Key Characteristics

• The t-distribution is used for estimating population means and hypothesis testing.
• It accounts for additional uncertainty by having “wider tails” compared to a normal distribution.
• As the sample size increases, the t-distribution approaches the standard normal distribution.

Finding the P-Value of a T-Value

Use the t.cdf() function in Python’s Scipy Stats library to find the probability for a given t-value:

import scipy.stats as stats
print(stats.t.cdf(2.1, 29))
        

Or, use the pt() function in R:

pt(2.1, 29)
        

Finding the T-Value of a P-Value

You can find the t-values of a p-value by using a t-table or with programming. For example, to find the t-value separating the top 25% from the bottom 75% with 29 degrees of freedom:

import scipy.stats as stats
print(stats.t.ppf(0.75, 29))
        

Or, use the qt() function in R:

qt(0.75, 29)