Alternative hypothesis
An alternative hypothesis is a statistical proposition that contrasts with the null hypothesis by asserting an effect, difference, relationship, or other departure.
Statistics Slam Dunk
An alternative hypothesis is a statistical proposition that contradicts the null hypothesis by asserting an effect, difference, or association.
- How it is used
- Frames decisions about whether observed group differences are chance variation or meaningful effects.
- How deep it goes
- Defines H1 against H0 and works through t-test p-value decisions without formal derivations.
- Examples
- Uses home-road foul calls, free-throw attempts, salary Gini coefficients, and championship outcomes.
- What you can do after
- Apply it via base R t.test to evaluate whether two group means differ under a chosen threshold.
Read how Statistics Slam Dunk explains alternative hypothesis →
Grokking Statistics
A hypothesis that challenges the null hypothesis by asserting a different population value or relationship.
- How it is used
- Frames the competing claim used to challenge a null hypothesis with sample data.
- How deep it goes
- Defines Ha, contrasts directional forms, and applies rejection rules without deriving test distributions.
- Examples
- Uses soda volumes, tea-order guessing, chip-bag weights, and sports-drink sales versus temperature.
- What you can do after
- Evaluate/understand whether sample evidence supports rejecting a stated null hypothesis for a mean or correlation.
Read how Grokking Statistics explains alternative hypothesis →
Causal AI
An alternative hypothesis is a statistical claim that contrasts with the null hypothesis and represents the effect or pattern a test may support.
- How it is used
- Frames statistical decisions about conditional independence, causal-model refutation, and the evidential status of observed patterns.
- How deep it goes
- Defines competing claims, explains p-value decisions, contrasts causal and traditional testing, and demonstrates chi-squared and refutation workflows.
- Examples
- Uses a transportation DAG, chi-squared tests, stock-price patterns, and DoWhy refuters as concrete cases.
- What you can do after
- Diagnose conditional-independence claims with p-values and interpret DoWhy refutation tests against causal assumptions.
Related concepts
- null hypothesiscontrasts with · A null hypothesis is a designated baseline statistical claim, typically asserting that an effect, difference, or association is absent.
- hypothesiskind of · A hypothesis is a provisional proposition, explanation, or prediction that can be evaluated against evidence.
- two-tailed testused by · A two-sided test is a hypothesis test in which sufficiently extreme results in either direction from the null value count as evidence against the null hypothesis.
- one-sided testconfigures · A one-sided test is a hypothesis test whose alternative hypothesis and rejection region concern a departure from the null in one prespecified direction.
These guides are generated from the text of Manning books by Manning's knowledge graph and link to the sections they draw on. The full books are available on liveBook and at manning.com.