B.1 Grados de Libertad (df)

As the number of degrees of freedom (df) grows, the $t$ distribution approaches the standard normal distribution ($N(0,1)$), and in fact the approximation is quite close for $\text{df} \geq 30$.³

Figure below shows a comparison of $t$ distributions with 1, 5, 10, and 30 df and the standard normal distribution. The distribution with the lowest peak is the 1 df distribution, the next lowest is 5 df, the lowest after that is 10 df, and the highest is the standard normal distribution.

Recall that with few degrees of freedom, the values of $t$ are much higher than the corresponding values for a normal distribution and that the difference decreases as the degrees of freedom increase.⁴

Tip
You can use this app Normal Distribution vs. t-distribution to know more about Normal Distribution vs. t-distribution.

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3. Adapted from here↩︎

4. From here↩︎