷࠩΛ̎৐͠ɺ  ͦͷ߹ܭΛσʔλͷ਺Ͱׂͬͨ΋ͷͷฏํࠜ ඪ४ภࠩ Group A Test A খ૔ ರ 70 Տ੢ େޒ࿠ 38 খਿ Ꮺ 58 ௶Ҫ ج༞ 48 ӬҪ ج༞ 28 ڮޱ ๏࢚ 54 ݪ ཽ໵ 58 ޿੉ ༎ 38 ౻ా ࢰಐ 42 (70-52.1)2 = 320.4 (38-52.1)2 = 198.8 (58-52.1)2 = 034.8 . . . ߹ܭ 6828.7 /30 = 227.6 √ 227.6 = 15.1 Group A ฏۉ஋ 52.1 ඪ४ภࠩ 15.1 ←ʢ෼ࢄʣ

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0 20 40 60 80 100 0.00 0.01 0.02 0.03 0.04 0 20 40 60 80 100 0.00 0.01 0.02 0.03 0.04 ฏۉ஋ = 50 ͷ৔߹ ඪ४ภࠩ = 10 ඪ४ภࠩ = 20 34.1% 13.6% 34.1% 34.1% 13.6% 34.1% 13.6% 13.6% ඪ४ภࠩ

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0 20 40 60 80 100 0.00 0.01 0.02 0.03 0.04 0 20 40 60 80 100 0.00 0.01 0.02 0.03 0.04 ฏۉ஋ = 50 ͷ৔߹ ඪ४ภࠩ ඪ४ภࠩ = 10 ඪ४ภࠩ = 20

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ʢ٢ా, 1998, p. 173ʣ ඪ४ภࠩ

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ʢ٢ా, 1998, p. 173ʣ ඪ४ภࠩ ࠩ͸ಉ͡

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ඪ४ภࠩ ॏͳΓͷྔ͕ҧ͏

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ݴ͑ͦ͏ͳ͜ͱ • ฏۉ஋ͷൺֱ͚ͩͰ͸ෆे෼ • σʔλͷ෼෍ʢ޿͕Γʣ΋߹Θͤͯݕ౼ • ෼෍ͷॏͳΓ͕গͳ͍ํ͕͕ࠩେ͖͍

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΋͏Ұ౓ൺ΂ͯΈΑ͏ Group A Group B 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0 20 40 60 80 100 0.000 0.005 0.010 0.015 0.020 0.025 0.030

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΋͏Ұ౓ൺ΂ͯΈΑ͏ 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 0,10" 11,20" 21,30" 31,40" 41,50" 51,60" 61,70" 71,80" 81,90" 91,100" Group"A" Group"B" ࣮ࡍͷ෼෍Λϓϩοτͨ͠΋ͷ

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΋͏Ұ౓ൺ΂ͯΈΑ͏ 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 0,10" 11,20" 21,30" 31,40" 41,50" 51,60" 61,70" 71,80" 81,90" 91,100" Group"A" Group"B" ͜ͷॏͳΓ͸େ͖͍ͷʁখ͍͞ͷʁ

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ࢦඪ͕΄͍͠

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ޮՌྔʢEﬀect Sizeʣ

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ޮՌྔʢEﬀect Sizeʣ • ޮՌͷେ͖͞Λ͋ΒΘ͢౷ܭతͳࢦඪ  ʢେٱอɾԬా, 2012, p. 44ʣ • ඪຊαΠζʢe.g., ਓ਺ʣʹґଘ͠ͳ͍

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༗ҙੑͱޮՌྔ

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Figure 1. (N = 10) Figure 2. (N = 119) r = .627 r = .184 p = .052 p = .045 > ༗ҙͰͳ͍ʛ༗ҙ 0 2 4 6 8 10 0 2 4 6 8 10 0 3 6 9 12 15 0 3 6 9 12 15

