版权声明：本套课程材料开源，使用和分享必须遵守「创作共用许可协议 CC BY-NC-SA」（来源引用-非商业用途使用-以相同方式共享）。
方差分析的统计知识回顾
【知识点】方差分析（ANOVA）统计术语
- 方差分析ANOVA（以2 × 2 “高低组别 ×
男女性别”两因素组间设计ANOVA为例）
- 主效应（main effect）
- 代表“平均效应”，某个因素在其他因素不同条件下的边际平均效应
- 例：高组和低组之间的总体差异（无论男性和女性，组别的平均效应）
- 交互作用（interaction）
- 代表“效应差异”，某个因素在其他因素不同条件下存在不同的效应
- 例：高低组间的差异在男性和女性群体之间也存在差异（差异的差异）
- 主效应（main effect）
- 交互作用显著后的简单效应检验
- 简单效应（simple
effect），也称“条件效应”（conditional effect）
- 通常特指：简单主效应（simple main effect），也称“条件主效应”（conditional main effect）
- 例：分别在男性或女性群体中，高低组间的差异（组别的简单主效应）
- （拓展）三阶交互作用（A × B × C）中的复杂情况
- 简单交互作用（simple interaction）：C不同条件下的A × B简单交互作用
- 简单简单效应（simple-simple effect）：B和C不同组合条件下的A简单主效应
- 简单效应（simple
effect），也称“条件效应”（conditional effect）
- 某个因素多个条件间（≥ 3）的两两对比
- 事后检验（post-hoc test）
- 通常特指：事后多重比较（post-hoc multiple comparison）
- 需要对p值做“多重比较校正”（adjust p-values for multiple comparisons）以降低假阳性概率（false discovery rate, FDR）
- 事后检验（post-hoc test）
多因素方差分析
完全随机/组间设计ANOVA
【实践1】组间设计ANOVA
A SCORE
1 1 3
2 1 6
3 1 4
4 1 3
5 1 5
6 1 7
7 1 5
8 1 2
9 2 4
10 2 6
11 2 4
12 2 2
13 2 4
14 2 5
15 2 3
16 2 3
17 3 8
18 3 9
19 3 8
20 3 7
21 3 5
22 3 6
23 3 7
24 3 6
25 4 9
26 4 8
27 4 8
28 4 7
29 4 12
30 4 13
31 4 12
32 4 11
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────
"A" Mean S.D. n
─────────────────────
A1 4.375 (1.685) 8
A2 3.875 (1.246) 8
A3 7.000 (1.309) 8
A4 10.000 (2.268) 8
─────────────────────
Total sample size: N = 32
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A
Within-subjects factor(s): –
Covariate(s): –
─────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
─────────────────────────────────────────────────────────────────
A 63.375 2.812 3 28 22.533 <.001 *** .707 [.526, .798] .707
─────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 3.235 3 28 .037 *
─────────────────────────────────────── A B SCORE
1 1 1 3
2 1 1 6
3 1 1 4
4 1 1 3
5 1 2 4
6 1 2 6
7 1 2 4
8 1 2 2
9 1 3 5
10 1 3 7
11 1 3 5
12 1 3 2
13 2 1 4
14 2 1 5
15 2 1 3
16 2 1 3
17 2 2 8
18 2 2 9
19 2 2 8
20 2 2 7
21 2 3 12
22 2 3 13
23 2 3 12
24 2 3 11
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 4.000 (1.414) 4
A1 B2 4.000 (1.633) 4
A1 B3 4.750 (2.062) 4
A2 B1 3.750 (0.957) 4
A2 B2 8.000 (0.816) 4
A2 B3 12.000 (0.816) 4
─────────────────────────
Total sample size: N = 24
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A, B
Within-subjects factor(s): –
Covariate(s): –
─────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
─────────────────────────────────────────────────────────────────────
A 80.667 1.861 1 18 43.343 <.001 *** .707 [.482, .817] .707
B 40.542 1.861 2 18 21.784 <.001 *** .708 [.470, .815] .708
A * B 28.292 1.861 2 18 15.201 <.001 *** .628 [.347, .763] .628
─────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 0.605 5 18 .697
───────────────────────────────────────## 使用 emmeans 包的 emmip() 函数绘制交互图
## 请查阅帮助文档：?emmeans::emmip()
m = MANOVA(between.2, dv="SCORE", between=c("A", "B"))
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 4.000 (1.414) 4
A1 B2 4.000 (1.633) 4
A1 B3 4.750 (2.062) 4
A2 B1 3.750 (0.957) 4
A2 B2 8.000 (0.816) 4
A2 B3 12.000 (0.816) 4
─────────────────────────
Total sample size: N = 24
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A, B
Within-subjects factor(s): –
Covariate(s): –
─────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
─────────────────────────────────────────────────────────────────────
A 80.667 1.861 1 18 43.343 <.001 *** .707 [.482, .817] .707
B 40.542 1.861 2 18 21.784 <.001 *** .708 [.470, .815] .708
A * B 28.292 1.861 2 18 15.201 <.001 *** .628 [.347, .763] .628
─────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 0.605 5 18 .697
───────────────────────────────────────
A B C SCORE
1 1 1 1 3
2 1 1 1 6
3 1 1 1 4
4 1 1 1 3
5 1 1 2 5
6 1 1 2 7
7 1 1 2 5
8 1 1 2 2
9 1 2 1 4
10 1 2 1 6
11 1 2 1 4
12 1 2 1 2
13 1 2 2 4
14 1 2 2 5
15 1 2 2 3
16 1 2 2 3
17 2 1 1 8
18 2 1 1 9
19 2 1 1 8
20 2 1 1 7
21 2 1 2 5
22 2 1 2 6
23 2 1 2 7
24 2 1 2 6
25 2 2 1 9
26 2 2 1 8
27 2 2 1 8
28 2 2 1 7
29 2 2 2 12
30 2 2 2 13
31 2 2 2 12
32 2 2 2 11
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────────────
"A" "B" "C" Mean S.D. n
─────────────────────────────
A1 B1 C1 4.000 (1.414) 4
A1 B1 C2 4.750 (2.062) 4
A1 B2 C1 4.000 (1.633) 4
A1 B2 C2 3.750 (0.957) 4
A2 B1 C1 8.000 (0.816) 4
A2 B1 C2 6.000 (0.816) 4
A2 B2 C1 8.000 (0.816) 4
A2 B2 C2 12.000 (0.816) 4
─────────────────────────────
Total sample size: N = 32
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A, B, C
Within-subjects factor(s): –
Covariate(s): –
──────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────
A 153.125 1.563 1 24 98.000 <.001 *** .803 [.670, .870] .803
B 12.500 1.563 1 24 8.000 .009 ** .250 [.042, .466] .250
C 3.125 1.563 1 24 2.000 .170 .077 [.000, .283] .077
A * B 24.500 1.563 1 24 15.680 <.001 *** .395 [.147, .585] .395
A * C 1.125 1.563 1 24 0.720 .405 .029 [.000, .204] .029
B * C 12.500 1.563 1 24 8.000 .009 ** .250 [.042, .466] .250
A * B * C 24.500 1.563 1 24 15.680 <.001 *** .395 [.147, .585] .395
──────────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 0.668 7 24 .697
───────────────────────────────────────重复测量/组内设计ANOVA
【实践2】组内设计ANOVA
ID A1 A2 A3 A4
1 S1 3 4 8 9
2 S2 6 6 9 8
3 S3 4 4 8 8
4 S4 3 2 7 7
5 S5 5 4 5 12
6 S6 7 5 6 13
7 S7 5 3 7 12
8 S8 2 3 6 11
Note:
dvs="A1:A4" is matched to variables:
A1, A2, A3, A4
====== ANOVA (Within-Subjects Design) ======
Descriptives:
─────────────────────
"A" Mean S.D. n
─────────────────────
A1 4.375 (1.685) 8
A2 3.875 (1.246) 8
A3 7.000 (1.309) 8
A4 10.000 (2.268) 8
─────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): A1, A2, A3, A4
Between-subjects factor(s): –
Within-subjects factor(s): A
Covariate(s): –
─────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
─────────────────────────────────────────────────────────────────
A 63.375 2.518 3 21 25.170 <.001 *** .782 [.609, .858] .707
─────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
No between-subjects factors. No need to do the Levene’s test.
Mauchly’s Test of Sphericity:
────────────────────────
Mauchly's W p
────────────────────────
A 0.1899 .095 .
────────────────────────# 相同：
MANOVA(within.1,
dvs = c("A1", "A2", "A3", "A4"),
dvs.pattern = "A(.)",
within = "AnyVarNameIsOK")
====== ANOVA (Within-Subjects Design) ======
Descriptives:
──────────────────────────────────
"AnyVarNameIsOK" Mean S.D. n
──────────────────────────────────
AnyVarNameIsOK1 4.375 (1.685) 8
AnyVarNameIsOK2 3.875 (1.246) 8
AnyVarNameIsOK3 7.000 (1.309) 8
AnyVarNameIsOK4 10.000 (2.268) 8
──────────────────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): A1, A2, A3, A4
Between-subjects factor(s): –
Within-subjects factor(s): AnyVarNameIsOK
Covariate(s): –
