F test : Variance Comparison

1. Data load

ftestdata <-  read.table("C:/Users/keunm/Desktop/R_Prac_Data/Ellie_SourceCode/Rdata/therbook/f.test.data.txt", header = TRUE)
ftestdata

##    gardenB gardenC
## 1        5       3
## 2        5       3
## 3        6       2
## 4        7       1
## 5        4      10
## 6        4       4
## 7        3       3
## 8        5      11
## 9        6       3
## 10       5      10

2. check variance of data

var(ftestdata$gardenB)

## [1] 1.333333

var(ftestdata$gardenC)

## [1] 14.22222

hist(ftestdata$gardenB)

hist(ftestdata$gardenC)

#Is it significant statistically?

3. understand the logic of percent and quantile

attach(ftestdata)
f.ratio <- var(gardenC)/var(gardenB)
# dof of garden B and c is 9
pf(f.ratio, 9,9) #prob(percent)

## [1] 0.9991879

qf(0.9991879,9,9) #find quantile (x axis value)

## [1] 10.66666

2*(1-qf(0.9991879,9,9))<0.05 # 2 tailed 

## [1] TRUE

4. confirm with built in function and analyze the meaning

#built in function

var.test(gardenB, gardenC)

## 
##  F test to compare two variances
## 
## data:  gardenB and gardenC
## F = 0.09375, num df = 9, denom df = 9, p-value = 0.001624
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.02328617 0.37743695
## sample estimates:
## ratio of variances 
##            0.09375

result - different variance between 2 gardens