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ʮʢ౷ܭతʣ༗ҙʯͱ͸ • ໨ͷલͷσʔλʢඪຊʣ͔ΒΑΓେ͖ͳจ຺ ʢ฼ूஂʣΛਪఆ͢Δ • ඪຊͰ؍࡯͞ΕΔࠩɾؔ܎͕ɺ฼ूஂ͔Βͷ ඪຊநग़࣌ͷޡࠩͰੜ͡Δ֬཰ʢp ஋ʣΛ  ܭࢉ͢Δ • p ஋͕ج४஋ʢྟք஋ʣҎԼͰ͋Ε͹ʮ༗ҙʯ Ͱ͋ΔʢޡࠩͰ͸ͳ͍ʣͱ൑அ͢Δ

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ʮʢ౷ܭతʣ༗ҙʯͱ͸ • ૬ؔ෼ੳͷ৔߹ɺඪຊͰݟΒΕΔ૬͕ؔແ૬ ؔʢ૬ؔθϩʣͷ฼ूஂ͔Βͷඪຊநग़࣌ͷ ޡࠩͰੜ͡Δ֬཰ʢp ஋ʣΛܭࢉ͢Δ

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฼ूஂ ඪɹຊ ਪఆ σʔλղੳ Σ, F, t, p... ฼ूஂͱඪຊ

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• ͋ΔඪຊͰಘΒΕͨ୅ද஋ʢe.g., ฏۉʣ ͱ฼ूஂͷ୅ද஋ͱͷࠩ ඪຊޡࠩ

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฼ूஂ  μ = 15.3 ඪຊA  M = 14.7 ඪຊB  M = 15.9 ඪຊC  M = 15.2 ඪຊD  M = 15.4 ඪຊE  M = 15.1

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฼ूஂ  μ = 14.7 ඪຊA  M = 14.7 ࣮ࡍ͸ M = μ ͱͯ͠ਪఆ

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• ඪຊͷαΠζ͕େ͖͚Ε͹େ͖͍΄Ͳɺ ඪຊޡࠩ͸খ͘͞ͳΔ • ͭ·Γਪఆͷਫ਼౓͕ߴ͘ͳΔ ඪຊޡࠩ

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N 3 4 5 10 20 30 ྟք஋ (α = .05) 0.997 0.950 0.878 0.632 0.444 0.361 N 40 50 100 200 500 1000 ྟք஋ (α = .05) 0.312 0.279 0.197 0.139 0.088 0.062 *͜ΕΑΓେ͖͍਺஋ͩͬͨΒۮવͰͳ͍ͱΈͳ͢ ૬ؔ܎਺ʢrʣͱྟք஋*

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ʢ٢ా, 1998, p. 75ʣ ૬ؔ܎਺ʢrʣͷҙຯ

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Figure 1. (N = 10) Figure 2. (N = 119) r = .627 r = .184 p = .052 p = .045 0 2 4 6 8 10 0 2 4 6 8 10 0 3 6 9 12 15 0 3 6 9 12 15 ΋͏Ұ౓ൺ΂ͯΈΑ͏