──────────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────────
AnyVarNameIsOK 63.375 2.518 3 21 25.170 <.001 *** .782 [.609, .858] .707
──────────────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
No between-subjects factors. No need to do the Levene’s test.
Mauchly’s Test of Sphericity:
─────────────────────────────────────
Mauchly's W p
─────────────────────────────────────
AnyVarNameIsOK 0.1899 .095 .
───────────────────────────────────── ID A1B1 A1B2 A1B3 A2B1 A2B2 A2B3
1 S1 3 4 5 4 8 12
2 S2 6 6 7 5 9 13
3 S3 4 4 5 3 8 12
4 S4 3 2 2 3 7 11
Note:
dvs="A1B1:A2B3" is matched to variables:
A1B1, A1B2, A1B3, A2B1, A2B2, A2B3
====== ANOVA (Within-Subjects Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 4.000 (1.414) 4
A1 B2 4.000 (1.633) 4
A1 B3 4.750 (2.062) 4
A2 B1 3.750 (0.957) 4
A2 B2 8.000 (0.816) 4
A2 B3 12.000 (0.816) 4
─────────────────────────
Total sample size: N = 4
ANOVA Table:
Dependent variable(s): A1B1, A1B2, A1B3, A2B1, A2B2, A2B3
Between-subjects factor(s): –
Within-subjects factor(s): A, B
Covariate(s): –
──────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────
A 80.667 1.111 1 3 72.600 .003 ** .960 [.699, .985] .707
B 40.542 0.264 2 6 153.632 <.001 *** .981 [.930, .991] .708
A * B 28.292 0.236 2 6 119.824 <.001 *** .976 [.911, .988] .628
──────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
No between-subjects factors. No need to do the Levene’s test.
Mauchly’s Test of Sphericity:
────────────────────────────
Mauchly's W p
────────────────────────────
B 0.0665 .066 .
A * B 0.2491 .249
────────────────────────────
ID A1B1C1 A1B1C2 A1B2C1 A1B2C2 A2B1C1 A2B1C2 A2B2C1 A2B2C2
1 S1 3 5 4 4 8 5 9 12
2 S2 6 7 6 5 9 6 8 13
3 S3 4 5 4 3 8 7 8 12
4 S4 3 2 2 3 7 6 7 11
Note:
dvs="A1B1C1:A2B2C2" is matched to variables:
A1B1C1, A1B1C2, A1B2C1, A1B2C2, A2B1C1, A2B1C2, A2B2C1, A2B2C2
====== ANOVA (Within-Subjects Design) ======
Descriptives:
─────────────────────────────
"A" "B" "C" Mean S.D. n
─────────────────────────────
A1 B1 C1 4.000 (1.414) 4
A1 B1 C2 4.750 (2.062) 4
A1 B2 C1 4.000 (1.633) 4
A1 B2 C2 3.750 (0.957) 4
A2 B1 C1 8.000 (0.816) 4
A2 B1 C2 6.000 (0.816) 4
A2 B2 C1 8.000 (0.816) 4
A2 B2 C2 12.000 (0.816) 4
─────────────────────────────
Total sample size: N = 4
ANOVA Table:
Dependent variable(s): A1B1C1, A1B1C2, A1B2C1, A1B2C2, A2B1C1, A2B1C2, A2B2C1, A2B2C2
Between-subjects factor(s): –
Within-subjects factor(s): A, B, C
Covariate(s): –
──────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────
A 153.125 1.875 1 3 81.667 .003 ** .965 [.727, .986] .803
B 12.500 0.583 1 3 21.429 .019 * .877 [.279, .953] .250
C 3.125 0.042 1 3 75.000 .003 ** .962 [.707, .985] .077
A * B 24.500 0.250 1 3 98.000 .002 ** .970 [.768, .989] .395
A * C 1.125 0.708 1 3 1.588 .297 .346 [.000, .749] .029
B * C 12.500 0.417 1 3 30.000 .012 * .909 [.411, .965] .250
A * B * C 24.500 1.083 1 3 22.615 .018 * .883 [.300, .956] .395
──────────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
No between-subjects factors. No need to do the Levene’s test.
Mauchly’s Test of Sphericity:
The repeated measures have only two levels. The assumption of sphericity is always met.混合设计ANOVA
【实践3】混合设计ANOVA
A B1 B2 B3
1 1 3 4 5
2 1 6 6 7
3 1 4 4 5
4 1 3 2 2
5 2 4 8 12
6 2 5 9 13
7 2 3 8 12
8 2 3 7 11
Note:
dvs="B1:B3" is matched to variables:
B1, B2, B3
====== ANOVA (Mixed Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 4.000 (1.414) 4
A1 B2 4.000 (1.633) 4
A1 B3 4.750 (2.062) 4
A2 B1 3.750 (0.957) 4
A2 B2 8.000 (0.816) 4
A2 B3 12.000 (0.816) 4
─────────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): B1, B2, B3
Between-subjects factor(s): A
Within-subjects factor(s): B
Covariate(s): –
──────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────
A 80.667 5.083 1 6 15.869 .007 ** .726 [.248, .871] .707
B 40.542 0.250 2 12 162.167 <.001 *** .964 [.918, .980] .708
A * B 28.292 0.250 2 12 113.167 <.001 *** .950 [.885, .971] .628
──────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
────────────────────────────────────
Levene’s F df1 df2 p
────────────────────────────────────
DV: B1 0.300 1 6 .604
DV: B2 0.600 1 6 .468
DV: B3 1.485 1 6 .269
────────────────────────────────────
Mauchly’s Test of Sphericity:
────────────────────────────
Mauchly's W p
────────────────────────────
B 0.1574 .010 **
A * B 0.1574 .010 **
────────────────────────────
The sphericity assumption is violated.
You may specify: sph.correction="GG" (or ="HF")MANOVA(mixed.2_1b1w,
dvs = "B1:B3",
dvs.pattern = "B(.)",
between = "A",
within = "B",
sph.correction = "GG")
Note:
dvs="B1:B3" is matched to variables:
B1, B2, B3
====== ANOVA (Mixed Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 4.000 (1.414) 4
A1 B2 4.000 (1.633) 4
A1 B3 4.750 (2.062) 4
A2 B1 3.750 (0.957) 4
A2 B2 8.000 (0.816) 4
A2 B3 12.000 (0.816) 4
─────────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): B1, B2, B3
Between-subjects factor(s): A
Within-subjects factor(s): B
Covariate(s): –
──────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────
A 80.667 5.083 1.000 6.000 15.869 .007 ** .726 [.248, .871] .707
B 74.702 0.461 1.085 6.513 162.167 <.001 *** .964 [.880, .983] .708
A * B 52.130 0.461 1.085 6.513 113.167 <.001 *** .950 [.833, .976] .628
──────────────────────────────────────────────────────────────────────────
Sphericity correction method: GG (Greenhouse-Geisser)
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
────────────────────────────────────
Levene’s F df1 df2 p
────────────────────────────────────
DV: B1 0.300 1 6 .604
DV: B2 0.600 1 6 .468
DV: B3 1.485 1 6 .269
────────────────────────────────────
Mauchly’s Test of Sphericity:
────────────────────────────
Mauchly's W p
────────────────────────────
B 0.1574 .010 **
A * B 0.1574 .010 **
──────────────────────────── A B1C1 B1C2 B2C1 B2C2
1 1 3 5 4 4
2 1 6 7 6 5
3 1 4 5 4 3
4 1 3 2 2 3
5 2 8 5 9 12
6 2 9 6 8 13
7 2 8 7 8 12
8 2 7 6 7 11MANOVA(mixed.3_1b2w,
dvs = "B1C1:B2C2",
dvs.pattern = "B(.)C(.)",
between = "A",
within = c("B", "C"))
Note:
dvs="B1C1:B2C2" is matched to variables:
B1C1, B1C2, B2C1, B2C2
====== ANOVA (Mixed Design) ======
Descriptives:
─────────────────────────────
"A" "B" "C" Mean S.D. n
─────────────────────────────
A1 B1 C1 4.000 (1.414) 4
A1 B1 C2 4.750 (2.062) 4
A1 B2 C1 4.000 (1.633) 4
A1 B2 C2 3.750 (0.957) 4
A2 B1 C1 8.000 (0.816) 4
A2 B1 C2 6.000 (0.816) 4
A2 B2 C1 8.000 (0.816) 4
A2 B2 C2 12.000 (0.816) 4
─────────────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): B1C1, B1C2, B2C1, B2C2
Between-subjects factor(s): A
Within-subjects factor(s): B, C
Covariate(s): –
──────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────
A 153.125 4.708 1 6 32.522 .001 ** .844 [.503, .926] .803
