Before using a t table
A t distribution may be used when making an inference about a mean using a sample standard deviation. For a one-sample test, the degrees of freedom are n − 1. Do not apply that formula directly to two independent samples: the approach assuming equal variances differs from the Welch approach.
A table heading can have two meanings
A column labelled “0.05” may refer to one tail or the combined probability in both tails. A two-tailed 5% test has 2.5% in the upper tail. The NIST t table defines the probability area in its heading. Check the same definition in any other table.
Two degrees of freedom in the F distribution
An F distribution has separate degrees of freedom for its numerator and denominator. Comparing variances and interpreting the F statistic in an ANOVA table involve different data arrangements. Read the hypothesis, the calculation of the statistic and its assumptions together.
Common errors
- Confusing sample size with degrees of freedom.
- Using a one-tailed critical value for a two-tailed test.
- Assuming equal variances without examining the assumption.
- Calling an effect large or important merely because a threshold was passed.
Start by reading the ELYADAL archive tables alongside the open NIST explanations. Match the definitions first when the notation differs.
Sources and provenance
Source check / web edition: 14 October 2026. Historical documents retain their own original dates.