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༗ҙͳࠩʢ·ͨ͸ɺ༗ҙͳ૬ؔʣ͕ಘΒΕ΍͍͢ݚڀΛ͢ΔͨΊ ͷ͖ΘΊͯ༗ޮͳํ๏͕͋Γ·͢ɻͦΕ͸ɺͱʹ͔͘ଟ͘ͷσʔ λΛूΊΔ͜ͱͰ͢ɻͳͥͳΒ͹ɽɽɽ౷ܭతݕఆͷ݁Ռ͸σʔ λ਺͕ଟ͍΄Ͳ༗ҙʹͳΓ΍͍͔͢ΒͰ͢ɻͦͷͨΊɺσʔλ਺ Λ૿΍͑͢͠͞Ε͹ɺ͖ΘΊͯখ͞ͳࠩͰ΋ “ʢ౷ܭతʹ͸ʣ༗ ҙͰ͋Δ” ͱ͍͏݁ՌʹͳΔՄೳੑ͕ߴ·Γ·͢ɻྫ͑͹ɺN = 1000 ͷ৔߹ʹ͸ɺr = 0.062 ͱ͍͏͖ΘΊͯখ͞ͳ૬ؔ܎਺ʢ͢ ͳΘͪɺඇৗʹऑ͍ؔ܎ʣͰ΋༗ҙʹͳΓ·͢ɽɽɽɻ͜ͷΑ͏ ʹɺ౷ܭతਪఆʹ͸ɺ“σʔλ਺ͱ͍͏ɺݚڀऀ͕೚ҙʹܾΊΒ ΕΔཁҼʹΑͬͯ݁Ռ͕ࠨӈ͞Εͯ͠·͏” ͱ͍͏ࠜຊతͳ໰୊ ͕͋Γ·͢ɻʢ٢ా, 1998, p. 232; Լઢ͸Ӝ໺ʹΑΔʣ ༗ҙੑݕఆͱඪຊαΠζ

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Ͳ͏͢Δʁ

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• ࠩ΍ؔ܎Λද͢ɺඪຊαΠζʹ  ґଘ͠ͳ͍ࢦඪ͕΄͍͠ • ͦΕ͕ޮՌྔʢeﬀect sizeʣ • ࣮͸૬ؔ܎਺ r ΋ޮՌྔͷࢦඪʢޙड़ʣ

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ޮՌྔͷछྨ

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• ࠩͷେ͖͞Λද͢ࢦඪʢd ଒ʣ • ؔ܎ͷڧ͞Λද͢ࢦඪʢr ଒ʣ େ͖͘෼͚ͯ̎ͭ

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ࠩͷେ͖͞Λද͢ࢦඪ Cohen’s d

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pooled SD X X d 2 1 − = ←ɹฏۉͷࠩ ←ɹඪ४ภࠩ Cohen’s d ʮ̎ͭͷάϧʔϓͷࠩ͸ඪ४ภࠩԿݸ෼ʯ

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pooled SD X X d 2 1 − = | 52.1 - 57.1| = (15.1 + 16.4) / 2* *ඪຊαΠζ͕ҟͳΔͱ͖ɺSDpooled ͷܭࢉ͸΋͏গ͠ෳࡶʹͳΓ·͢ Cohen’s d Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ 15.1 16.4

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pooled SD X X d 2 1 − = 5.0 = 15.75 *ඪຊαΠζ͕ҟͳΔͱ͖ɺSDpooled ͷܭࢉ͸΋͏গ͠ෳࡶʹͳΓ·͢ Cohen’s d Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ 15.1 16.4 = 0.32

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d 0 0.1 0.2 0.3 0.4 0.5 0.6 ॏͳΓ ʢˋʣ 100 92.3 85.7 78.7 72.6 67 61.8 d 0.7 0.8 0.9 1 1.1 1.2 1.3 ॏͳΓ ʢˋʣ 57 52.6 48.4 44.6 41.1 37.8 34.7 ޮՌྔ d ͱ෼෍ͷॏͳΓ

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0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 0,10" 11,20" 21,30" 31,40" 41,50" 51,60" 61,70" 71,80" 81,90" 91,100" Group"A" Group"B" d = 0.32 ͳͷͰॏͳΓ͸ 3/4 ͙Β͍ ࠶ͼ͜ͷάϥϑ

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ͭ·Γ

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Group A ͱ Group B ͸ɺ ฏۉ఺ʹ 5 ఺͕ࠩ͋Δ͕ɺ શମͷ 3/4 ͸ॏͳ͍ͬͯΔɻ

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ޮՌྔ d ͱॏͳΓͷؔ܎

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pooled SD X X d 2 1 − = ←ɹখ͍͞ํ͕ྑ͍ ←ɹେ͖͍ํ͕ྑ͍ d ஋͕େ͖͘ͳΔʹ͸ ʮฏۉͷ͕ࠩେ͖͘ɺඪ४ภ͕ࠩখ͘͞ͳΔͱɺ ޮՌྔ͸େ͖͘ͳΔɻʯ