B 12.500 0.417 1 6 30.000 .002 ** .833 [.474, .921] .250
A * B 24.500 0.417 1 6 58.800 <.001 *** .907 [.684, .956] .395
C 3.125 0.375 1 6 8.333 .028 * .581 [.064, .801] .077
A * C 1.125 0.375 1 6 3.000 .134 .333 [.000, .671] .029
B * C 12.500 0.750 1 6 16.667 .006 ** .735 [.264, .875] .250
A * B * C 24.500 0.750 1 6 32.667 .001 ** .845 [.505, .927] .395
──────────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
──────────────────────────────────────
Levene’s F df1 df2 p
──────────────────────────────────────
DV: B1C1 1.000 1 6 .356
DV: B1C2 1.485 1 6 .269
DV: B2C1 0.600 1 6 .468
DV: B2C2 0.500 1 6 .506
──────────────────────────────────────
Mauchly’s Test of Sphericity:
The repeated measures have only two levels. The assumption of sphericity is always met. A C B1 B2
1 1 1 3 4
2 1 1 6 6
3 1 1 4 4
4 1 1 3 2
5 1 2 5 4
6 1 2 7 5
7 1 2 5 3
8 1 2 2 3
9 2 1 8 9
10 2 1 9 8
11 2 1 8 8
12 2 1 7 7
13 2 2 5 12
14 2 2 6 13
15 2 2 7 12
16 2 2 6 11
Note:
dvs="B1:B2" is matched to variables:
B1, B2
====== ANOVA (Mixed Design) ======
Descriptives:
─────────────────────────────
"A" "C" "B" Mean S.D. n
─────────────────────────────
A1 C1 B1 4.000 (1.414) 4
A1 C1 B2 4.000 (1.633) 4
A1 C2 B1 4.750 (2.062) 4
A1 C2 B2 3.750 (0.957) 4
A2 C1 B1 8.000 (0.816) 4
A2 C1 B2 8.000 (0.816) 4
A2 C2 B1 6.000 (0.816) 4
A2 C2 B2 12.000 (0.816) 4
─────────────────────────────
Total sample size: N = 16
ANOVA Table:
Dependent variable(s): B1, B2
Between-subjects factor(s): A, C
Within-subjects factor(s): B
Covariate(s): –
──────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────
A 153.125 2.542 1 12 60.246 <.001 *** .834 [.639, .906] .803
C 3.125 2.542 1 12 1.230 .289 .093 [.000, .390] .077
A * C 1.125 2.542 1 12 0.443 .518 .036 [.000, .305] .029
B 12.500 0.583 1 12 21.429 <.001 *** .641 [.308, .795] .250
A * B 24.500 0.583 1 12 42.000 <.001 *** .778 [.532, .874] .395
C * B 12.500 0.583 1 12 21.429 <.001 *** .641 [.308, .795] .250
A * C * B 24.500 0.583 1 12 42.000 <.001 *** .778 [.532, .874] .395
──────────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
────────────────────────────────────
Levene’s F df1 df2 p
────────────────────────────────────
DV: B1 0.946 3 12 .449
DV: B2 0.423 3 12 .740
────────────────────────────────────
Mauchly’s Test of Sphericity:
The repeated measures have only two levels. The assumption of sphericity is always met.简单效应检验与多重比较
多重比较
【实践4】组间设计ANOVA的多重比较
EMMEANS()函数帮助文档（Estimated Marginal Means，估计边际均值）
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────
"A" Mean S.D. n
─────────────────────
A1 4.375 (1.685) 8
A2 3.875 (1.246) 8
A3 7.000 (1.309) 8
A4 10.000 (2.268) 8
─────────────────────
Total sample size: N = 32
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A
Within-subjects factor(s): –
Covariate(s): –
─────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
─────────────────────────────────────────────────────────────────
A 63.375 2.812 3 28 22.533 <.001 *** .707 [.526, .798] .707
─────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 3.235 3 28 .037 *
───────────────────────────────────────
------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────
Effect df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────
A 3 28 22.533 <.001 *** .707 [.526, .798]
────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
Mean: "A" 190.125 3 63.375 22.533 <.001 ***
Residuals 78.750 28 2.812
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
───────────────────────────────────
"A" Mean [95% CI of Mean] S.E.
───────────────────────────────────
A1 4.375 [3.160, 5.590] (0.593)
A2 3.875 [2.660, 5.090] (0.593)
A3 7.000 [5.785, 8.215] (0.593)
A4 10.000 [8.785, 11.215] (0.593)
───────────────────────────────────
Pairwise Comparisons of "A":
──────────────────────────────────────────────────────────────────────
Contrast Estimate S.E. df t p Cohen’s d [95% CI of d]
──────────────────────────────────────────────────────────────────────
A2 - A1 -0.500 (0.839) 28 -0.596 .556 -0.298 [-1.322, 0.726]
A3 - A1 2.625 (0.839) 28 3.130 .004 ** 1.565 [ 0.541, 2.589]
A3 - A2 3.125 (0.839) 28 3.727 <.001 *** 1.863 [ 0.839, 2.888]
A4 - A1 5.625 (0.839) 28 6.708 <.001 *** 3.354 [ 2.330, 4.378]
A4 - A2 6.125 (0.839) 28 7.304 <.001 *** 3.652 [ 2.628, 4.676]
A4 - A3 3.000 (0.839) 28 3.578 .001 ** 1.789 [ 0.765, 2.813]
──────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.677
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────
Effect df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────
A 3 28 22.533 <.001 *** .707 [.526, .798]
────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
Mean: "A" 190.125 3 63.375 22.533 <.001 ***
Residuals 78.750 28 2.812
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
───────────────────────────────────
"A" Mean [95% CI of Mean] S.E.
───────────────────────────────────
A1 4.375 [3.160, 5.590] (0.593)
A2 3.875 [2.660, 5.090] (0.593)
A3 7.000 [5.785, 8.215] (0.593)
A4 10.000 [8.785, 11.215] (0.593)
───────────────────────────────────
Pairwise Comparisons of "A":
──────────────────────────────────────────────────────────────────────
Contrast Estimate S.E. df t p Cohen’s d [95% CI of d]
──────────────────────────────────────────────────────────────────────
A2 - A1 -0.500 (0.839) 28 -0.596 1.000 -0.298 [-1.718, 1.121]
A3 - A1 2.625 (0.839) 28 3.130 .024 * 1.565 [ 0.146, 2.985]
A3 - A2 3.125 (0.839) 28 3.727 .005 ** 1.863 [ 0.444, 3.283]
A4 - A1 5.625 (0.839) 28 6.708 <.001 *** 3.354 [ 1.935, 4.774]
A4 - A2 6.125 (0.839) 28 7.304 <.001 *** 3.652 [ 2.233, 5.072]
A4 - A3 3.000 (0.839) 28 3.578 .008 ** 1.789 [ 0.369, 3.208]
──────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.677
P-value adjustment: Bonferroni method for 6 tests.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────
Effect df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────
A 3 28 22.533 <.001 *** .707 [.526, .798]
────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
Mean: "A" 190.125 3 63.375 22.533 <.001 ***
Residuals 78.750 28 2.812
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
───────────────────────────────────
"A" Mean [95% CI of Mean] S.E.
───────────────────────────────────
A1 4.375 [3.160, 5.590] (0.593)
A2 3.875 [2.660, 5.090] (0.593)
A3 7.000 [5.785, 8.215] (0.593)
A4 10.000 [8.785, 11.215] (0.593)
───────────────────────────────────
Consecutive (Sequential) Comparisons of "A":
──────────────────────────────────────────────────────────────────────
Contrast Estimate S.E. df t p Cohen’s d [95% CI of d]
──────────────────────────────────────────────────────────────────────
A2 - A1 -0.500 (0.839) 28 -0.596 1.000 -0.298 [-1.571, 0.975]
A3 - A2 3.125 (0.839) 28 3.727 .003 ** 1.863 [ 0.590, 3.137]
