# What is the t-statistic?

Sep 7, 2016

Small sample, normal distribution and you can compute standard deviation and mean, t statistics is used

#### Explanation:

For a large sample, Z statistics (Z score) has approximately a standard normal distribution. When sample is small, the variability in the distribution of Z arises from randomness. This implies that the probability distribution will be more spread out than the standard normal distribution. When n is sample number and df=n-1, t score (t statistics) can be computed by

t = (x¯ -μ0)/(s/n^0.5)

x¯ = sample mean
μ0 = hypothesized population mean
s= sample standard deviation
n= sample size