外国語教育（研究）における量的データの視覚化と解釈

FLEAT VII (LET2019) ワークショップ
2019/08/06
@早稲田大学

Transcript

1. ֎ࠃޠڭҭʢݚڀʣʹ͓͚Δ
   ྔతσʔλͷࢹ֮Խͱղऍ
   Ӝ໺ ݚʢ๺ւֶԂେֶʣ
   email: urano@hgu.jp
   FLEAT VII / LET2019 @ Waseda University
   ɹɹ2019. 8. 6.
   https://www.urano-ken.com/research/let2019
   

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2. ຊ೔ͷࢿྉ
   

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3. ֎ࠃޠڭҭʹܞΘΔࢲͨͪ͸ɺݚڀʹ͓͍͚ͯͩͰͳ
   ͘ɺςετ΍੒੷ॲཧͱ͍ͬͨ৔໘Ͱ೔͝Ζ͔Β਺ྔԽ
   ͞ΕͨσʔλΛѻ͍ͬͯ·͢ɻຊϫʔΫγϣοϓͰ͸ɺ
   ڭҭ΍ݚڀͰྔతσʔλΛѻ͏ࡍʹ·ͣߦ͏΂͖σʔλ
   ͷࢹ֮Խͱɺσʔλͷಛ௃Λཧղ͢ΔͨΊͷجຊతͳ֓
   ೦ͱͯ͠ͷ୅ද஋ɾ෼෍ɾޮՌྔͷҙຯʹֶ͍ͭͯͼɺ
   ϑϦʔͰΦʔϓϯιʔεͷ౷ܭιϑτ jamovi Λ࢖ͬͯɺ
   ࣮ࡍʹσʔλͷ؆୯ͳ෼ੳ͕Ͱ͖ΔΑ͏ʹͳΔ͜ͱΛ໨
   ࢦ͠·͢ɻ
   ཁࢫ
   

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4. ՍۭͷσʔλΛ
   ༻ҙ͠·ͨ͠
   

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5. 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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6. 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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7. 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
   ൺ΂ͯΈΑ͏
   How?
   

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8. ᶃ
   ਤʹͯ͠ΈΑ͏
   

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9. ώετάϥϜ (Histogram)
   B
   A
   20 40 60 80 100
   Score
   Group
   

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10. ๘܈ਤ (Beeswarm)
    20
    40
    60
    80
    A B
    Group
    Score
    

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11. ശͻ͛ਤ (Box Plot)
    20
    40
    60
    80
    A B
    Group
    Score
    

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12. ϰΝΠΦϦϯਤ (Violin Plot)
    20
    40
    60
    80
    A B
    Group
    Score
    

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13. ֬཰ີ౓ (Density)
    B
    A
    30 60 90
    Score
    Group
    

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14. ֬཰ີ౓ (Density)
    B
    A
    30 60 90
    Score
    Group
    

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15. ਤʹͯ͠ΈΑ͏
    • ऩूͨ͠σʔλʹͲͷΑ͏ͳಛ௃͕͋Δ͔ɺ
    ͬ͘͟Γ೺Ѳ͢Δ͜ͱ͕Ͱ͖Δɻ
    • ໨ͰݟΔ͚ͩͳͷͰɺݫີͳൺֱ΍෼ੳʹ͸
    ద͞ͳ͍ɻ
    

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16. ᶄ
    ཁ໿ͯ͠ΈΑ͏
    

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17. σʔλͷத৺ͱ
    ͹Β͖ͭ
    σʔλͷத৺
    

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18. ฏۉ஋ ͢΂ͯͷσʔλͷ߹ܭΛσʔλͷݸ਺Ͱ
    ׂͬͨ΋ͷ
    தԝ஋ ͢΂ͯͷσʔλΛখ͍͞ॱʢ·ͨ͸େ͖͍
    ॱʣʹฒ΂ͨͱ͖ɺਅΜதʹདྷΔ஋
    ࠷ස஋ ͢΂ͯͷσʔλͷதͰग़ݱճ਺͕࠷΋ଟ͍
    ஋
    σʔλͷத৺
    

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19. Group A Group B
    ฏۉ஋ 52.1 57.1
    தԝ஋ 49.0 53.5
    ࠷ස஋ 38, 58 41, 51
    σʔλͷத৺
    

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20. ඪ४ภࠩ
    σʔλͷ͹Β͖ͭ
    

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21. • ݸʑͷ਺஋ͱฏۉ஋ͱͷࠩΛ̎৐͠ɺ

    ͦͷ߹ܭΛσʔλͷ਺Ͱׂͬͨ΋ͷͷฏํࠜ
    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
    ←ʢ෼ࢄʣ
    ඪ४ภࠩ
    