A4 - A3 3.000 (0.839) 28 3.578 .004 ** 1.789 [ 0.516, 3.062]
──────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.677
P-value adjustment: Bonferroni method for 3 tests.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────
Effect df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────
A 3 28 22.533 <.001 *** .707 [.526, .798]
────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
Mean: "A" 190.125 3 63.375 22.533 <.001 ***
Residuals 78.750 28 2.812
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
───────────────────────────────────
"A" Mean [95% CI of Mean] S.E.
───────────────────────────────────
A1 4.375 [3.160, 5.590] (0.593)
A2 3.875 [2.660, 5.090] (0.593)
A3 7.000 [5.785, 8.215] (0.593)
A4 10.000 [8.785, 11.215] (0.593)
───────────────────────────────────
Polynomial Contrasts of "A":
───────────────────────────────────────────────
Contrast Estimate S.E. df t p
───────────────────────────────────────────────
linear 20.000 (2.652) 28 7.542 <.001 ***
quadratic 3.500 (1.186) 28 2.951 .006 **
cubic -3.750 (2.652) 28 -1.414 .168
───────────────────────────────────────────────
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.简单效应检验
【实践5】组间设计ANOVA的简单效应检验
EMMEANS()函数帮助文档（Estimated Marginal Means，估计边际均值）
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 4.000 (1.414) 4
A1 B2 4.000 (1.633) 4
A1 B3 4.750 (2.062) 4
A2 B1 3.750 (0.957) 4
A2 B2 8.000 (0.816) 4
A2 B3 12.000 (0.816) 4
─────────────────────────
Total sample size: N = 24
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A, B
Within-subjects factor(s): –
Covariate(s): –
─────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
─────────────────────────────────────────────────────────────────────
A 80.667 1.861 1 18 43.343 <.001 *** .707 [.482, .817] .707
B 40.542 1.861 2 18 21.784 <.001 *** .708 [.470, .815] .708
A * B 28.292 1.861 2 18 15.201 <.001 *** .628 [.347, .763] .628
─────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 0.605 5 18 .697
───────────────────────────────────────
------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────────
Effect "B" df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────────
A B1 1 18 0.067 .798 .004 [.000, .137]
A B2 1 18 17.194 <.001 *** .489 [.198, .674]
A B3 1 18 56.485 <.001 *** .758 [.564, .849]
────────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
B1: "A" 0.125 1 0.125 0.067 .798
B2: "A" 32.000 1 32.000 17.194 <.001 ***
B3: "A" 105.125 1 105.125 56.485 <.001 ***
Residuals 33.500 18 1.861
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
────────────────────────────────────────
"A" "B" Mean [95% CI of Mean] S.E.
────────────────────────────────────────
A1 B1 4.000 [ 2.567, 5.433] (0.682)
A2 B1 3.750 [ 2.317, 5.183] (0.682)
A1 B2 4.000 [ 2.567, 5.433] (0.682)
A2 B2 8.000 [ 6.567, 9.433] (0.682)
A1 B3 4.750 [ 3.317, 6.183] (0.682)
A2 B3 12.000 [10.567, 13.433] (0.682)
────────────────────────────────────────
Pairwise Comparisons of "A":
──────────────────────────────────────────────────────────────────────────
Contrast "B" Estimate S.E. df t p Cohen’s d [95% CI of d]
──────────────────────────────────────────────────────────────────────────
A2 - A1 B1 -0.250 (0.965) 18 -0.259 .798 -0.183 [-1.669, 1.302]
A2 - A1 B2 4.000 (0.965) 18 4.147 <.001 *** 2.932 [ 1.446, 4.418]
A2 - A1 B3 7.250 (0.965) 18 7.516 <.001 *** 5.314 [ 3.829, 6.800]
──────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.364
No need to adjust p values.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.
------ EMMEANS (effect = "B") ------
Joint Tests of "B":
────────────────────────────────────────────────────────
Effect "A" df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────────
B A1 2 18 0.403 .674 .043 [.000, .205]
B A2 2 18 36.582 <.001 *** .803 [.631, .876]
────────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "B":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
A1: "B" 1.500 2 0.750 0.403 .674
A2: "B" 136.167 2 68.083 36.582 <.001 ***
Residuals 33.500 18 1.861
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "B":
────────────────────────────────────────
"B" "A" Mean [95% CI of Mean] S.E.
────────────────────────────────────────
B1 A1 4.000 [ 2.567, 5.433] (0.682)
B2 A1 4.000 [ 2.567, 5.433] (0.682)
B3 A1 4.750 [ 3.317, 6.183] (0.682)
B1 A2 3.750 [ 2.317, 5.183] (0.682)
B2 A2 8.000 [ 6.567, 9.433] (0.682)
B3 A2 12.000 [10.567, 13.433] (0.682)
────────────────────────────────────────
Pairwise Comparisons of "B":
──────────────────────────────────────────────────────────────────────────
Contrast "A" Estimate S.E. df t p Cohen’s d [95% CI of d]
──────────────────────────────────────────────────────────────────────────
B2 - B1 A1 -0.000 (0.965) 18 -0.000 1.000 -0.000 [-1.866, 1.866]
B3 - B1 A1 0.750 (0.965) 18 0.777 1.000 0.550 [-1.316, 2.416]
B3 - B2 A1 0.750 (0.965) 18 0.777 1.000 0.550 [-1.316, 2.416]
B2 - B1 A2 4.250 (0.965) 18 4.406 .001 ** 3.115 [ 1.249, 4.981]
B3 - B1 A2 8.250 (0.965) 18 8.552 <.001 *** 6.047 [ 4.181, 7.914]
B3 - B2 A2 4.000 (0.965) 18 4.147 .002 ** 2.932 [ 1.066, 4.798]
──────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.364
P-value adjustment: Bonferroni method for 3 tests.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.## 使用管道操作符 %>% 连接多个 EMMEANS()
MANOVA(between.3, dv="SCORE", between=c("A", "B", "C")) %>%
EMMEANS("A", by="B") %>%
EMMEANS(c("A", "B"), by="C") %>%
EMMEANS("A", by=c("B", "C"))
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────────────
"A" "B" "C" Mean S.D. n
─────────────────────────────
A1 B1 C1 4.000 (1.414) 4
A1 B1 C2 4.750 (2.062) 4
A1 B2 C1 4.000 (1.633) 4
A1 B2 C2 3.750 (0.957) 4
A2 B1 C1 8.000 (0.816) 4
A2 B1 C2 6.000 (0.816) 4
A2 B2 C1 8.000 (0.816) 4
A2 B2 C2 12.000 (0.816) 4
─────────────────────────────
Total sample size: N = 32
ANOVA Table:
Dependent variable(s): SCORE
Between-subjects factor(s): A, B, C
Within-subjects factor(s): –
Covariate(s): –
──────────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────────
A 153.125 1.563 1 24 98.000 <.001 *** .803 [.670, .870] .803
B 12.500 1.563 1 24 8.000 .009 ** .250 [.042, .466] .250
C 3.125 1.563 1 24 2.000 .170 .077 [.000, .283] .077
A * B 24.500 1.563 1 24 15.680 <.001 *** .395 [.147, .585] .395
A * C 1.125 1.563 1 24 0.720 .405 .029 [.000, .204] .029
B * C 12.500 1.563 1 24 8.000 .009 ** .250 [.042, .466] .250
A * B * C 24.500 1.563 1 24 15.680 <.001 *** .395 [.147, .585] .395
──────────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:
───────────────────────────────────────
Levene’s F df1 df2 p
───────────────────────────────────────
DV: SCORE 0.668 7 24 .697
───────────────────────────────────────
