Alternative Hypothesis
The substantive claim a researcher hopes to support, written H₁ or Hₐ. It states that an effect, difference, or relationship exists in the population — for example, that a vocabulary intervention produces higher post-test scores than a control condition, or that two proficiency groups differ on a comprehension measure. The Null Hypothesis is rejected when the observed data are sufficiently incompatible with it; under the Neyman–Pearson framework, that rejection is interpreted as a decision to act in line with H₁.
One-Tailed vs Two-Tailed
A two-tailed (non-directional) H₁ asserts only that the parameter differs from the null value: μ₁ ≠ μ₂. A one-tailed (directional) H₁ asserts a specific direction: μ₁ > μ₂ or μ₁ < μ₂. One-tailed tests place the entire α in a single tail of the sampling distribution and so are more sensitive to differences in the predicted direction, but blind to differences in the other. Methodological writing in applied linguistics — including Larson-Hall (2016) and Field (2018) — recommends two-tailed tests by default, reserving one-tailed tests for cases where a directional prediction is genuinely defensible before data collection.
Specification
H₁ should be written before data are inspected and tied to a defined population and operational measure. A vague "instruction works" is not testable; a specific H₁ — "Year 11 learners receiving form-focused feedback show higher mean accuracy on the past-simple post-test than learners receiving meaning-focused feedback" — points to a parameter, a population, and a direction (or its absence).
Statistical vs Substantive
Rejecting H₀ in favour of H₁ does not establish that the effect is large or pedagogically meaningful. The substantive question — how big, for whom, under what conditions — is answered by Effect Size estimates, confidence intervals, and Replication, not by the test decision alone.
References
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). London: Sage.
- Larson-Hall, J. (2016). A Guide to Doing Statistics in Second Language Research Using SPSS and R (2nd ed.). New York: Routledge.
- Plonsky, L., & Oswald, F. L. (2014). How big is "big"? Interpreting effect sizes in L2 research. Language Learning, 64(4), 878–912.