Bước 4: Phân tích ANOVA 2 yếu tố CRD

Tính p-value

# Compute two-way ANOVA test
res.aov2 <- aov(stability ~ diet + time, data = my_data)
# summary(res.aov2)
anova(res.aov2)

Analysis of Variance Table

Response: stability
          Df  Sum Sq Mean Sq  F value    Pr(>F)    
diet       7  15.999   2.286   2.5966   0.02672 *  
time       1 142.822 142.822 162.2555 1.781e-15 ***
Residuals 39  34.329   0.880                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Compute two-way ANOVA test with interaction effect
res.aov3 <- aov(stability ~ diet + time + diet:time, data = my_data)
anova(res.aov3)

Analysis of Variance Table

Response: stability
          Df  Sum Sq Mean Sq  F value   Pr(>F)    
diet       7  15.999   2.286   2.8340  0.02041 *  
time       1 142.822 142.822 177.0920 1.37e-14 ***
diet:time  7   8.521   1.217   1.5094  0.19953    
Residuals 32  25.807   0.806                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Phân hạng

library(agricolae)
LSD.test(res.aov2, c("diet", "time"), console = TRUE) 

Study: res.aov2 ~ c("diet", "time")

LSD t Test for stability 

Mean Square Error:  0.8802287 

diet:time,  means and individual ( 95 %) CI

           stability        std r      LCL      UCL      Min      Max
NT1:10-min  89.49940 0.29641311 3 88.40376 90.59503 89.17712 89.76035
NT1:5-min   86.20000 1.48386449 3 85.10436 87.29564 84.50821 87.28091
NT2:10-min  89.12396 0.66835713 3 88.02832 90.21959 88.51183 89.83705
NT2:5-min   85.68620 1.00057733 3 84.59057 86.78184 84.58238 86.53363
NT3:10-min  89.18181 2.50740722 3 88.08617 90.27744 86.30768 90.92160
NT3:5-min   87.52492 0.92028383 3 86.42929 88.62056 86.48140 88.22052
NT4:10-min  91.05804 0.07653564 3 89.96240 92.15367 90.97900 91.13180
NT4:5-min   87.67940 0.23150732 3 86.58376 88.77504 87.41313 87.83304
NT5:10-min  90.58711 0.34015176 3 89.49147 91.68275 90.33636 90.97430
NT5:5-min   87.27551 0.48216583 3 86.17988 88.37115 86.72079 87.59405
NT6:10-min  90.45218 0.26375280 3 89.35654 91.54781 90.21814 90.73797
NT6:5-min   86.86873 0.39883737 3 85.77310 87.96437 86.45951 87.25631
NT7:10-min  90.67417 0.17203343 3 89.57853 91.76981 90.56533 90.87250
NT7:5-min   86.61908 0.65352540 3 85.52344 87.71472 85.88389 87.13404
NT8:10-min  90.66600 0.49282165 3 89.57036 91.76164 90.10980 91.04827
NT8:5-min   85.78958 0.83445867 3 84.69395 86.88522 84.82913 86.33665

Alpha: 0.05 ; DF Error: 39
Critical Value of t: 2.022691 

least Significant Difference: 1.549465 

Treatments with the same letter are not significantly different.

           stability groups
NT4:10-min  91.05804      a
NT7:10-min  90.67417     ab
NT8:10-min  90.66600    abc
NT5:10-min  90.58711    abc
NT6:10-min  90.45218    abc
NT1:10-min  89.49940     bc
NT3:10-min  89.18181    bcd
NT2:10-min  89.12396     cd
NT4:5-min   87.67940     de
NT3:5-min   87.52492      e
NT5:5-min   87.27551     ef
NT6:5-min   86.86873    efg
NT7:5-min   86.61908    efg
NT1:5-min   86.20000    efg
NT8:5-min   85.78958     fg
NT2:5-min   85.68620      g

duncan.test(res.aov2, c("diet", "time"), console = TRUE) 

Study: res.aov2 ~ c("diet", "time")

Duncan's new multiple range test
for stability 

Mean Square Error:  0.8802287 

diet:time,  means

           stability        std r      Min      Max
NT1:10-min  89.49940 0.29641311 3 89.17712 89.76035
NT1:5-min   86.20000 1.48386449 3 84.50821 87.28091
NT2:10-min  89.12396 0.66835713 3 88.51183 89.83705
NT2:5-min   85.68620 1.00057733 3 84.58238 86.53363
NT3:10-min  89.18181 2.50740722 3 86.30768 90.92160
NT3:5-min   87.52492 0.92028383 3 86.48140 88.22052
NT4:10-min  91.05804 0.07653564 3 90.97900 91.13180
NT4:5-min   87.67940 0.23150732 3 87.41313 87.83304
NT5:10-min  90.58711 0.34015176 3 90.33636 90.97430
NT5:5-min   87.27551 0.48216583 3 86.72079 87.59405
NT6:10-min  90.45218 0.26375280 3 90.21814 90.73797
NT6:5-min   86.86873 0.39883737 3 86.45951 87.25631
NT7:10-min  90.67417 0.17203343 3 90.56533 90.87250
NT7:5-min   86.61908 0.65352540 3 85.88389 87.13404
NT8:10-min  90.66600 0.49282165 3 90.10980 91.04827
NT8:5-min   85.78958 0.83445867 3 84.82913 86.33665

