Normal vs Student t Distribution
Use this guide to quickly decide whether normal or Student t is the right model for your inference setup.
Jump directly into the interval probability workflow and apply this guide on a live distribution chart.
Open Interactive Interval ProbabilityCore Difference
Both are symmetric and centered, but Student t has heavier tails. Those heavier tails reflect additional uncertainty from estimating standard deviation from data.
As degrees of freedom increase, the Student t distribution approaches normal.
When Normal Is Usually Fine
Normal-based methods are often fine when sample sizes are large and variance is known or estimated with low uncertainty.
Many large-sample confidence intervals and z-tests rely on this setup.
When Student t Is Safer
For small samples with unknown variance, Student t is usually the default for means.
Using t rather than z helps avoid underestimating tail risk and overly narrow intervals.