ANOVA

Read ANOVA for the logics of ANOVA
also read: 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
1. 의도. 목록을 따라 읽도록 지시 - 나중에 회상을 요구받을 것이라고 하여 일부러 암기하도록 지시
우연학습
1. 낱자세기. 낱자세기 - 각 단어의 숫자를 세어보도록 지시
2. 운율. 운율이 같은 단어 생각해보도록 지시
3. 형용사. 형용사를 사용하여 단어를 수식해보도록 지시
4. 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

>