r:oneway_anova
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Table of Contents
Oneway ANOVA
| (온도조건)x1 | 50.5 | 52.1 | 51.9 | 52.4 | 50.6 | 51.4 | 51.2 | 52.2 | 51.5 | 50.8 |
| (온도조건)x2 | 47.5 | 47.7 | 46.6 | 47.1 | 47.2 | 47.8 | 45.2 | 47.4 | 45.0 | 47.9 |
| (온도조건)x3 | 46.0 | 47.1 | 45.6 | 47.1 | 47.2 | 46.4 | 45.9 | 47.1 | 44.9 | 46.2 |
x1 <- c(50.5, 52.1, 51.9, 52.4, 50.6, 51.4, 51.2, 52.2, 51.5, 50.8) x2 <- c(47.5, 47.7, 46.6, 47.1, 47.2, 47.8, 45.2, 47.4, 45.0, 47.9) x3 <- c(46.0, 47.1, 45.6, 47.1, 47.2, 46.4, 45.9, 47.1, 44.9, 46.2) x1 x2 x3
> xc <- data.frame(x1,x2,x3)
> xc
x1 x2 x3
1 50.5 47.5 46.0
2 52.1 47.7 47.1
3 51.9 46.6 45.6
4 52.4 47.1 47.1
5 50.6 47.2 47.2
6 51.4 47.8 46.4
7 51.2 45.2 45.9
8 52.2 47.4 47.1
9 51.5 45.0 44.9
10 50.8 47.9 46.2
> xs <- stack(xc)
> xs
values ind
1 50.5 x1
2 52.1 x1
3 51.9 x1
4 52.4 x1
5 50.6 x1
6 51.4 x1
7 51.2 x1
8 52.2 x1
9 51.5 x1
10 50.8 x1
11 47.5 x2
12 47.7 x2
13 46.6 x2
14 47.1 x2
15 47.2 x2
16 47.8 x2
17 45.2 x2
18 47.4 x2
19 45.0 x2
20 47.9 x2
21 46.0 x3
22 47.1 x3
23 45.6 x3
24 47.1 x3
25 47.2 x3
26 46.4 x3
27 45.9 x3
28 47.1 x3
29 44.9 x3
30 46.2 x3
> aggregate(values~ind, data=xs, mean) ind values 1 x1 51.46 2 x2 46.94 3 x3 46.35 # or use, tapply function as shown the below
> x.mod <- aov(values~ind,data=xs)
> x.mod
Call:
aov(formula = values ~ ind, data = xs)
Terms:
ind Residuals
Sum of Squares 156.302 19.393
Deg. of Freedom 2 27
Residual standard error: 0.8475018
Estimated effects may be unbalanced
> summary(x.mod)
Df Sum Sq Mean Sq F value Pr(>F)
ind 2 156.30 78.15 108.8 1.2e-13 ***
Residuals 27 19.39 0.72
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
>
> TukeyHSD(x.mod)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = values ~ ind, data = xs)
$ind
diff lwr upr p adj
x2-x1 -4.52 -5.459735 -3.5802652 0.0000000
x3-x1 -5.11 -6.049735 -4.1702652 0.0000000
x3-x2 -0.59 -1.529735 0.3497348 0.2813795
> tapply(xs$values, xs$ind, mean) x1 x2 x3 51.46 46.94 46.35
SSbetween
> meanxs <- mean(xs$values) > mx1 <- mean(x1) > mx2 <- mean(x2) > mx3 <- mean(x3) > x2ss <- 10*((meanxs - mx2)^2) > x3ss <- 10*((meanxs - mx3)^2) > x1ss <- 10*((meanxs - mx1)^2) > xss <- x1ss+x2ss+x3ss > xss [1] 156.302
E.g. 1
> data(InsectSprays)
> str(InsectSprays)
'data.frame': 72 obs. of 2 variables:
$ count: num 10 7 20 14 14 12 10 23 17 20 ...
$ spray: Factor w/ 6 levels "A","B","C","D",..: 1 1 1 1 1 1 1 1 1 1 ...
