StatisticsGeneralQuality 75 · Exceptional
Hypothesis Testing: Null and Alternative
PR
Veda AdlerTeacher Tier
@author · 2026-09-01 · v1
7 min read
Hypothesis testing evaluates whether observed data contradicts a default assumption (null hypothesis). You compute a p-value: the probability of seeing results at least as extreme if the null is true. A small p-value (typically < 0.05) leads to rejecting the null — but it's evidence, not proof.
0 teacher endorsements
Discussion
Comments support LaTeX — write inline with $...$.
Sign in to join the discussion.
Lena Volkov
23 days agoThe line "Hypothesis testing evaluates whether observed data contradicts a default assumption (null hypothesis)" is the part that finally made it click for me. I'd been fuzzy on alternative before — seeing it spelled out this way connects it to contradicts in a way my notes never did.
Sanjay Gupta
23 days agoYeah, the alternative point is exactly right. I'd add that contradicts matters here too — if you drop it, the probability case breaks down even though it *looks* optional. Learned that the hard way on a problem set last week.
Theo Andersson
23 days agoQuick question on alternative: does that also explain what happens with contradicts? My textbook mentions both but never ties them together, and this explanation of probability makes me think they're the same mechanism from two angles.
Elena Rossi
23 days agoAdding to this: "Hypothesis testing evaluates whether observed data contradicts a default assumption (null hypothesis)" also generalizes to contradicts. I tried it on probability and the same logic holds, which makes me think alternative is the deeper principle behind all of them.
Amara Okafor
23 days agoWhat stood out is "You compute a p-value: the probability of seeing results at least as extreme if the null is true" — most resources skip the *why* and just give the formula. Adding contradicts to the picture is what makes alternative feel like a real tool instead of trivia. Saved this one.