t-test “by hand”

# R from zero to hero
# Marco Plebani 18 May 2018
# let's perform a T test "by hand" (with a little help from R)

Enter the data. You could enter them in Excel, save them as a csv file and then open them in R using read.csv("FILE DIRECTORY HERE/twogroups.csv").
In this case it’s a handful of data so I’m doing it by hand as follows:

# Group 1
g1 <- c(6,7,7.2,8,9)
# Group 2
g2 <- c(1.5,2.5,2.6,5,5.5)

# t = (mean.g1 - mean.g2) / SE(mean.g1 - mean.g2)

mean.g1 <- mean(g1)
mean.g2 <- mean(g2)

se.g1g2 <- sqrt((sd(g1)^2)/length(g1) + (sd(g2)^2)/length(g2))

t.value <- (mean.g1 - mean.g2)/se.g1g2

For the t test, df = number of values in g1 + number of values in g2 – 2
In R:

degs.of.freedom <- length(g1) + length(g2) - 2
# we can either look it up un a table, or ask R!
qt(p=0.95, df = degs.of.freedom)

# qf() is a function that gives you the Quantiles for the t distribution - basically it's a t-value calculator. Like a table of t values, just fancier.

So, are the two groups significantly different?