> summary(InsectSprays)
count spray
Min. : 0.00 A:12
1st Qu.: 3.00 B:12
Median : 7.00 C:12
Mean : 9.50 D:12
3rd Qu.:14.25 E:12
Max. :26.00 F:12
> attach(InsectSprays)
> tapply(count, spray, mean)
A B C D E F
14.500000 15.333333 2.083333 4.916667 3.500000 16.666667
> tapply(count, spray, var)
A B C D E F
22.272727 18.242424 3.901515 6.265152 3.000000 38.606061
> tapply(count, spray, length) # okay, as there are no missing values
A B C D E F
12 12 12 12 12 12
> boxplot(count ~ spray) # boxplot(count~spray, data=InsectSprays) if not attached
> oneway.test(count ~ spray) # oneway.test(count~spray, data=InsectSprays) if not attached
One-way analysis of means (not assuming equal variances)
data: count and spray
F = 36.0654, num df = 5.000, denom df = 30.043, p-value = 8e-12
By default, oneway.test() applies a Welch-like correction for nonhomogeneity. To turn off it, set the “var.equal=” option to TRUE.
ANOVA 그룹간 homogeneity를 요구하는데, oneway.test는 이를 보정하여 F값을 구한다.
> aov.out = aov(count ~ spray, data=InsectSprays)
> summary(aov.out)
Df Sum Sq Mean Sq F value Pr(>F)
spray 5 2668.83 533.77 34.702 <2.2e-16 ***
Residuals 66 1015.17 15.38
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
if we use var.eq=TRUE option, the result would be the same.
> oneway.test(count ~ spray, data=InsectSprays, var.eq=T) One-way analysis of means data: count and spray F = 34.7023, num df = 5, denom df = 66, p-value < 2.2e-16
> pairwise.t.test(InsectSprays$count, InsectSprays$spray) Pairwise comparisons using t tests with pooled SD data: InsectSprays$count and InsectSprays$spray A B C D E B 1.00 - - - - C 8.7e-10 1.2e-10 - - - D 6.9e-07 9.7e-08 0.49 - - E 2.5e-08 3.6e-09 1.00 1.00 - F 0.90 1.00 4.2e-12 4.0e-09 1.4e-10 P value adjustment method: holm >
> TukeyHSD(aov.out)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = count ~ spray, data = InsectSprays)
$spray
diff lwr upr p adj
B-A 0.8333333 -3.866075 5.532742 0.9951810
C-A -12.4166667 -17.116075 -7.717258 0.0000000
D-A -9.5833333 -14.282742 -4.883925 0.0000014
E-A -11.0000000 -15.699409 -6.300591 0.0000000
F-A 2.1666667 -2.532742 6.866075 0.7542147
C-B -13.2500000 -17.949409 -8.550591 0.0000000
D-B -10.4166667 -15.116075 -5.717258 0.0000002
E-B -11.8333333 -16.532742 -7.133925 0.0000000
F-B 1.3333333 -3.366075 6.032742 0.9603075
D-C 2.8333333 -1.866075 7.532742 0.4920707
E-C 1.4166667 -3.282742 6.116075 0.9488669
F-C 14.5833333 9.883925 19.282742 0.0000000
E-D -1.4166667 -6.116075 3.282742 0.9488669
F-D 11.7500000 7.050591 16.449409 0.0000000
F-E 13.1666667 8.467258 17.866075 0.0000000
Ex 1
약의 종류에 따른 효과의 차이
Drug A 4 5 4 3 2 4 3 4 4 Drug B 6 8 4 5 4 6 5 8 6 Drug C 6 7 6 6 7 5 6 5 5
A <- c(4, 5, 4, 3, 2, 4, 3, 4, 4) B <- c(6, 8, 4, 5, 4, 6, 5, 8, 6) C <- c(6, 7, 6, 6, 7, 5, 6, 5, 5)
Ex 2
download dataset_anova_comparisonMethods.csv data file
- dataset_ANOVA_OneWayComparisons.csv
Treatment StressReduction mental 2 mental 2 mental 3 mental 4 mental 4 mental 5 mental 3 mental 4 mental 4 mental 4 physical 4 physical 4 physical 3 physical 5 physical 4 physical 1 physical 1 physical 2 physical 3 physical 3 medical 1 medical 2 medical 2 medical 2 medical 3 medical 2 medical 3 medical 1 medical 3 medical 1
dd <- read.csv("http://commres.net/wiki/_media/dataset_anova_comparisonmethods.csv", sep=",")
In class exercise
위의 데이터를 이용하여 아래를 수행하시오.
1. F test 가설을 세우시오
2. 각 그룹의 평균과 표준편차 그리고 분산값을 구하시오.
3. F test를 하시오
4. 그룹간 비교를 하시오 (post hoc)
5. 분석결과를 정리하여 설명하시오.
r/oneway_anova.1543860971.txt.gz · Last modified: 2018/12/04 03:16 by hkimscil