T Distribution Simulator

Visualize degrees of freedom, t statistic, and tail behavior

Degrees of freedom

t statistic

T Distribution Rules

Small degrees of freedom create heavier tails.
As degrees of freedom increase, the t distribution approaches the normal distribution.
Positive and negative t values are symmetric around zero.
Large absolute t values indicate results farther from the null value.

Example: df = 5 has visibly heavier tails than df = 100. This reflects extra uncertainty from estimating standard deviation in small samples.

Frequently Asked Questions

What is the t distribution?▼

The t distribution is a probability distribution used when estimating means with small samples and unknown population standard deviation.

What are degrees of freedom?▼

Degrees of freedom control the shape of the t distribution. More degrees of freedom make it closer to the normal distribution.

Why does the t distribution have heavier tails?▼

It accounts for extra uncertainty when the population standard deviation is estimated from sample data.

When is t distribution used?▼

It is commonly used for t-tests and confidence intervals for means when population standard deviation is unknown.

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