------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────────
Effect "B" df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────────
A B1 1 24 17.640 <.001 *** .424 [.173, .607]
A B2 1 24 96.040 <.001 *** .800 [.665, .868]
C B1 1 24 1.000 .327 .040 [.000, .226]
C B2 1 24 9.000 .006 ** .273 [.055, .486]
A * C B1 1 24 4.840 .038 * .168 [.006, .388]
A * C B2 1 24 11.560 .002 ** .325 [.090, .530]
────────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
─────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────
B1: "A" 27.562 1 27.562 17.640 <.001 ***
B2: "A" 150.063 1 150.063 96.040 <.001 ***
Residuals 37.500 24 1.563
─────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
───────────────────────────────────────
"A" "B" Mean [95% CI of Mean] S.E.
───────────────────────────────────────
A1 B1 4.375 [3.463, 5.287] (0.442)
A2 B1 7.000 [6.088, 7.912] (0.442)
A1 B2 3.875 [2.963, 4.787] (0.442)
A2 B2 10.000 [9.088, 10.912] (0.442)
───────────────────────────────────────
Pairwise Comparisons of "A":
─────────────────────────────────────────────────────────────────────────
Contrast "B" Estimate S.E. df t p Cohen’s d [95% CI of d]
─────────────────────────────────────────────────────────────────────────
A2 - A1 B1 2.625 (0.625) 24 4.200 <.001 *** 2.100 [1.068, 3.132]
A2 - A1 B2 6.125 (0.625) 24 9.800 <.001 *** 4.900 [3.868, 5.932]
─────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.250
Results are averaged over the levels of: C
No need to adjust p values.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.
------ EMMEANS (effect = "A" & "B") ------
Joint Tests of "A" & "B":
────────────────────────────────────────────────────────
Effect "C" df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────────
A C1 1 24 40.960 <.001 *** .631 [.414, .754]
A C2 1 24 57.760 <.001 *** .706 [.521, .806]
B C1 1 24 0.000 1.000 .000 [.000, .000]
B C2 1 24 16.000 <.001 *** .400 [.151, .589]
A * B C1 1 24 0.000 1.000 .000 [.000, .000]
A * B C2 1 24 31.360 <.001 *** .566 [.331, .710]
────────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A" & "B":
─────────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
─────────────────────────────────────────────────────────────
C1: "A" & "B" 0.000 1 0.000 0.000 1.000
C2: "A" & "B" 49.000 1 49.000 31.360 <.001 ***
Residuals 37.500 24 1.563
─────────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A" & "B":
────────────────────────────────────────
"A" "B" Mean [95% CI of Mean] S.E.
────────────────────────────────────────
A1 B1 4.000 [ 2.710, 5.290] (0.625)
A2 B1 8.000 [ 6.710, 9.290] (0.625)
A1 B2 4.000 [ 2.710, 5.290] (0.625)
A2 B2 8.000 [ 6.710, 9.290] (0.625)
A1 B1 4.750 [ 3.460, 6.040] (0.625)
A2 B1 6.000 [ 4.710, 7.290] (0.625)
A1 B2 3.750 [ 2.460, 5.040] (0.625)
A2 B2 12.000 [10.710, 13.290] (0.625)
────────────────────────────────────────
Pairwise Comparisons of "A" & "B":
───────────────────────────────────────────────────────────────────────────────
Contrast "C" Estimate S.E. df t p Cohen’s d [95% CI of d]
───────────────────────────────────────────────────────────────────────────────
A2 B1 - A1 B1 C1 4.000 (0.884) 24 4.525 <.001 *** 3.200 [ 1.167, 5.233]
A1 B2 - A1 B1 C1 -0.000 (0.884) 24 -0.000 1.000 -0.000 [-2.033, 2.033]
A1 B2 - A2 B1 C1 -4.000 (0.884) 24 -4.525 <.001 *** -3.200 [-5.233, -1.167]
A2 B2 - A1 B1 C1 4.000 (0.884) 24 4.525 <.001 *** 3.200 [ 1.167, 5.233]
A2 B2 - A2 B1 C1 -0.000 (0.884) 24 -0.000 1.000 -0.000 [-2.033, 2.033]
A2 B2 - A1 B2 C1 4.000 (0.884) 24 4.525 <.001 *** 3.200 [ 1.167, 5.233]
A2 B1 - A1 B1 C2 1.250 (0.884) 24 1.414 1.000 1.000 [-1.033, 3.033]
A1 B2 - A1 B1 C2 -1.000 (0.884) 24 -1.131 1.000 -0.800 [-2.833, 1.233]
A1 B2 - A2 B1 C2 -2.250 (0.884) 24 -2.546 .107 -1.800 [-3.833, 0.233]
A2 B2 - A1 B1 C2 7.250 (0.884) 24 8.202 <.001 *** 5.800 [ 3.767, 7.833]
A2 B2 - A2 B1 C2 6.000 (0.884) 24 6.788 <.001 *** 4.800 [ 2.767, 6.833]
A2 B2 - A1 B2 C2 8.250 (0.884) 24 9.334 <.001 *** 6.600 [ 4.567, 8.633]
───────────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.250
P-value adjustment: Bonferroni method for 6 tests.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.
------ EMMEANS (effect = "A") ------
Joint Tests of "A":
────────────────────────────────────────────────────────────
Effect "B" "C" df1 df2 F p η²p [90% CI of η²p]
────────────────────────────────────────────────────────────
A B1 C1 1 24 20.480 <.001 *** .460 [.210, .634]
A B2 C1 1 24 20.480 <.001 *** .460 [.210, .634]
A B1 C2 1 24 2.000 .170 .077 [.000, .283]
A B2 C2 1 24 87.120 <.001 *** .784 [.639, .858]
────────────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
────────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
────────────────────────────────────────────────────────────
B1 & C1: "A" 32.000 1 32.000 20.480 <.001 ***
B2 & C1: "A" 32.000 1 32.000 20.480 <.001 ***
B1 & C2: "A" 3.125 1 3.125 2.000 .170
B2 & C2: "A" 136.125 1 136.125 87.120 <.001 ***
Residuals 37.500 24 1.563
────────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
────────────────────────────────────────────
"A" "B" "C" Mean [95% CI of Mean] S.E.
────────────────────────────────────────────
A1 B1 C1 4.000 [ 2.710, 5.290] (0.625)
A2 B1 C1 8.000 [ 6.710, 9.290] (0.625)
A1 B2 C1 4.000 [ 2.710, 5.290] (0.625)
A2 B2 C1 8.000 [ 6.710, 9.290] (0.625)
A1 B1 C2 4.750 [ 3.460, 6.040] (0.625)
A2 B1 C2 6.000 [ 4.710, 7.290] (0.625)
A1 B2 C2 3.750 [ 2.460, 5.040] (0.625)
A2 B2 C2 12.000 [10.710, 13.290] (0.625)
────────────────────────────────────────────
Pairwise Comparisons of "A":
─────────────────────────────────────────────────────────────────────────────
Contrast "B" "C" Estimate S.E. df t p Cohen’s d [95% CI of d]
─────────────────────────────────────────────────────────────────────────────
A2 - A1 B1 C1 4.000 (0.884) 24 4.525 <.001 *** 3.200 [ 1.741, 4.659]
A2 - A1 B2 C1 4.000 (0.884) 24 4.525 <.001 *** 3.200 [ 1.741, 4.659]
A2 - A1 B1 C2 1.250 (0.884) 24 1.414 .170 1.000 [-0.459, 2.459]
A2 - A1 B2 C2 8.250 (0.884) 24 9.334 <.001 *** 6.600 [ 5.141, 8.059]
─────────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.250
No need to adjust p values.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.* 拓展：特殊情况
【探索发现】对于两因素方差分析（A × B），以下情况都有可能发生吗？
交互作用 & 主效应：
交互作用 & 简单效应：
（例如：A在B1、B2水平上的两个简单主效应）
“Seeing is believing.”（眼见为实）
【实践6】交互作用显著，但A的两个简单效应都不显著
data1 = data.table(
A = c(1, 1, 1, 1, 2, 2, 2, 2),
B = c(1, 1, 2, 2, 1, 1, 2, 2),
Y = c(0, 7, 10, 12, 12, 10, 7, 0)
)
m = MANOVA(data1, dv="Y", between=c("A", "B"))
====== ANOVA (Between-Subjects Design) ======
Descriptives:
─────────────────────────
"A" "B" Mean S.D. n
─────────────────────────
A1 B1 3.500 (4.950) 2
A1 B2 11.000 (1.414) 2
A2 B1 11.000 (1.414) 2
A2 B2 3.500 (4.950) 2