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22. • ݸʑͷ਺஋ͱฏۉ஋ͱͷࠩΛ̎৐͠ɺ

    ͦͷ߹ܭΛσʔλͷ਺Ͱׂͬͨ΋ͷͷฏํࠜ
    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
    ඪ४ภࠩ
    

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23. 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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24. 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
    ඪ४ภࠩ
    

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25. ʢ٢ా, 1998, p. 173ʣ
    ඪ४ภࠩ
    

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26. ʢ٢ా, 1998, p. 173ʣ
    ࠩ͸ಉ͡
    ඪ४ภࠩ
    

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27. ॏͳΓͷྔ͕ҧ͏
    ඪ४ภࠩ
    

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28. Group A Group B
    ฏۉ஋ 52.1 57.1
    ඪ४ภࠩ 15.1 16.4
    

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29. 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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30. 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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31. 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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32. ݴ͑ͦ͏ͳ͜ͱ
    • ฏۉ஋ͷൺֱ͚ͩͰ͸ෆे෼
    • σʔλͷ෼෍ʢ͹Β͖ͭʣ΋߹Θͤͯݕ౼
    • ෼෍ͷॏͳΓ͕গͳ͍ํ͕͕ࠩେ͖͍
    

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33. ΋͏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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34. ΋͏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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35. ΋͏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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36. ࢦඪ͕΄͍͠
    

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37. ޮՌྔʢEffect Sizeʣ
    • ޮՌͷେ͖͞Λ͋ΒΘ͢౷ܭతͳࢦඪ

    ʢେٱอɾԬా, 2012, p. 44ʣ
    

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38. ޮՌྔͷछྨ
    

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39. • ࠩͷେ͖͞Λද͢ࢦඪʢd ଒ʣ
    • ؔ܎ͷڧ͞Λද͢ࢦඪʢr ଒ʣ
    େ͖͘෼͚ͯ̎ͭ
    

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40. ࠩͷେ͖͞Λද͢ࢦඪ
    Cohen’s d
    

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

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

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

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44. 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 1.0 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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45. 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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46. ͭ·Γ
    

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

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48. ޮՌྔ d ͱॏͳΓͷؔ܎
    

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49. pooled
    SD
    X
    X
    d
    2
    1 −
    =
    ←ɹখ͍͞ํ͕ྑ͍
    ←ɹେ͖͍ํ͕ྑ͍
    d ஋͕େ͖͘ͳΔʹ͸
    ʮฏۉͷ͕ࠩେ͖͘ɺඪ४ภ͕ࠩখ͘͞ͳΔ
    ͱɺޮՌྔ͸େ͖͘ͳΔɻʯ
    

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

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52. ͨͩ͠
    

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53. • ͜ͷΑ͏ͳࢦඪ͸͋͘·Ͱ໨҆
    • ࣮ࡍͷղऍ͸ݚڀऀࣗ਎ͷ੹೚Ͱ
    

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54. ༗ҙੑݕఆ
    ॏͳΓͷେ͖͞͸Θ͔͚ͬͨͲɺ

    ͜ͷࠩ͸ۮવʁ
    

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55. ؍࡯͞Ε͕ͨࠩۮવੜͨ͡΋ͷͰ͋Δ
    Մೳੑʢ֬཰ʣ
    ༗ҙੑݕఆ
    

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56. ʮʢ౷ܭతʣ༗ҙੑʯͱ͸
    • ໨ͷલͷσʔλʢඪຊʣ͔ΒΑΓେ͖ͳจ຺
    ʢ฼ूஂʣΛਪఆ͢Δ
    • ඪຊͰ؍࡯͞ΕΔࠩɾؔ܎͕ɺ฼ूஂ͔Βͷ
    ඪຊநग़࣌ͷޡࠩͰੜ͡Δ֬཰ʢp ஋ʣΛ

    ܭࢉ͢Δ
    • p ஋͕ج४஋ʢྟք஋ʣҎԼͰ͋Ε͹ʮ༗ҙʯ
    Ͱ͋ΔʢޡࠩͰ͸ͳ͍ʣͱ൑அ͢Δ
    

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57. ฼ूஂ ඪɹຊ
    ਪఆ
    σʔλղੳ
    Σ, F, t, p...
    ฼ूஂͱඪຊ
    

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

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59. ฼ूஂ

    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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60. ฼ूஂ

