How to Calculate Pooled Standard Deviation in R
In this article, we will learn How to Calculate Pooled Standard Deviation in R.
Pooled Standard Deviation
This is a weighted average of standard deviations of two or more groups which are independent.
In statistics, it is used to test whether or not the means of two populations are equal.
Mathematically, it is defined as
Pooled standard deviation =
[Tex]\sqrt{(n_1-1)s_1^2 + (n_2-1)s_2^2 / (n_1+n_2-2)}[/Tex]
where:
- n1, n2: Sample size for both groups
- s1, s2: Standard deviation for both groups
Method 1: Calculate Pooled Standard Deviation Manually
Step 1: Creating Dataset
data1 <- c(21, 19, 19, 8, 8, 10, 11, 13, 15, 15, 16, 17, 7, 6, 6) data2 <- c(10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29)
Step 2: Finding standard deviation
s1 <- sd(data1) s2 <- sd(data2)
Step 3: Finding sample size
n1 <- length(data1) n2 <- length(data2)
Step 4: Calculate pooled standard deviation
pooled <- sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1+n1-2))
Code
#Step 1: Creating Dataset
data1 <- c(21, 19, 19, 8, 8, 10, 11, 13, 15, 15, 16, 17, 7, 6, 6)
data2 <- c(10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29)
#Step 2: Finding standard deviation
s1 <- sd(data1)
s2 <- sd(data2)
#Step 3: Finding sample size
n1 <- length(data1)
n2 <- length(data2)
#Step 4: Calculate pooled standard deviation
pooled <- sqrt(((n1-1)*s1^2 + (n2-1)*s2^2) / (n1+n1-2))
Output
5.789564
Method 2: Using effectsize library
Step 1: Installing Package
install.packages("effectsize") library(effectsize)
Step 2: Creating Dataset
data1 <- c(21, 19, 19, 8, 8, 10, 11, 13, 15, 15, 16, 17, 7, 6, 6) data2 <- c(10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29)
Step 3: Calculate pooled standard deviation
sd_pooled(data1, data2)
Code
#Step 1: Installing Package
install.packages("effectsize")
library(effectsize)
#Step 2: Creating Dataset
data1 <- c(21, 19, 19, 8, 8, 10, 11, 13, 15, 15, 16, 17, 7, 6, 6)
data2 <- c(10, 11, 13, 13, 15, 17, 17, 19, 20, 22, 24, 25, 27, 29, 29)
#Step 3: Calculate pooled standard deviation
sd_pooled(data1, data2)
Output
5.789564
Conclusion
In this article, we learnt about How to Calculate Pooled Standard Deviation in R. This is a weighted average of standard deviations of two or more groups which are independent. In statistics, it is used to test whether or not the means of two populations are equal.
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