Timeline for How to mathematically express a p-value in terms of the t-statistic in a one-sample t-test
Current License: CC BY-SA 4.0
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| Nov 13, 2022 at 22:54 | comment | added | utobi | Glad to see it helps. Sure. Indeed, you will typically get a higher $p$-value (and wider CIs) since the $t$ distribution has heavier tails than the standard normal. However, this will help you prevent your test from having higher $\alpha$ (or the CI to have confidence than 1-$\alpha$ lower) when you are not too far from the limiting normal distribution. | |
| Nov 13, 2022 at 22:46 | vote | accept | jglad | ||
| Nov 13, 2022 at 22:44 | comment | added | jglad | Thank you for the excellent and thorough answer! This helps a lot. If you don't mind me asking a follow-up question--let's assume that we are indeed using the $t_{n-1}$ distribution instead of the $N(0,1)$ distribution as you mention some statisticians prefer. In the given example (and following the assumptions of Case IV), does it make sense to express the $p$-value as $P(t_{35} \geq 3.428571 ) = 0.00078$, similar to the expression in Case I? | |
| Nov 13, 2022 at 21:41 | history | answered | utobi | CC BY-SA 4.0 |