Glossary
Alternative Hypothesis
The alternative hypothesis is the statement a statistical hypothesis test aims to establish evidence for. If the data provide sufficient grounds to reject the null hypothesis, the conclusion favours the alternative. Denoted Hₐ, it represents the research claim the analyst wish...
Definition
The alternative hypothesis is the statement a statistical hypothesis test aims to establish evidence for. If the data provide sufficient grounds to reject the null hypothesis, the conclusion favours the alternative. Denoted Hₐ, it represents the research claim the analyst wishes to support.
Why It Matters
The alternative hypothesis defines the direction and scope of a statistical investigation. Whether the test is one-sided or two-sided depends on how the alternative is formulated: a two-sided alternative claims that two group means differ in either direction, while a one-sided alternative specifies a particular direction. Choosing the correct alternative hypothesis directly determines the critical region and, consequently, the statistical power of the test.
Example
A pharmaceutical company wants to prove that a new drug lowers blood pressure more than a placebo. The null hypothesis states there is no difference (H₀: μ_drug = μ_placebo), while the alternative hypothesis states the drug is more effective (Hₐ: μ_drug < μ_placebo). If the clinical trial data yield a p-value below the significance level, the null is rejected and the alternative is supported.
Related Terms
Software Notes
- SPSS: Analyze > Compare Means > Independent-Samples T Test; define groups and set alternative direction under Options
- R:
t.test(x, y, alternative = "two.sided")— change to"less"or"greater"for one-sided alternatives - Stata:
ttest var1 == var2, alternative(two)— replacetwowithlowerorupperfor directional tests