Dispersion Analysis

Dataset summary

https://github.com/bioinformatics-core-shared-training/linear-models-r/blob/master/data/amess.csv

df = read.csv("amess.csv")
View(df)

summary(df)

     folate         treatmnt    
 Min.   :206.0   Min.   :1.000  
 1st Qu.:249.5   1st Qu.:1.000  
 Median :274.0   Median :2.000  
 Mean   :283.2   Mean   :1.864  
 3rd Qu.:305.5   3rd Qu.:2.000  
 Max.   :392.0   Max.   :3.000  

df$treatmnt <- factor(df$treatmnt)
summary(df)

     folate      treatmnt
 Min.   :206.0   1:8     
 1st Qu.:249.5   2:9     
 Median :274.0   3:5     
 Mean   :283.2           
 3rd Qu.:305.5           
 Max.   :392.0           

levels(df$treatmnt)

[1] "1" "2" "3"

stripchart(df$folate ~ df$treatmnt, col = c("blue", "green", "black"))

tapply(df$folate, df$treatmnt, mean)

       1        2        3 
316.6250 256.4444 278.0000 

boxplot(df$folate ~ df$treatmnt)

One-Way ANOVA assumptions

1. Assumption of normality
2. Assumption of homogeneity of variance
3. Assumption of independence

shapiro.test(df$folate[df$treatmnt == "1"])

    Shapiro-Wilk normality test

data:  df$folate[df$treatmnt == "1"]
W = 0.90704, p-value = 0.3337

shapiro.test(df$folate[df$treatmnt == "2"])

    Shapiro-Wilk normality test

data:  df$folate[df$treatmnt == "2"]
W = 0.9469, p-value = 0.6561

shapiro.test(df$folate[df$treatmnt == "3"])

    Shapiro-Wilk normality test

data:  df$folate[df$treatmnt == "3"]
W = 0.96355, p-value = 0.8325

bartlett.test(df$folate ~ df$treatmnt)

    Bartlett test of homogeneity of variances

data:  df$folate by df$treatmnt
Bartlett's K-squared = 2.0951, df = 2, p-value = 0.3508

Fit an Analysis of Variance Model

summary(aov(df$folate ~ df$treatmnt))

            Df Sum Sq Mean Sq F value Pr(>F)  
df$treatmnt  2  15516    7758   3.711 0.0436 *
Residuals   19  39716    2090                 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

contrasts(df$treatmnt)

  2 3
1 0 0
2 1 0
3 0 1

summary(lm(df$folate ~ df$treatmnt))

Call:
lm(formula = df$folate ~ df$treatmnt)

Residuals:
    Min      1Q  Median      3Q     Max 
-73.625 -35.361  -4.444  35.625  75.375 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)    316.62      16.16  19.588 4.65e-14 ***
df$treatmnt2   -60.18      22.22  -2.709   0.0139 *  
df$treatmnt3   -38.62      26.06  -1.482   0.1548    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 45.72 on 19 degrees of freedom
Multiple R-squared:  0.2809,    Adjusted R-squared:  0.2052 
F-statistic: 3.711 on 2 and 19 DF,  p-value: 0.04359

tapply(df$folate, df$treatmnt, mean)

       1        2        3 
316.6250 256.4444 278.0000 

mean(tapply(df$folate, df$treatmnt, mean))

[1] 283.6898

contrasts(df$treatmnt) <- contr.sum
contrasts(df$treatmnt)

  [,1] [,2]
1    1    0
2    0    1
3   -1   -1

summary(lm(df$folate ~ df$treatmnt))

Call:
lm(formula = df$folate ~ df$treatmnt)

Residuals:
    Min      1Q  Median      3Q     Max 
-73.625 -35.361  -4.444  35.625  75.375 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)    283.69      10.06  28.188   <2e-16 ***
df$treatmnt1    32.94      13.73   2.400   0.0268 *  
df$treatmnt2   -27.25      13.37  -2.038   0.0557 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 45.72 on 19 degrees of freedom
Multiple R-squared:  0.2809,    Adjusted R-squared:  0.2052 
F-statistic: 3.711 on 2 and 19 DF,  p-value: 0.04359