THE SAMPLING LAB
From samples
to t scores.
Each sample has its own mean and standard deviation. Draw a few, then many, to see how those means vary and where their t scores land under a null hypothesis.
01 Choose populations
02 Draw samples
03 Compare t scores
Null samples0
Alternative samples0
Reference mean50
01 / THE SOURCE
Two possible populations
The curves describe individual observations. The dots show the observations in the selected sample.
Null Alternative
Draw a sample to see its observations here.
02 / THE ESTIMATE
Sample means ȳ
Every sample contributes one mean. As you draw more, their spread becomes visible.
Null Alternative
The dashed line marks μ₀. Each color is scaled to its own number of samples.
03 / THE TEST STATISTIC
The t-score distribution
Each sample becomes t = (ȳ − μ₀) / (s / √n). Both populations are tested against the same μ₀.
Null Alternative t curve
Turn on the theoretical curve to compare simulation with the exact null distribution.
A CLOSER LOOK
No sample selectedOne sample, step by step
Draw one sample to inspect its observations, mean, standard deviation, and t score.
Sample mean—ȳ
→Sample SD—s
→t score—df = 15
View this sample’s observations
Compare recent samples
Why t instead of z? We estimate the standard error using each sample’s s. When the null population is normal, those null t scores follow a Student t distribution with n − 1 degrees of freedom. Samples from the alternative need not follow that central t curve.