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ޮՌྔͷղऍ

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• Cohen (1988) • small: d = 0.2, overlap: 85.7% • e.g., 15ࡀͱ16ࡀͷঁࢠͷ਎௕ࠩ • medium: d = 0.5, overlap: 67.0% • e.g., 14ࡀͱ18ࡀͷঁࢠͷ਎௕ࠩ • large: d = 0.8, overlap: 52.6% • e.g., େֶ৽ೖੜͱPhDऔಘऀͷIQࠩ ޮՌྔͷղऍ

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• Plonsky & Oswald (2014) • “L2 field-specific benchmarks” ޮՌྔͷղऍ ܈ؒൺֱ ܈಺ൺֱ small d = 0.40 d = 0.60 medium d = 0.70 d = 1.00 large d = 1.00 d = 1.40

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ͨͩ͠

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• ͜ͷΑ͏ͳࢦඪ͸͋͘·Ͱ໨҆ • ࣮ࡍͷղऍ͸ݚڀऀࣗ਎ͷ੹೚Ͱ

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༗ҙੑݕఆ

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༗ҙੑݕఆ ॏͳΓͷେ͖͞͸Θ͔͚ͬͨͲɺ  ͜ͷࠩ͸ۮવʁ

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༗ҙੑݕఆ ؍࡯͞Ε͕ͨࠩۮવੜͨ͡΋ͷͰ͋Δ Մೳੑʢ֬཰ʣΛܭࢉ͠·͠ΐ͏

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t ݕఆ

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t ݕఆ ← ฏۉͷࠩ ← ඪ४ภࠩ2ͷ࿨  1 2 2 2 1 2 1 − + − = n SD SD X X t ↑ ʢ֤܈ͷඪຊαΠζʣ ʢඪຊαΠζ͕౳͍͠৔߹ʣ ʢ٢ా, 1998, p. 186ʣ

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͜Ε͖ͬ͞ݟͨʁ

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pooled SD X X d 2 1 − = ←ɹฏۉͷࠩ ←ɹඪ४ภࠩ Cohen’s d ʮ͜Εʹ n Λ଍͢ͱ t ͬΆ͍ʂʯ

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pooled SD X X d 2 1 − = 1 2 2 2 1 2 1 − + − = n SD SD X X t ʮt ͸ɺޮՌྔʹඪຊαΠζΛՃຯͨ͠΋ͷʯ

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←ɹখ͍͞ํ͕ྑ͍ ←ɹେ͖͍ํ͕ྑ͍ t ஋͕େ͖͘ͳΔʹ͸ 1 2 2 2 1 2 1 − + − = n SD SD X X t ↑ɹେ͖͍ํ͕ྑ͍

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n 1 2 3 4 5 ྟք஋ ྆ଆݕఆ5% 12.71 4.3 3.18 2.78 2.57 n 10 20 50 100 200 ྟք஋ ྆ଆݕఆ5% 2.23 2.09 2.01 1.98 1.97 *͜ΕΑΓେ͖͍਺஋ͩͬͨΒۮવͰͳ͍ͱΈͳ͢ t ͷྟք஋*

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1 2 2 2 1 2 1 − + − = n SD SD X X t *2܈Ͱ n ͕ҟͳΔͱ͖ͷܭࢉ͸΋   ͏গ͠ෳࡶʹͳΓ·͢ * | 52.1-57.1| = √(15.32 + 16.72) / (30 - 1) ܭࢉͯ͠ΈΑ͏ Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ** 15.3 16.7 **ਪଌ౷ܭʢ༗ҙੑݕఆʣͰ࢖͏ͷ͸  ෆภ෼ࢄʹجͮ͘ඪ४ภࠩɻn ͷ  ୅ΘΓʹ n–1 Λܭࢉʹ࢖͍·͢ɻ

