t-Test or z-Test?
A flowchart for choosing between a t-test and z-test where every path leads to the t-test, unless you're inside a textbook's first section.
Use this cartoon
Free for classrooms, worksheets, slides and other non-commercial use under CC BY-NC 4.0, with credit to Ben Orlin.
Cartoon by Ben Orlin, Math with Bad Drawings. https://cartoons.mathwithbaddrawings.com/2025-04-25-t-test-or-z-test/ (CC BY-NC 4.0)Transcript
[Title] "Should I Run a t-Test or z-Test?" "Do you already know the population variance, or are you estimating it from a sample?" → Already know it → "Because you're omniscient, or because you're lying?" → Omniscient → "Then why not just directly observe the population mean?" → "Oops, did I say 'omniscient'? I meant 'lying'" → t Test. / Okay, you caught me → t Test. / Estimating it, obviously → t Test. [Footnote] "Or, if you're trapped inside the first section of a textbook chapter on hypothesis testing, try a z test!"