calculate t-statistic and p-value from group means, SDs, and sample size

David Kaiser 2018/02/23

Description

A function to calculate the t-statistic and the p-value from the means, standard deviations, and sample size of two groups. The sample size can be equal or not equal but two values need to be supplied. The t-statistic, the variance of the two groups and the degrees of freedom are calculated as described in wikipedia. The p-value is calculated as described in a post by Kelly Black.

Arguments

• mean1 -- mean value of group 1
• mean2 -- mean value of group 2
• sd1 -- standard deviation of group 1
• sd2 -- standard deviation of group 2
• n1 -- sample size of group 1
• n2 -- sample size of group 2
• equal.variance -- logical; are group variances assumed to be equal? defaults to FALSE

Value

A named list in which

• "diff" = difference between the means
• "var" = variance of the two groups
• "t" = t-statistic
• "df" = degrees of freedom
• "p" = p-value

Example

a <- rnorm(100)
b <- rnorm(200)
t.test.mean.sd(mean(a), mean(b), sd(a), sd(b), length(a), length(b))

## $diff
## [1] -0.0008404071
## 
## $var
## [1] 0.1125538
## 
## $t
## [1] -0.007466716
## 
## $df
## [1] 182.0833
## 
## $p
## [1] 0.9940507

mean(a) - mean(b)

## [1] -0.0008404071

t.test(a, b)

## 
##  Welch Two Sample t-test
## 
## data:  a and b
## t = -0.0074667, df = 235.49, p-value = 0.994
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.2225814  0.2209006
## sample estimates:
##   mean of x   mean of y 
## 0.004289820 0.005130227