• ࠩؔΛද͢ɺඪຊαΠζʹ
ґଘ͠ͳ͍ࢦඪ͕΄͍͠
• ͦΕ͕ޮՌྔʢeffect sizeʣ
• ࣮૬ؔ r ޮՌྔͷࢦඪʢޙड़ʣ
Slide 45
Slide 45 text
ޮՌྔͷछྨ
Slide 46
Slide 46 text
• ࠩͷେ͖͞Λද͢ࢦඪʢd ʣ
• ؔͷڧ͞Λද͢ࢦඪʢr ʣ
େ͖͚ͯ̎ͭ͘
Slide 47
Slide 47 text
ࠩͷେ͖͞Λද͢ࢦඪ
Cohen’s d
Slide 48
Slide 48 text
pooled
SD
X
X
d
2
1 −
=
←ɹฏۉͷࠩ
←ɹඪ४ภࠩ
Cohen’s d
ʮ̎ͭͷάϧʔϓͷࠩඪ४ภࠩԿݸʯ
Slide 49
Slide 49 text
pooled
SD
X
X
d
2
1 −
=
| 52.1 - 57.1|
=
(15.1 + 16.4) / 2*
*ඪຊαΠζ͕ҟͳΔͱ͖ɺSDpooled
ͷܭࢉ͏গ͠ෳࡶʹͳΓ·͢
Cohen’s d
Group A Group B
ฏۉ 52.1 57.1
ඪ४ภࠩ 15.1 16.4
Slide 50
Slide 50 text
pooled
SD
X
X
d
2
1 −
=
5.0
=
15.75
*ඪຊαΠζ͕ҟͳΔͱ͖ɺSDpooled
ͷܭࢉ͏গ͠ෳࡶʹͳΓ·͢
Cohen’s d
Group A Group B
ฏۉ 52.1 57.1
ඪ४ภࠩ 15.1 16.4
= 0.32
• 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
Slide 60
Slide 60 text
ͨͩ͠
Slide 61
Slide 61 text
• ͜ͷΑ͏ͳࢦඪ͋͘·Ͱ҆
• ࣮ࡍͷղऍݚڀऀࣗͷͰ
Slide 62
Slide 62 text
༗ҙੑݕఆ
Slide 63
Slide 63 text
༗ҙੑݕఆ
ॏͳΓͷେ͖͞Θ͔͚ͬͨͲɺ
͜ͷࠩۮવʁ
Slide 64
Slide 64 text
༗ҙੑݕఆ
؍͞Ε͕ͨࠩۮવੜͨ͡ͷͰ͋Δ
Մೳੑʢ֬ʣΛܭࢉ͠·͠ΐ͏
Slide 65
Slide 65 text
t ݕఆ
Slide 66
Slide 66 text
t ݕఆ
← ฏۉͷࠩ
← ඪ४ภࠩ2ͷ
1
2
2
2
1
2
1
−
+
−
=
n
SD
SD
X
X
t
↑ ʢ֤܈ͷඪຊαΠζʣ
ʢඪຊαΠζ͕͍͠߹ʣ
ʢ٢ా, 1998, p. 186ʣ
Slide 67
Slide 67 text
͜Ε͖ͬ͞ݟͨʁ
Slide 68
Slide 68 text
pooled
SD
X
X
d
2
1 −
=
←ɹฏۉͷࠩ
←ɹඪ४ภࠩ
Cohen’s d
ʮ͜Εʹ n Λ͢ͱ t ͬΆ͍ʂʯ
Slide 69
Slide 69 text
pooled
SD
X
X
d
2
1 −
=
1
2
2
2
1
2
1
−
+
−
=
n
SD
SD
X
X
t
ʮt ɺޮՌྔʹඪຊαΠζΛՃຯͨ͠ͷʯ
Slide 70
Slide 70 text
←ɹখ͍͞ํ͕ྑ͍
←ɹେ͖͍ํ͕ྑ͍
t ͕େ͖͘ͳΔʹ
1
2
2
2
1
2
1
−
+
−
=
n
SD
SD
X
X
t
↑ɹେ͖͍ํ͕ྑ͍
Slide 71
Slide 71 text
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
*͜ΕΑΓେ͖͍ͩͬͨΒۮવͰͳ͍ͱΈͳ͢
t ͷྟք*
Slide 72
Slide 72 text
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༗ҙੑݕఆʣͰ͏ͷ
ෆภࢄʹجͮ͘ඪ४ภࠩɻn ͷ
ΘΓʹ n–1 Λܭࢉʹ͍·͢ɻ
Slide 73
Slide 73 text
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༗ҙੑݕఆʣͰ͏ͷ
ෆภࢄʹجͮ͘ඪ४ภࠩɻn ͷ
ΘΓʹ n–1 Λܭࢉʹ͍·͢ɻ
Slide 74
Slide 74 text
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
Slide 75
Slide 75 text
͜͜·Ͱͷ·ͱΊ
Slide 76
Slide 76 text
• ޮՌྔ Cohen’s d
• 2ͭͷάϧʔϓؒͷࠩΛඪ४Խͨ͠ͷ
• t ݕఆ
• ޮՌྔʹඪຊޡࠩͷӨڹΛՃຯͯ͠ɺͦͷ͕ࠩ
ۮવ؍͞ΕΔ֬Λࣔͨ͠ͷ
• ݕఆ౷ܭྔ = ޮՌͷେ͖͞ x ඪຊͷେ͖͞
ʢೆ෩ݪ, 2002, p. 163ʣ
Slide 77
Slide 77 text
• Cohen’s d ͷؒ:
• Hedges’ g
• ʹूஂͷඪ४ภࠩʢෆภࢄʹ
جͮ͘ඪ४ภࠩʣΛ͏
• Glass’ ⊿
• ʹ౷੍܈ͷඪ४ภࠩΛ͏
Slide 78
Slide 78 text
ؔͷڧ͞Λද͢ࢦඪ
Pearson’s r / r2
Slide 79
Slide 79 text
• มؒͷؔͷେ͖͞Λද͢
• ࠷େ: 1.0ʢઈରʣ
• ࠷খ: 0
• ϐΞιϯͷੵ૬ؔ r
• r2 ʢࢄઆ໌ʣ
Pearson’s r / r2
Slide 80
Slide 80 text
ࢄੳͷ߹
Slide 81
Slide 81 text
ࢄੳͷ߹
ௐ͍ͨཁҼͷࢄ
η2 =
૯ࢄ
SSA
=
SST
Slide 82
Slide 82 text
ҰཁҼࢄੳ
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 ʹଐͷσʔλΛͬͯ MacR Ͱܭࢉ
Slide 83
Slide 83 text
ҰཁҼࢄੳ
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
Slide 84
Slide 84 text
ҰཁҼࢄੳ
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
Slide 85
Slide 85 text
ҰཁҼࢄੳ
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