Alpha: 0.05 ; DF Error: 39 

Critical Range
       2        3        4        5        6        7        8        9 
1.549465 1.629128 1.681203 1.718713 1.747311 1.769943 1.788331 1.803563 
      10       11       12       13       14       15       16 
1.816368 1.827257 1.836601 1.844677 1.851698 1.857828 1.863200 

Means with the same letter are not significantly different.

           stability groups
NT4:10-min  91.05804      a
NT7:10-min  90.67417     ab
NT8:10-min  90.66600     ab
NT5:10-min  90.58711     ab
NT6:10-min  90.45218     ab
NT1:10-min  89.49940     ab
NT3:10-min  89.18181     bc
NT2:10-min  89.12396     bc
NT4:5-min   87.67940     cd
NT3:5-min   87.52492    cde
NT5:5-min   87.27551    def
NT6:5-min   86.86873    def
NT7:5-min   86.61908    def
NT1:5-min   86.20000    def
NT8:5-min   85.78958     ef
NT2:5-min   85.68620      f

HSD.test(res.aov2, c("diet", "time"), console = TRUE) 

Study: res.aov2 ~ c("diet", "time")

HSD Test for stability 

Mean Square Error:  0.8802287 

diet:time,  means

           stability        std r      Min      Max
NT1:10-min  89.49940 0.29641311 3 89.17712 89.76035
NT1:5-min   86.20000 1.48386449 3 84.50821 87.28091
NT2:10-min  89.12396 0.66835713 3 88.51183 89.83705
NT2:5-min   85.68620 1.00057733 3 84.58238 86.53363
NT3:10-min  89.18181 2.50740722 3 86.30768 90.92160
NT3:5-min   87.52492 0.92028383 3 86.48140 88.22052
NT4:10-min  91.05804 0.07653564 3 90.97900 91.13180
NT4:5-min   87.67940 0.23150732 3 87.41313 87.83304
NT5:10-min  90.58711 0.34015176 3 90.33636 90.97430
NT5:5-min   87.27551 0.48216583 3 86.72079 87.59405
NT6:10-min  90.45218 0.26375280 3 90.21814 90.73797
NT6:5-min   86.86873 0.39883737 3 86.45951 87.25631
NT7:10-min  90.67417 0.17203343 3 90.56533 90.87250
NT7:5-min   86.61908 0.65352540 3 85.88389 87.13404
NT8:10-min  90.66600 0.49282165 3 90.10980 91.04827
NT8:5-min   85.78958 0.83445867 3 84.82913 86.33665

Alpha: 0.05 ; DF Error: 39 
Critical Value of Studentized Range: 5.171129 

Minimun Significant Difference: 2.801061 

Treatments with the same letter are not significantly different.

           stability groups
NT4:10-min  91.05804      a
NT7:10-min  90.67417      a
NT8:10-min  90.66600      a
NT5:10-min  90.58711      a
NT6:10-min  90.45218     ab
NT1:10-min  89.49940    abc
NT3:10-min  89.18181   abcd
NT2:10-min  89.12396   abcd
NT4:5-min   87.67940   bcde
NT3:5-min   87.52492    cde
NT5:5-min   87.27551    cde
NT6:5-min   86.86873    cde
NT7:5-min   86.61908     de
NT1:5-min   86.20000      e
NT8:5-min   85.78958      e
NT2:5-min   85.68620      e

Tham khảo

1. http://www.sthda.com/english/wiki/two-way-anova-test-in-r

2. https://stackoverflow.com/questions/43123462/how-to-obtain-rmse-out-of-lm-result

3. https://online.stat.psu.edu/stat501/lesson/2/2.6

4. https://rcompanion.org/handbook/G_14.html

5. RMSE (Root Mean Square Error) https://agronomy4future.org/?p=15930

6. https://stats.stackexchange.com/questions/445200/coefficient-of-variation-for-beween-groups

Sơ kết

Trên đây là format phân tích ANOVA 2 yếu tố trong R. Để học R bài bản từ A đến Z, thân mời Bạn tham gia khóa học “HDSD R để xử lý dữ liệu” để có nền tảng vững chắc về R nhằm tự tay làm các câu chuyện dữ liệu của riêng mình!

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