20190816
Created my own anova function for practicing R function.

0. packages

library(reshape2) #melt()

1. Create data.frame

G1 <- c(52, 43, 40, 47, 45)
G2 <- c(49, 52, 46, 43, 40)
G3 <- c(55, 51, 53, 55, 49)
G4 <- c(49, 52, 55, 54, 48)
random_df <- data.frame(G1, G2, G3, G4)
random_df

##   G1 G2 G3 G4
## 1 52 49 55 49
## 2 43 52 51 52
## 3 40 46 53 55
## 4 47 43 55 54
## 5 45 40 49 48

2. Custom ANOVA function

#One_way ANOVA function
My_anova <- function(df) {
  ANOVA <- list()            #create an empty list that will be returned at the end
  
  N <- ncol(df)*nrow(df)     #the total number of observations
  k <- ncol(df)              #the number of groups
  n <- nrow(df)              #the number of obs in each group  
  
  #Mean by group (for reference)
  ANOVA$group_mean <- summary(df)[4, 1:k]
  
  #SST
  SST <- data.frame()
  for (i in 1:k) {
    for (j in 1:n) {
      
      SST[i, j] <- (df[[i]][j] - sum(df)/N)^2 #squre sum of (each obs - total mean value)
    }
  }
  SST <- sum(SST)
  
  ANOVA$SST <- SST
  
  #SSB
  SSB <- data.frame()
  for (i in 1:k) {
    for(j in 1:n) {
      
      SSB[i, j] <- (sum(df[[i]])/n - sum(df)/N)^2 #square sum of (mean of each group - total mean value)
    }
  }
  SSB <- sum(SSB)
  
  ANOVA$SSB <- SSB
  
  #SSW
  SSW <- SST-SSB
  ANOVA$SSW <- SSW                                #SST = SSB + SSW
  
  #ANOVA
  df1 <- melt(df)                                 #tidy form for anova function
  pre_anova <- lm(value~variable, data=df1)       #variable: group  #value: each obs
  model <- anova(pre_anova)                       #ANOVA result
  
  ANOVA$anova <- model
  
  #ANOVA table
  source <- c("inter_group", "intra_group")
  square_sum <- c(SSB, SSW) 
  df <- c(k-1, N-k)
    MSB <- SSB/(k-1)                             #MSB = SSB/(df of SSB) #df: the number of groups - 1
    MSW <- SSW/(N-k)                             #MSW = SSW/(df of SSW) #df: the number of total obs - the number of groups
  Mean <- c(MSB, MSW)
  F_value <- c(MSB/MSW, 0) #0 means NA
  
  ANOVA$table <- data.frame(source, square_sum, df, Mean, F_value)
  
  #explanatory power
  eta_square <- SSB/SST                       
  ANOVA$eta_square <- eta_square
  
  print(ANOVA)
  }

3. Check the result

My_anova(random_df)

## No id variables; using all as measure variables

## $group_mean
##               G1               G2               G3               G4 
## "Mean   :45.4  "   "Mean   :46  " "Mean   :52.6  " "Mean   :51.6  " 
## 
## $SST
## [1] 443.8
## 
## $SSB
## [1] 208.2
## 
## $SSW
## [1] 235.6
## 
## $anova
## Analysis of Variance Table
## 
## Response: value
##           Df Sum Sq Mean Sq F value  Pr(>F)  
## variable   3  208.2  69.400  4.7131 0.01529 *
## Residuals 16  235.6  14.725                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## $table
##        source square_sum df   Mean  F_value
## 1 inter_group      208.2  3 69.400 4.713073
## 2 intra_group      235.6 16 14.725 0.000000
## 
## $eta_square
## [1] 0.4691302