─────────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): Y
Between-subjects factor(s): A, B
Within-subjects factor(s): –
Covariate(s): –
──────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
──────────────────────────────────────────────────────────────────────
A 0.000 13.250 1 4 0.000 1.000 .000 [.000, .000] .000
B 0.000 13.250 1 4 0.000 1.000 .000 [.000, .000] .000
A * B 112.500 13.250 1 4 8.491 .044 * .680 [.025, .867] .680
──────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:Warning in anova.lm(lm(resp ~ group)): 对几乎是完全拟合进行ANOVA
F-检验的结果不会可靠─────────────────────────────────────────────────────────────
Levene’s F df1 df2 p
─────────────────────────────────────────────────────────────
DV: Y 11361861823696222742664246882006.000 3 4 <.001 ***
─────────────────────────────────────────────────────────────
------ EMMEANS (effect = "A") ------
Joint Tests of "A":
───────────────────────────────────────────────────────
Effect "B" df1 df2 F p η²p [90% CI of η²p]
───────────────────────────────────────────────────────
A B1 1 4 4.245 .108 .515 [.000, .798]
A B2 1 4 4.245 .108 .515 [.000, .798]
───────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
────────────────────────────────────────────────────────
B1: "A" 56.250 1 56.250 4.245 .108
B2: "A" 56.250 1 56.250 4.245 .108
Residuals 53.000 4 13.250
────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
────────────────────────────────────────
"A" "B" Mean [95% CI of Mean] S.E.
────────────────────────────────────────
A1 B1 3.500 [-3.646, 10.646] (2.574)
A2 B1 11.000 [ 3.854, 18.146] (2.574)
A1 B2 11.000 [ 3.854, 18.146] (2.574)
A2 B2 3.500 [-3.646, 10.646] (2.574)
────────────────────────────────────────
Pairwise Comparisons of "A":
──────────────────────────────────────────────────────────────────────────
Contrast "B" Estimate S.E. df t p Cohen’s d [95% CI of d]
──────────────────────────────────────────────────────────────────────────
A2 - A1 B1 7.500 (3.640) 4 2.060 .108 2.060 [-0.716, 4.837]
A2 - A1 B2 -7.500 (3.640) 4 -2.060 .108 -2.060 [-4.837, 0.716]
──────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 3.640
No need to adjust p values.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.
【实践7】交互作用不显著，但A的简单效应一个显著、一个不显著
data2 = data.table(
A = c(1, 1, 1, 1, 2, 2, 2, 2),
B = c(1, 1, 2, 2, 1, 1, 2, 2),
Y = c(0, 1, 0, 4, 5, 6, 2, 4)
)
m = MANOVA(data2, dv="Y", between=c("A", "B"))
====== ANOVA (Between-Subjects Design) ======
Descriptives:
────────────────────────
"A" "B" Mean S.D. n
────────────────────────
A1 B1 0.500 (0.707) 2
A1 B2 2.000 (2.828) 2
A2 B1 5.500 (0.707) 2
A2 B2 3.000 (1.414) 2
────────────────────────
Total sample size: N = 8
ANOVA Table:
Dependent variable(s): Y
Between-subjects factor(s): A, B
Within-subjects factor(s): –
Covariate(s): –
────────────────────────────────────────────────────────────────────
MS MSE df1 df2 F p η²p [90% CI of η²p] η²G
────────────────────────────────────────────────────────────────────
A 18.000 2.750 1 4 6.545 .063 . .621 [.000, .843] .621
B 0.500 2.750 1 4 0.182 .692 .043 [.000, .495] .043
A * B 8.000 2.750 1 4 2.909 .163 .421 [.000, .756] .421
────────────────────────────────────────────────────────────────────
MSE = mean square error (the residual variance of the linear model)
η²p = partial eta-squared = SS / (SS + SSE) = F * df1 / (F * df1 + df2)
ω²p = partial omega-squared = (F - 1) * df1 / (F * df1 + df2 + 1)
η²G = generalized eta-squared (see Olejnik & Algina, 2003)
Cohen’s f² = η²p / (1 - η²p)
Levene’s Test for Homogeneity of Variance:Warning in anova.lm(lm(resp ~ group)): 对几乎是完全拟合进行ANOVA
F-检验的结果不会可靠─────────────────────────────────────────────────────────────
Levene’s F df1 df2 p
─────────────────────────────────────────────────────────────
DV: Y 13645983859487056935286622800820.000 3 4 <.001 ***
─────────────────────────────────────────────────────────────
------ EMMEANS (effect = "A") ------
Joint Tests of "A":
───────────────────────────────────────────────────────
Effect "B" df1 df2 F p η²p [90% CI of η²p]
───────────────────────────────────────────────────────
A B1 1 4 9.091 .039 * .694 [.043, .874]
A B2 1 4 0.364 .579 .083 [.000, .551]
───────────────────────────────────────────────────────
Note. Simple effects of repeated measures with 3 or more levels
are different from the results obtained with SPSS MANOVA syntax.
Univariate Tests of "A":
────────────────────────────────────────────────────────
Sum of Squares df Mean Square F p
────────────────────────────────────────────────────────
B1: "A" 25.000 1 25.000 9.091 .039 *
B2: "A" 1.000 1 1.000 0.364 .579
Residuals 11.000 4 2.750
────────────────────────────────────────────────────────
Note. Identical to the results obtained with SPSS GLM EMMEANS syntax.
Estimated Marginal Means of "A":
──────────────────────────────────────
"A" "B" Mean [95% CI of Mean] S.E.
──────────────────────────────────────
A1 B1 0.500 [-2.756, 3.756] (1.173)
A2 B1 5.500 [ 2.244, 8.756] (1.173)
A1 B2 2.000 [-1.256, 5.256] (1.173)
A2 B2 3.000 [-0.256, 6.256] (1.173)
──────────────────────────────────────
Pairwise Comparisons of "A":
─────────────────────────────────────────────────────────────────────────
Contrast "B" Estimate S.E. df t p Cohen’s d [95% CI of d]
─────────────────────────────────────────────────────────────────────────
A2 - A1 B1 5.000 (1.658) 4 3.015 .039 * 3.015 [ 0.239, 5.792]
A2 - A1 B2 1.000 (1.658) 4 0.603 .579 0.603 [-2.173, 3.379]
─────────────────────────────────────────────────────────────────────────
Pooled SD for computing Cohen’s d: 1.658
No need to adjust p values.
Disclaimer:
By default, pooled SD is Root Mean Square Error (RMSE).
There is much disagreement on how to compute Cohen’s d.
You are completely responsible for setting `sd.pooled`.
You might also use `effectsize::t_to_d()` to compute d.【作业8】方差分析练习
作业要求：
- 基于【作业4】和【作业6】的期末自选数据和代码积累，运用本章所学的方差分析方法和代码，练习方差分析（根据自己的数据情况选择最合适的一种方差分析类型）
- 使用R Markdown完成，对关键代码及结果要有注释说明
平台提交：
- 运行得到HTML网页文件的关键部分截图（只需上传截图）
© 包寒吴霜
---
title: "《R语言》第8章：方差分析"
subtitle: <a href="https://psychbruce.github.io/RCourse/">返回课程主页</a>
author: "授课教师：包寒吴霜"
# date: "`r Sys.Date()`"
output:
  html_document:
    toc: true
    toc_depth: 3
    toc_float:
      collapsed: false
    code_download: true
    anchor_sections: true
    highlight: pygments
    css: RmdCSS.css
---

```{=html}
<p style="font-size: 12px">版权声明：本套课程材料开源，使用和分享必须遵守「创作共用许可协议 CC BY-NC-SA」（来源引用-非商业用途使用-以相同方式共享）。<img src="img/CC-BY-NC-SA.jpg" width="120px" height="42px" style="float: right" /></p>
```

```{r Config, include=FALSE}
options(
  knitr.kable.NA = "",
  digits = 4
)
knitr::opts_chunk$set(
  comment = "",
  fig.width = 6,
  fig.height = 4,
  dpi = 300
)
```