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1 2 2 2 1 2 1 − + − = n SD SD X X t * 5 = 4.21 ܭࢉͯ͠ΈΑ͏ = 1.18 Group A Group B ฏۉ஋ 52.1 57.1 ඪ४ภࠩ** 15.3 16.7 *2܈Ͱ n ͕ҟͳΔͱ͖ͷܭࢉ͸΋   ͏গ͠ෳࡶʹͳΓ·͢ **ਪଌ౷ܭʢ༗ҙੑݕఆʣͰ࢖͏ͷ͸  ෆภ෼ࢄʹجͮ͘ඪ४ภࠩɻn ͷ  ୅ΘΓʹ n–1 Λܭࢉʹ࢖͍·͢ɻ

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n 1 2 3 4 5 ྟք஋ ྆ଆݕఆ5% 12.71 4.3 3.18 2.78 2.57 n 10 20 50 100 200 ྟք஋ ྆ଆݕఆ5% 2.23 2.09 2.01 1.98 1.97 t ͷྟք஋ t = 1.18 ͸༗ҙͰͳ͍

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͜͜·Ͱͷ·ͱΊ

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• ޮՌྔ Cohen’s d • 2ͭͷάϧʔϓؒͷࠩΛඪ४Խͨ͠΋ͷ • t ݕఆ • ޮՌྔʹඪຊޡࠩͷӨڹΛՃຯͯ͠ɺͦͷ͕ࠩ ۮવ؍࡯͞ΕΔ֬཰Λࣔͨ͠΋ͷ • ݕఆ౷ܭྔ = ޮՌͷେ͖͞ x ඪຊͷେ͖͞ ʢೆ෩ݪ, 2002, p. 163ʣ

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• Cohen’s d ͷ஥ؒ: • Hedges’ g • ෼฼ʹ฼ूஂͷඪ४ภࠩʢෆภ෼ࢄʹ جͮ͘ඪ४ภࠩʣΛ࢖͏ • Glass’ ⊿ • ෼฼ʹ౷੍܈ͷඪ४ภࠩΛ࢖͏

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ؔ܎ͷڧ͞Λද͢ࢦඪ Pearson’s r / r2

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• ม਺ؒͷؔ܎ͷେ͖͞Λද͢ • ࠷େ: 1.0ʢઈର஋ʣ • ࠷খ: 0 • ϐΞιϯͷੵ཰૬ؔ܎਺ r • r2 ʢ෼ࢄઆ໌཰ʣ Pearson’s r / r2

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෼ࢄ෼ੳͷ৔߹

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෼ࢄ෼ੳͷ৔߹ ௐ΂͍ͨཁҼͷ෼ࢄ η2 = ૯෼ࢄ SSA = SST

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ҰཁҼ෼ࢄ෼ੳ SS df MS F p η2 A 847.609 2 423.805 0.955 .389 .022 Error 37259.655 84 443.567 Total 38107.264 MacR ʹ෇ଐͷσʔλΛ࢖ͬͯ MacR Ͱܭࢉ

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ҰཁҼ෼ࢄ෼ੳ SS df MS F p η2 A 847.609 2 423.805 0.955 .389 .022 Error 37259.655 84 443.567 Total 38107.264 / = / = MS = SS / df

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ҰཁҼ෼ࢄ෼ੳ SS df MS F p η2 A 847.609 2 423.805 0.955 .389 .022 Error 37259.655 84 443.567 Total 38107.264 / = ↑ɹඪຊαΠζ͕େ͖͍ͱ F ஋͕େ͖͘ͳΔ F = MSA / MSE = 423.805 / 443.567 = 0.955

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ҰཁҼ෼ࢄ෼ੳ SS df MS F p η2 A 847.609 2 423.805 0.955 .389 .022 Error 37259.655 84 443.567 Total 38107.264 + = η2 = SSA / SST = 847.609 / 38107.264 = .022

