COMMunication
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====== 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

<code>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</code>
{{: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

<code>> 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

</code>
====== eg. p.473 ======
<code>> 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

> </code>