------------------------------------------------------------------------

# Chap08：方差分析

#### 往期要点回顾

- [Chap07 \# 描述统计与相关分析](https://psychbruce.github.io/RCourse/Chap07#%E6%8F%8F%E8%BF%B0%E7%BB%9F%E8%AE%A1%E4%B8%8E%E7%9B%B8%E5%85%B3%E5%88%86%E6%9E%90){.uri}
- [Chap07 \# t检验](https://psychbruce.github.io/RCourse/Chap07#t%E6%A3%80%E9%AA%8C){.uri}

#### 本章要点目录

- [【知识点】方差分析（ANOVA）统计术语](#知识点方差分析anova统计术语)
- [【实践1】组间设计ANOVA](#实践1组间设计anova)（重点）
- [【实践2】组内设计ANOVA](#实践2组内设计anova)
- [【实践3】混合设计ANOVA](#实践3混合设计anova)
- [【实践4】组间设计ANOVA的多重比较](#实践4组间设计anova的多重比较)（重点）
- [【探索发现】多重比较的p值校正方法](#探索发现多重比较的p值校正方法)
- [【实践5】组间设计ANOVA的简单效应检验](#实践5组间设计anova的简单效应检验)（重点）
- [【探索发现】对于两因素方差分析（A × B），以下情况都有可能发生吗？](#探索发现对于两因素方差分析a-b以下情况都有可能发生吗)
- [【实践6】交互作用显著，但A的两个简单效应都不显著](#实践6交互作用显著但a的两个简单效应都不显著)
- [【实践7】交互作用不显著，但A的简单效应一个显著、一个不显著](#实践7交互作用不显著但a的简单效应一个显著一个不显著)

```{r, message=FALSE, warning=FALSE}
## 本章所需R包
library(bruceR)
```

# 方差分析的统计知识回顾

#### 【知识点】方差分析（ANOVA）统计术语 {#知识点方差分析anova统计术语}

![↑ 图源：<https://www.nature.com/articles/s41598-023-47057-0>](images/clipboard-2342090980.png)

- **方差分析ANOVA**（以2 × 2 “高低组别 × 男女性别”两因素组间设计ANOVA为例）
  - **主效应（main effect）**
    - 代表“平均效应”，某个因素在其他因素不同条件下的边际平均效应
    - [例：高组和低组之间的总体差异（无论男性和女性，组别的平均效应）]{.underline}
  - **交互作用（interaction）**
    - 代表“效应差异”，某个因素在其他因素不同条件下存在不同的效应
    - [例：高低组间的差异在男性和女性群体之间也存在差异（差异的差异）]{.underline}
- **交互作用显著后的简单效应检验**
  - **简单效应（simple effect）**，也称“条件效应”（conditional effect）
    - 通常特指：简单主效应（simple main effect），也称“条件主效应”（conditional main effect）
    - [例：分别在男性或女性群体中，高低组间的差异（组别的简单主效应）]{.underline}
  - （拓展）三阶交互作用（A × B × C）中的复杂情况
    - 简单交互作用（simple interaction）：C不同条件下的A × B简单交互作用
    - 简单简单效应（simple-simple effect）：B和C不同组合条件下的A简单主效应
- **某个因素多个条件间（≥ 3）的两两对比**
  - 事后检验（post-hoc test）
    - 通常特指：**事后多重比较（post-hoc multiple comparison）**
    - 需要对*p*值做**“多重比较校正”（adjust *p*-values for multiple comparisons）**以降低假阳性概率（false discovery rate, FDR）

![](images/clipboard-353831722.png)

# 多因素方差分析

![](images/clipboard-1237835581.png)

## 完全随机/组间设计ANOVA

#### 【实践1】组间设计ANOVA {#实践1组间设计anova}

- [`MANOVA()`函数帮助文档](https://psychbruce.github.io/bruceR/reference/MANOVA.html){.uri}

```{r}
between.1  # 单因素四水平组间设计
MANOVA(between.1, dv="SCORE", between="A")
```

```{r}
between.2  # 2×3两因素组间设计
MANOVA(between.2, dv="SCORE", between=c("A", "B"))

## 使用 emmeans 包的 emmip() 函数绘制交互图
## 请查阅帮助文档：?emmeans::emmip()
m = MANOVA(between.2, dv="SCORE", between=c("A", "B"))
emmip(m, ~ A | B, CIs=TRUE)
emmip(m, ~ B | A, CIs=TRUE)
emmip(m, B ~ A, CIs=TRUE)
emmip(m, A ~ B, CIs=TRUE)
```

```{r}
between.3  # 2×2×2三因素组间设计
MANOVA(between.3, dv="SCORE", between=c("A", "B", "C"))
```

## 重复测量/组内设计ANOVA

#### 【实践2】组内设计ANOVA {#实践2组内设计anova}

- [`MANOVA()`函数帮助文档](https://psychbruce.github.io/bruceR/reference/MANOVA.html){.uri}

```{r}
within.1  # 单因素四水平组内设计
MANOVA(within.1,
       dvs = "A1:A4",
       dvs.pattern = "A(.)",
       within = "A")

# 相同：
MANOVA(within.1,
       dvs = c("A1", "A2", "A3", "A4"),
       dvs.pattern = "A(.)",
       within = "AnyVarNameIsOK")
```

```{r}
within.2  # 2×3两因素组内设计
m = MANOVA(within.2,
           dvs = "A1B1:A2B3",
           dvs.pattern = "A(.)B(.)",
           within = c("A", "B"))
emmip(m, ~ A | B, CIs=TRUE)
emmip(m, ~ B | A, CIs=TRUE)
emmip(m, B ~ A, CIs=TRUE)
emmip(m, A ~ B, CIs=TRUE)
```

```{r}
within.3  # 2×2×2三因素组内设计
MANOVA(within.3,
       dvs = "A1B1C1:A2B2C2",
       dvs.pattern = "A(.)B(.)C(.)",
       within = c("A", "B", "C"))
```