    μ = 14.7
    ඪຊA

    M = 14.7
    ࣮ࡍ͸ M = μ ͱͯ͠ਪఆ
    

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

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62. 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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63. ͜Ε͖ͬ͞ݟͨʁ
    

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

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

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67. ࣗ༝౓** 3 4 5 10 20 30
    ྟք஋
    ྆ଆݕఆ5%
    3.182 2.776 2.571 2.228 2.086 2.042
    ࣗ༝౓
    40 50 100 200 500 1,000
    ྟք஋
    ྆ଆݕఆ5%
    2.021 2.009 1.984 1.972 1.965 1.962
    *͜ΕΑΓେ͖͍਺஋ͩͬͨΒۮવͰͳ͍ͱΈͳ͢
    **n1
    +n2
    -2
    t ͷྟք஋*
    

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68. 1
    2
    2
    2
    1
    2
    1
    −
    +
    −
    =
    n
    SD
    SD
    X
    X
    t
    *2܈Ͱ n ͕ҟͳΔͱ͖ͷܭࢉ͸΋ 

    ͏গ͠ෳࡶʹͳΓ·͢
    *
    | 52.1-57.1|
    =
    √(15.12 + 16.42) / (30 - 1)
    ܭࢉͯ͠ΈΑ͏
    Group A Group B
    ฏۉ஋ 52.1 57.1
    ඪ४ภࠩ 15.1 16.4
    

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69. 1
    2
    2
    2
    1
    2
    1
    −
    +
    −
    =
    n
    SD
    SD
    X
    X
    t
    *
    5
    =
    4.14
    ܭࢉͯ͠ΈΑ͏
    = 1.21
    Group A Group B
    ฏۉ஋ 52.1 57.1
    ඪ४ภࠩ 15.1 16.4
    *2܈Ͱ n ͕ҟͳΔͱ͖ͷܭࢉ͸΋ 

    ͏গ͠ෳࡶʹͳΓ·͢
    

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70. ࣗ༝౓** 3 4 5 10 20 30
    ྟք஋
    ྆ଆݕఆ5%
    3.182 2.776 2.571 2.228 2.086 2.042
    ࣗ༝౓
    40 50 100 200 500 1,000
    ྟք஋
    ྆ଆݕఆ5%
    2.021 2.009 1.984 1.972 1.965 1.962
    t ͷྟք஋
    t (58) = 1.21 ͸༗ҙͰͳ͍
    

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71. ͜͜·Ͱͷ·ͱΊ
    

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72. • ޮ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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73. • Cohen’s d ͷ஥ؒ:
    • Hedges’ g
    • ෼฼ʹ฼ूஂͷඪ४ภࠩʢෆภ෼ࢄʹ
    جͮ͘ඪ४ภࠩʣΛ࢖͏
    • Glass’ ⊿
    • ෼฼ʹ౷੍܈ͷඪ४ภࠩΛ࢖͏
    

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74. ؔ܎ͷڧ͞Λද͢ࢦඪ
    Pearson’s r / r2
    

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

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76. ෼ࢄ෼ੳͷ৔߹
    ௐ΂͍ͨཁҼͷ෼ࢄ
    η2 =
    ૯෼ࢄ
    SSA
    =
    SSTotal
    

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77. ҰཁҼ෼ࢄ෼ੳ
    SS df MS F p η2
    A 

    (Class)
    848 2 424 0.955 .389 .022
    Error
    (Residuals)
    37260 84 444
    ஛಺ɾਫຊ (2014) ୈ6ষͷσʔλΛ࢖ͬͯ jamovi Ͱܭࢉ
    

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78. ҰཁҼ෼ࢄ෼ੳ
    SS df MS F p η2
    A 

    (Class)
    848 2 424 0.955 .389 .022
    Error
    (Residuals)
    37260 84 444
    / =
    / =
    MS = SS / df
    

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79. ҰཁҼ෼ࢄ෼ੳ
    SS df MS F p η2
    A 

    (Class)
    848 2 424 0.955 .389 .022
    Error
    (Residuals)
    37260 84 444
    /
    =
    ↑ɹඪຊαΠζ͕େ͖͍ͱ F ஋͕େ͖͘ͳΔ
    F = MSA
    / MSError
    = 424 / 444 = 0.955
    

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80. ҰཁҼ෼ࢄ෼ੳ
    SS df MS F p η2
    A 