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ޮՌྔͷղऍ

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• small: η2 = .01 • medium: η2 = .06 • large: η2 = .14 ਫຊɾ஛಺ (2008) • ͜ͷΑ͏ͳࢦඪ͸͋͘·Ͱ໨҆ • ࣮ࡍͷղऍ͸ݚڀऀࣗ਎ͷ੹೚Ͱ

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͜͜·Ͱͷ·ͱΊ

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• r ଒ͷޮՌྔ • ม਺ؒͷؔ܎ͷڧ͞Λ਺஋Ͱࣔͨ͠΋ͷ • ࠷େͰ 1.0ɺ࠷খͰ 0 • ෼ࢄ෼ੳͰ࢖͏ η2 ͸ r2 ͱࣅͨײ͡ • F ͱ η2 ͷҧ͍͸ඪຊαΠζΛߟྀ͢Δ͔Ͳ͏͔ • ݕఆ౷ܭྔ = ޮՌͷେ͖͞ x ඪຊͷେ͖͞ ʢೆ෩ݪ, 2002, p. 163ʣ

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• η2 ͷ஥ؒ: • partial η2 • ෼฼ʹ SSA + SSE Λ࢖͏ • ω2 • ฼෼ࢄਪఆͷͨΊͷόΠΞεΛऔΓআ ͍ͨ΋ͷ

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ޮՌྔͷ৴པ۠ؒ

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ޮՌྔͷ৴པ۠ؒ • ฼ूஂͷਪఆΛલఏͱ͢ΔޮՌྔ͸఺ਪఆ • ඪຊޡࠩΛߟྀ͢Δඞཁ͕͋Δ • ޮՌྔͷ۠ؒਪఆ΋ߦ͏ͱΑ͍

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• ఺ਪఆ • ฼ूஂΛ୅ද͢Δ఺ͷਪఆ • ۠ؒਪఆ • ఺ਪఆͷ͹Β͖ͭͷਪఆ • ৴པ۠ؒ • ͋Δ֬཰ʢe.g., 95%ʣͰਪఆ͞Εͨ۠ؒ ޮՌྔͷ৴པ۠ؒ

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࣮ࡍʹ ܭࢉͯ͠Έ·͠ΐ͏

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http://www.mizumot.com/stats/eﬀectsize.xls ޮՌྔͷܭࢉγʔτ

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http://www.mizumot.com/stats/eﬀectsize.xls

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Cohen’s d Λܭࢉͯ͠ΈΑ͏

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Cohen’s d Λܭࢉͯ͠ΈΑ͏

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Cohen’s d Λܭࢉͯ͠ΈΑ͏

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Cohen’s d Λܭࢉͯ͠ΈΑ͏

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η2 Λܭࢉͯ͠ΈΑ͏

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η2 Λܭࢉͯ͠ΈΑ͏

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http://www.langtest.jp Eﬀect Size Calculator @

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• σʔλ෼ੳ͕ͳΜͰ΋  Ͱ͖ͪΌ͏΋ͷ͍͢͝  ΢ΣϒΞϓϦ • ޮՌྔ d, g ͱͦͷ৴པ۠ ؒΛܭࢉͯ͘͠ΕΔ • ਫຊಞ͞Μʢؔ੢େֶʣ ͕։ൃ͠ɺແྉͰެ։ • ͓ྱ͸Ϗʔϧ·ͨ͸  νϣίϨʔτͰ

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ࢀߟจݙ

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ࢀߟจݙ • ӳޠڭࢣͷͨΊͷڭҭσʔλ ෼ੳೖ໳ • ༗ҙੑݕఆͷ͘͠Έ΍ͦͷݶ քʹ͍ͭͯ΋ղઆ

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ࢀߟจݙ • ຊ౰ʹΘ͔Γ΍͍͘͢͢͝େ ੾ͳ͜ͱ͕ॻ͍ͯΔ͘͝ॳา ͷ౷ܭͷຊ • େ੾ͳ͜ͱΛ਺ࣜΛަ͑ͯஸ ೡʹղઆ

