====== ANOVA ======
Read [[:ANOVA]] for the logics of ANOVA
also read: [[:r:oneway_anova|Oneway ANOVA R]]
{{:anova_egs.xlsx}}
Eysenck는 (1974) 단어자료를 기억하는 정도는 단어를 외울 때 사용한 처리방법에 따라서 다르게 나타날 것이라고 예측 (p. 426) 55-65세 50명을 다섯 그룹에 무작위배치(random assignment)
- 의도학습
- **의도.** 목록을 따라 읽도록 지시 - 나중에 회상을 요구받을 것이라고 하여 일부러 암기하도록 지시
- 우연학습
- **낱자세기.** 낱자세기 - 각 단어의 숫자를 세어보도록 지시
- **운율.** 운율이 같은 단어 생각해보도록 지시
- **형용사.** 형용사를 사용하여 단어를 수식해보도록 지시
- **심상.** 단어를 심상(머리)에 세겨보도록 지시
GROUP RECALL
1 9
1 8
1 6
1 8
1 10
1 4
1 6
1 5
1 7
1 7
2 7
2 9
2 6
2 6
2 6
2 11
2 6
2 3
2 8
2 7
3 11
3 13
3 8
3 6
3 14
3 11
3 13
3 13
3 10
3 11
4 12
4 11
4 16
4 11
4 9
4 23
4 12
4 10
4 19
4 11
5 10
5 19
5 14
5 5
5 10
5 11
5 14
5 15
5 11
5 11
{{:Tab16-1.csv}}
^ ^ 낱자세기 ^ 운율 ^ 형용사 ^ 심상 ^ 의도 ^
| | 9 | 7 | 11 | 12 | 10 |
| | 8 | 9 | 13 | 11 | 19 |
| | 6 | 6 | 8 | 16 | 14 |
| | 8 | 6 | 6 | 11 | 5 |
| | 10 | 6 | 14 | 9 | 10 |
| | 4 | 11 | 11 | 23 | 11 |
| | 6 | 6 | 13 | 12 | 14 |
| | 5 | 3 | 13 | 10 | 15 |
| | 7 | 8 | 10 | 19 | 11 |
| | 7 | 7 | 11 | 11 | 11 |
| 평균 | 7 | 6.9 | 11 | 13.4 | 12 |
| 표준편차 | 1.83 | 2.13 | 2.49 | 4.50 | 3.74 |
| 변량 | 3.33 | 4.54 | 6.22 | 20.27 | 14.00 |
| SS | 30 | 40.9 | 56 | 182.4 | 126 |
| | | | | | 435.3 |
| 전체평균 | 10.06 |
| 전체표준편차 | 4.01 |
| 전체변량 | 16.06 |
| 전체n | 50 |
| 전체SS | 786.82 |
| BetweenVar | 351.52 |
가정.
- 정상성
- 변량동질성
- 관찰독립성
> a.data <- read.csv("http://commres.net/wiki/_media/tab16-1.csv")
> a.data$GROUP <- factor(a.data$GROUP)
> a.data
GROUP RECALL
1 1 9
2 1 8
3 1 6
4 1 8
5 1 10
6 1 4
7 1 6
8 1 5
9 1 7
10 1 7
11 2 7
12 2 9
13 2 6
14 2 6
15 2 6
16 2 11
17 2 6
18 2 3
19 2 8
20 2 7
21 3 11
22 3 13
23 3 8
24 3 6
25 3 14
26 3 11
27 3 13
28 3 13
29 3 10
30 3 11
31 4 12
32 4 11
33 4 16
34 4 11
35 4 9
36 4 23
37 4 12
38 4 10
39 4 19
40 4 11
41 5 10
42 5 19
43 5 14
44 5 5
45 5 10
46 5 11
47 5 14
48 5 15
49 5 11
50 5 11
> a.out <- aov(RECALL~GROUP, data=a.data)
> a.out
Call:
aov(formula = RECALL ~ GROUP, data = a.data)
Terms:
GROUP Residuals
Sum of Squares 351.52 435.30
Deg. of Freedom 4 45
Residual standard error: 3.110198
Estimated effects may be unbalanced
>
> summary(a.out)
Df Sum Sq Mean Sq F value Pr(>F)
GROUP 4 351.5 87.88 9.085 1.82e-05 ***
Residuals 45 435.3 9.67
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> TukeyHSD(a.out)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = RECALL ~ GROUP, data = a.data)
$GROUP
diff lwr upr p adj
2-1 -0.1 -4.05223799 3.852238 0.9999937
3-1 4.0 0.04776201 7.952238 0.0460196
4-1 6.4 2.44776201 10.352238 0.0003180
5-1 5.0 1.04776201 8.952238 0.0068354
3-2 4.1 0.14776201 8.052238 0.0385792
4-2 6.5 2.54776201 10.452238 0.0002524
5-2 5.1 1.14776201 9.052238 0.0055623
4-3 2.4 -1.55223799 6.352238 0.4291513
5-3 1.0 -2.95223799 4.952238 0.9510451
5-4 -1.4 -5.35223799 2.552238 0.8510119
====== eg. p.473 ======
> ns <- c(27, 34, 19, 20, 56, 35, 23, 37, 4, 30, 4, 42, 34, 19, 49)
> ds <- c(48, 29, 34, 6, 18, 63, 9, 54, 28, 71, 60, 54, 51, 25, 49)
> as <- c(34, 65, 55, 33, 42, 54, 21, 44, 61, 38, 75, 61, 51, 32, 47)
>
> smoke <- data.frame(ns,ds,as)
> smoke
ns ds as
1 27 48 34
2 34 29 65
3 19 34 55
4 20 6 33
5 56 18 42
6 35 63 54
7 23 9 21
8 37 54 44
9 4 28 61
10 30 71 38
11 4 60 75
12 42 54 61
13 34 51 51
14 19 25 32
15 49 49 47
> smoke.st <- stack(smoke)
> smoke.st
values ind
1 27 ns
2 34 ns
3 19 ns
4 20 ns
5 56 ns
6 35 ns
7 23 ns
8 37 ns
9 4 ns
10 30 ns
11 4 ns
12 42 ns
13 34 ns
14 19 ns
15 49 ns
16 48 ds
17 29 ds
18 34 ds
19 6 ds
20 18 ds
21 63 ds
22 9 ds
23 54 ds
24 28 ds
25 71 ds
26 60 ds
27 54 ds
28 51 ds
29 25 ds
30 49 ds
31 34 as
32 65 as
33 55 as
34 33 as
35 42 as
36 54 as
37 21 as
38 44 as
39 61 as
40 38 as
41 75 as
42 61 as
43 51 as
44 32 as
45 47 as
> smoke.mod <- aov(values~ind,data=smoke.st)
> smoke.mod
Call:
aov(formula = values ~ ind, data = smoke.st)
Terms:
ind Residuals
Sum of Squares 2643.378 11700.400
Deg. of Freedom 2 42
Residual standard error: 16.69074
Estimated effects may be unbalanced
> summary(smoke.mod)
Df Sum Sq Mean Sq F value Pr(>F)
ind 2 2643 1321.7 4.744 0.0139 *
Residuals 42 11700 278.6
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> TukeyHSD(smoke.mod)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = values ~ ind, data = smoke.st)
$ind
diff lwr upr p adj
ds-as -7.60000 -22.40679 7.206788 0.4327383
ns-as -18.66667 -33.47345 -3.859878 0.0104480
ns-ds -11.06667 -25.87345 3.740122 0.1768164
>