    (Class)
    848 2 424 0.955 .389 .022
    Error
    (Residuals)
    37260 84 444
    +
    η2 = SSA
    / SSTotal
    = 848 / 38108 = .022
    SSTotal
    = SSA
    + SSError
    = 848 + 37260 = 38108
    

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81. ޮՌྔͷղऍ
    

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

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83. ͜͜·Ͱͷ·ͱΊ
    

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84. • 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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85. • η2 ͷ஥ؒ:
    • partial η2
    • ෼฼ʹ SSA
    + SSError Λ࢖͏
    • ω2
    • ฼෼ࢄਪఆͷͨΊͷόΠΞεΛऔΓআ
    ͍ͨ΋ͷ
    

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86. ࣮ࡍʹ
    ܭࢉͯ͠Έ·͠ΐ͏
    

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87. • Φʔϓϯιʔεͷ౷ܭϓϩάϥϛϯάݴޠ

    ɹɹΛ࢖͍΍͍͢ܗʹͨ͠ιϑτ΢ΣΞɻ
    • GUIͷͨΊ௚ײతʹ࢖͑Δɻ
    • ΦʔϓϯιʔεͰແྉͰ࢖͑Δɻ
    

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88. https://www.jamovi.org
    

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89. ϋϯζΦϯ
    

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90. • Must-read:
    • Navarro, D. J., & Foxcroft, D. R. (2019). Learning
    statistics with jamovi: A tutorial for psychology
    students and other beginners. (Version 0.70).

    DOI: 10.24384/hgc3-7p15
    • ೔ຊޠ༁΋͋Γ·͢:
    • ࣳా੐࢘༁. jamoviͰֶͿ৺ཧ౷ܭ.

    https://bookdown.org/sbtseiji/lswjamoviJ/
    

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91. ஫ҙ఺
    

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92. View Slide

93. • ϑΝΠϧಡΈࠐΈ࣌ʹࣗಈత
    ʹ൑அ͞ΕΔม਺ͷछྨ͕ؒ
    ҧ͍ͬͯΔ͜ͱ͕͋Δɻ
    • Continuous ࿈ଓม਺
    • Ordinal ॱংม਺
    • Nominal ໊ٛม਺
    

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

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95. • σʔλ෼ੳ͕ͳΜͰ΋

    Ͱ͖ͪΌ͏΋ͷ͍͢͝

    ΢ΣϒΞϓϦ
    • ޮՌྔ d, g ͱͦͷ৴པ۠
    ؒΛܭࢉͯ͘͠ΕΔ
    • ਫຊಞ͞Μʢؔ੢େֶʣ
    ͕։ൃ͠ɺແྉͰެ։
    • ͓ྱ͸Ϗʔϧ·ͨ͸

    നϫΠϯͰ
    

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96. View Slide

97. View Slide

98. ஫. ਪଌ౷ܭʢ༗ҙੑݕఆʣͰ࢖͏
    ඪ४ภࠩʢSDʣ͸ෆภ෼ࢄʹجͮ͘
    ΋ͷɻn ͷ୅ΘΓʹ n–1 Λܭࢉʹ࢖
    ͍·͢ɻ
    

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99. View Slide

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

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

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

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103. ࢀߟจݙ
     • ఻͑ΔͨΊͷ৺ཧ౷ܭ
     • ޮՌྔʹ͍ͭͯษڧ͢ΔͳΒ
     ඞಡ
     

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

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105. 1. σʔλͷࢹ֮Խʢਤࣔʣ
     2. σʔλͷཁ໿ʢத৺ͱ͹Β͖ͭʣ
     3. ޮՌྔ
     • ࠩͷେ͖͞Λද͢ d ଒
     • ؔ܎ͷڧ͞Λද͢ r ଒
     4. ༗ҙੑݕఆʢਪଌ౷ܭʣ
     5. jamovi ͱ langtest.jp Ken Urano
     urano@hgu.jp
     https://www.urano-ken.com/research/let2019
     ֎ࠃޠڭҭʢݚڀʣʹ͓͚Δ
     ྔతσʔλͷࢹ֮Խͱղऍ
     

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106. 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. http://www.mizumot.com/files/
     EffectSize_KELES31.pdf
     • Navarro, D. J., & Foxcroft, D. R. (2019). Learning statistics with jamovi: A tutorial for
     psychology students and other beginners. (Version 0.70). doi: 10.24384/hgc3-7p15

     ʢࣳా੐࢘༁. jamoviͰֶͿ৺ཧ౷ܭ. https://bookdown.org/sbtseiji/lswjamoviJ/ʣ
     • େ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๪.
     

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