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ࢀߟจݙ • ֎ࠃޠڭҭݚڀϋϯυϒοΫ • هड़౷ܭɺਪଌ౷ܭɺޮՌྔ ΋ؚΊͯ໢ཏతͳҰ࡭

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ࢀߟจݙ • ఻͑ΔͨΊͷ৺ཧ౷ܭ • ޮՌྔʹ͍ͭͯษڧ͢ΔͳΒ ඞಡ

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ࢀߟจݙ • ͸͡Ίͯͷӳޠڭҭݚڀ • ݚڀͷೖޱΛղઆ͢ΔҰ࡭ɻ ࠓ೔ͷ಺༰͸ୈ6ষΛิ଍͢ Δ΋ͷ

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1. ෼෍ͱඪ४ภࠩ 2. ༗ҙੑʢݕఆʣͱޮՌྔ 3. ޮՌྔͷछྨ • ࠩͷେ͖͞Λද͢ d ଒ • ؔ܎ͷڧ͞Λද͢ r ଒ 4. ޮՌྔͷ৴པ۠ؒ 5. ޮՌྔͷܭࢉ Ken Urano urano@hgu.jp http://bit.ly/let2016ws ྔతσʔλΛѻ͏ͱ͖ʹ ஌͓͖͍ͬͯͨ͜ͱ —σʔλͷ෼෍ɺ༗ҙੑɺޮՌྔɺ৴པ۠ؒ—

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ࢀߟจݙ • Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates. • ೆ෩ݪே࿨. (2002). ʰ৺ཧ౷ܭֶͷجૅ: ౷߹తཧղͷͨΊʹʱ౦ژ: ༗൹ֳ. • લాܒ࿕ɾࢁ৿ޫཅ (ฤ). (2004). ʰӳޠڭࢣͷͨΊͷڭҭσʔλ෼ੳೖ໳: तۀ͕มΘ ΔςετɾධՁɾݚڀʱ౦ژ: େमؗॻళ. • ਫຊಞɾ஛಺ཧ. (2008). ʮݚڀ࿦จʹ͓͚ΔޮՌྔͷใࠂͷͨΊʹ: جૅత֓೦ͱ஫ҙ ఺ʯʰӳޠڭҭݚڀʱୈ31߸, 57–66. Retrieved from http://www.mizumot.com/files/ EﬀectSize_KELES31.pdf • େٱอ֗ѥɾԬాݠհ. (2012). ʰ఻͑ΔͨΊͷ৺ཧ౷ܭ: ޮՌྔɾ৴པ۠ؒɾݕఆྗʱ ౦ژ: Ⴛ૲ॻ๪. • Plonsly, L., & Oswald, F. (2014). How big is “big”? Interpreting eﬀect Sizes in L2 research. Language Learning, 64, 878–912. doi:10.1111/lang.12079 • ஛಺ཧɾਫຊಞ (ฤ). (2014). ʰ֎ࠃޠڭҭݚڀϋϯυϒοΫ: ݚڀख๏ͷΑΓྑ͍ཧղ ͷͨΊʹ (վగ൛)ʱ౦ژ: দദࣾ. • Ӝ໺ݚɾ࿱ཧཅҰɾాத෢෉ɾ౻ా୎࿠ɾ∁໦ѥرࢠɾञҪӳथ. (2016). ʰ͸͡Ίͯͷ ӳޠڭҭݚڀ: ԡ͓͖͍͑ͯͨ͞ίπͱϙΠϯτʱ౦ژ: ݚڀࣾ. • ٢ాण෉. (1998). ʰຊ౰ʹΘ͔Γ΍͍͘͢͢͝େ੾ͳ͜ͱ͕ॻ͍ͯ͋Δ͘͝ॳาͷ౷ܭ ͷຊʱژ౎: ๺େ࿏ॻ๪.