Student's T Distribution - rFronteddu/general_wiki GitHub Wiki

• To figure out a normal distribution we need lots of values or we risk outliers to drastically affect our analysis.
• This distribution provides an approximation for smaller sample sizes.

X ~ t(k): "Variable X follows a Student's T distribution with a degree of freedom k."

• t has fatter tails to accommodate for values far away from the mean, if these values appear in the smaller sample data we assume they will be more frequent in the real distribution.
• Frequently used for hypothesis testing with limited data.
• Has a CDF table for its most common values (t-table)
• If k > 2
  • E(Y) = µ
  • Var(t)= $\frac{k*S^2}{k−2}$

Where:

The Student’s T distribution is used predominantly for creating confidence intervals and testing hypotheses with normally distributed populations when the sample sizes are small. It is particularly useful when we don’t have enough information or it is too costly