Skip to main content
Statistics LibreTexts

11.7: On the Relationship Between ANOVA and the Student t Test

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    There’s one last thing before moving on to non-parametric alternatives to ANOVA. It’s something that a lot of students ask about, and many people find the answer surprising, but it’s worth knowing about: an ANOVA with two groups is identical to the Student t-test. No, really. It’s not just that they are similar, but they are actually equivalent in every meaningful way.

    You are encouraged to try this yourself!  Iif you do conduct an independent samples t-test and a BG ANOVA on the same data, you will get different calculated answers but statistical software will show you that that the actual p-value is identical.   What's more, if you square the calculated t-score, you should get pretty close to the calculated F-value!  Math is so weird.

    Dr. MO has been tempted to turn to ANOVAs because it takes into account within-group variation, but it turns out, mathematically, it doesn't matter!  When you only have two groups, use whichever analysis you prefer! 

    This page titled 11.7: On the Relationship Between ANOVA and the Student t Test is shared under a CC BY-SA license and was authored, remixed, and/or curated by Michelle Oja.