tukey multiple comprison in R

最新推荐文章于 2025-06-04 09:24:46 发布

转载最新推荐文章于 2025-06-04 09:24:46 发布 · 1.3k 阅读

本文详细介绍了如何使用Tukey方法进行ANOVA（方差分析）和Tukey多重比较测试，通过创建虚构的数据集来展示分析过程，并使用R语言实现。文章进一步解释了如何解释ANOVA结果和Tukey HSD测试结果，得出所有三个群体的平均值都存在显著差异的结论。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

from http://faculty.wwu.edu/jmcl/Biostat/mm.tukey

mm.tukey
				JFM  2/8/2010

ANOVA using m&m positions for three kinds of m&ms, followed by
Tukey multiple comparisons test (Tukey's Honest Significant Difference test).  
Data fabricated: random (uniform) distributions from overlapping ranges. 
In R.

First, ANOVA:

> # m&m ANOVA example
> # Fabricate data
> mm.pl <- sort(sample(0:40, replace=TRUE, size=10))
> mm.pl
 [1] 10 21 25 29 31 31 34 36 39 39
> mean(mm.pl)
[1] 29.5
> sqrt(var(mm.pl))
[1] 8.947377
> 
> mm.pnut <- sort(sample(30:70, replace=TRUE, size=10))
> mm.pnut
 [1] 33 34 41 55 56 61 63 65 66 68
> mean(mm.pnut)
[1] 54.2
> sqrt(var(mm.pnut))
[1] 13.35665
> 
> mm.al <- sort(sample(60:100, replace=TRUE, size=10))
> mm.al
 [1] 64 74 77 82 82 85 85 87 87 98
> mean(mm.al)
[1] 82.1
> sqrt(var(mm.al))
[1] 9.048634
> 
> # Combine as single variable, "mm.pos"
> mm.pos <- c(mm.pl, mm.pnut, mm.al)
> mm.pos
 [1] 10 21 25 29 31 31 34 36 39 39 33 34 41 55 56 61 63 65 66 68 64 74 77 82 82
[26] 85 85 87 87 98
> 
> # Create factor variable (mm type)
> mm.type <- rep(c("Plain", "Peanut", "Almond"), c(10, 10, 10))
> mm.type <- factor(mm.type)
> 
> # View data in strip plot
> stripplot(mm.type ~ mm.pos)
> # Better: add "jitter" to view overlapping points:
> stripplot(mm.type ~ jitter(mm.pos, 0.4), xlim=c(0,100),
+ 	xlab="m&m position (cm)")
> 
> # Analysis of Variance:
> # H_o: all 4 means equal
> # select alpha = 0.05
> 
> mm.aov <- aov(mm.pos ~ mm.type)
> anova(mm.aov)
Analysis of Variance Table

Response: mm.pos

Terms added sequentially (first to last)
          Df Sum of Sq  Mean Sq  F Value        Pr(F) 
mm.type    2  13850.87 6925.433 61.04691 9.587497e-11
Residuals 27   3063.00  113.444                      
>
> # Conclusion: Reject H_o; conclude not all means equal (P < 10^-10)

********************************************************************
Next, Tukey multiple comparisons test 
(Tukey's Honest Significant Difference test). 

> # Apply TukeyHSD function to output of ANOVA:

> TukeyHSD(mm.aov)
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = mm.pos ~ mm.type)

$mm.type
               diff       lwr       upr    p adj
Peanut-Almond -27.9 -39.71017 -16.08983 9.00e-06
Plain-Almond  -52.6 -64.41017 -40.78983 0.00e+00
Plain-Peanut  -24.7 -36.51017 -12.88983 5.36e-05

> # Conclusion: Means of all three populations differ from each other.
> #             (i.e., all pairs differ)

> # To plot means and confidence intervals:
> plot(TukeyHSD(mm.aov))
> 
> # Alternatively, perform multiple comparisons test using R's pairwise.t.test. 
> # Specify the response variable first ("mm.pos"),
> #   followed by factor variable ("mm.type"), delimited by a comma ",".

> pairwise.t.test(mm.pos, mm.type)

        Pairwise comparisons using t tests with pooled SD 

data:  mm.pos and mm.type 

       Almond  Peanut 
Peanut 6.2e-06 -      
Plain  4.9e-11 1.9e-05

P value adjustment method: holm 
> 
> # Conclusion: Same as above, means of all three populations differ.