## 混合设计ANOVA

#### 【实践3】混合设计ANOVA {#实践3混合设计anova}

- [`MANOVA()`函数帮助文档](https://psychbruce.github.io/bruceR/reference/MANOVA.html){.uri}

```{r}
mixed.2_1b1w  # 2×3两因素混合设计（A为组间，B为组内）
MANOVA(mixed.2_1b1w,
       dvs = "B1:B3",
       dvs.pattern = "B(.)",
       between = "A",
       within = "B")
MANOVA(mixed.2_1b1w,
       dvs = "B1:B3",
       dvs.pattern = "B(.)",
       between = "A",
       within = "B",
       sph.correction = "GG")
```

```{r}
mixed.3_1b2w  # 2×2×2三因素混合设计（A为组间，B、C为组内）
MANOVA(mixed.3_1b2w,
       dvs = "B1C1:B2C2",
       dvs.pattern = "B(.)C(.)",
       between = "A",
       within = c("B", "C"))
```

```{r}
mixed.3_2b1w  # 2×2×2三因素混合设计（A、C为组间，B为组内）
MANOVA(mixed.3_2b1w,
       dvs = "B1:B2",
       dvs.pattern = "B(.)",
       between = c("A", "C"),
       within = "B")
```

# 简单效应检验与多重比较

## 多重比较

#### 【实践4】组间设计ANOVA的多重比较 {#实践4组间设计anova的多重比较}

- [`EMMEANS()`函数帮助文档](https://psychbruce.github.io/bruceR/reference/EMMEANS.html){.uri}（**E**stimated **M**arginal **Means**，估计边际均值）

```{r}
m = MANOVA(between.1, dv="SCORE", between="A")
emmip(m, ~ A, CIs=TRUE)

EMMEANS(m, "A", p.adjust="none")
EMMEANS(m, "A", p.adjust="bonferroni")
EMMEANS(m, "A", contrast="seq")
EMMEANS(m, "A", contrast="poly")
```

#### 【探索发现】多重比较的p值校正方法 {#探索发现多重比较的p值校正方法}

`p.adjust`参数

- `"none"`（无校正）
- `"fdr"`
- `"hochberg"`
- `"hommel"`
- `"holm"`
- `"tukey"`
- `"mvt"`
- `"dunnettx"`
- `"sidak"`
- `"scheffe"`
- `"bonferroni"`（默认，最严格）
  - Bonferroni校正：直接将原始*p*值与多重比较次数*n*相乘，得到校正后的*p*值
    - 比如，3个条件之间的两两比较组合有C(3, 2) = 3次，某效应的原始*p* = .04，校正后*p* = .04 × 3 = .12，不再显著

## 简单效应检验

#### 【实践5】组间设计ANOVA的简单效应检验 {#实践5组间设计anova的简单效应检验}

- [`EMMEANS()`函数帮助文档](https://psychbruce.github.io/bruceR/reference/EMMEANS.html){.uri}（**E**stimated **M**arginal **Means**，估计边际均值）

```{r}
m = MANOVA(between.2, dv="SCORE", between=c("A", "B"))

emmip(m, ~ A | B, CIs=TRUE)
EMMEANS(m, "A", by="B")

emmip(m, ~ B | A, CIs=TRUE)
EMMEANS(m, "B", by="A")
```

```{r}
## 使用管道操作符 %>% 连接多个 EMMEANS()
MANOVA(between.3, dv="SCORE", between=c("A", "B", "C")) %>%
  EMMEANS("A", by="B") %>%
  EMMEANS(c("A", "B"), by="C") %>%
  EMMEANS("A", by=c("B", "C"))
```

# \* 拓展：特殊情况

#### 【探索发现】对于两因素方差分析（A × B），以下情况都有可能发生吗？ {#探索发现对于两因素方差分析a-b以下情况都有可能发生吗}

**交互作用 & 主效应：**

- [x] 交互作用**显著**，A和B的主效应**都显著**（很正常）
- [x] 交互作用**显著**，A和B的主效应**都不显著**（很正常，只有交互作用）
- [x] 交互作用**不显著**，A和B的主效应**都显著**（很正常，只有主效应）
- [x] 交互作用**不显著**，A和B的主效应**都不显著**（很正常，啥效应都没）

**交互作用 & 简单效应：**\
（例如：A在B1、B2水平上的两个简单主效应）

- [x] 交互作用**显著**，A的两个简单效应**都显著**\
  （很正常，交互作用体现了简单效应的定量差异）
- [x] 交互作用**显著**，A的两个简单效应**都不显著**❓️\
  （比较少见，但有概率发生！）
- [x] 交互作用**显著**，A的简单效应一个**显著**、一个**不显著**\
  （很正常，交互作用体现了简单效应的定性差异）
- [x] 交互作用**不显著**，A的两个简单效应**都显著**\
  （很正常，主效应为主）
- [x] 交互作用**不显著**，A的两个简单效应**都不显著**\
  （很正常，啥效应都没）
- [x] 交互作用**不显著**，A的简单效应一个**显著**、一个**不显著**❓️\
  （并不少见，显著的简单效应恰好卡在了临界点附近！）

> “Seeing is believing.”（眼见为实）

#### 【实践6】交互作用显著，但A的两个简单效应都不显著 {#实践6交互作用显著但a的两个简单效应都不显著}

```{r}
data1 = data.table(
  A = c(1, 1, 1, 1, 2, 2, 2, 2),
  B = c(1, 1, 2, 2, 1, 1, 2, 2),
  Y = c(0, 7, 10, 12, 12, 10, 7, 0)
)
m = MANOVA(data1, dv="Y", between=c("A", "B"))
emmip(m, B ~ A, CIs=TRUE)
EMMEANS(m, "A", by="B")
```

![](images/clipboard-2805730961.png)

#### 【实践7】交互作用不显著，但A的简单效应一个显著、一个不显著 {#实践7交互作用不显著但a的简单效应一个显著一个不显著}

```{r}
data2 = data.table(
  A = c(1, 1, 1, 1, 2, 2, 2, 2),
  B = c(1, 1, 2, 2, 1, 1, 2, 2),
  Y = c(0, 1, 0, 4, 5, 6, 2, 4)
)
m = MANOVA(data2, dv="Y", between=c("A", "B"))
emmip(m, B ~ A, CIs=TRUE)
EMMEANS(m, "A", by="B")
```

# 【作业8】方差分析练习

作业要求：

- 基于[【作业4】](https://psychbruce.github.io/RCourse/Chap03#%E4%BD%9C%E4%B8%9A4%E6%9C%9F%E6%9C%AB%E8%87%AA%E9%80%89%E5%85%AC%E5%BC%80%E6%95%B0%E6%8D%AE%E5%AF%BC%E5%85%A5)和[【作业6】](https://psychbruce.github.io/RCourse/Chap05#%E4%BD%9C%E4%B8%9A6%E6%9C%9F%E6%9C%AB%E4%BD%9C%E4%B8%9A%E6%95%B0%E6%8D%AE%E5%8F%98%E9%87%8F%E8%AE%A1%E7%AE%97){.uri}的期末自选数据和代码积累，运用本章所学的方差分析方法和代码，练习**方差分析**（根据自己的数据情况选择最合适的一种方差分析类型）
- 使用R Markdown完成，对关键代码及结果要有注释说明

平台提交：

- 运行得到HTML网页文件的**关键部分截图（只需上传截图）**

------------------------------------------------------------------------

[返回课程主页](https://psychbruce.github.io/RCourse/)

© 包寒吴霜
