Hypothesis Formulation — Null vs Alternative Hypotheses

Null (H0) vs Alternative (H1): What Each Actually Claims

Every statistical test evaluates two competing statements. The null hypothesis (H0) claims there’s no effect, no difference, or no relationship, whatever the “boring” outcome would be. The alternative hypothesis (H1) claims there is one. A test doesn’t prove H1 true; it either provides enough evidence to reject H0, or it doesn’t. This distinction matters because a non-significant result never lets you “accept” the null; it only means you failed to find enough evidence to reject it.

Directional vs Non-Directional Hypotheses

An alternative hypothesis can be stated two ways. A non-directional (two-tailed) hypothesis simply claims a difference or relationship exists, without specifying direction (“Group A and Group B will differ”). A directional (one-tailed) hypothesis specifies which way the effect will go (“Group A will score higher than Group B”). Directional hypotheses require strong prior justification, since choosing one after seeing your data, rather than before, is a form of bias. Most SPSS output defaults to two-tailed significance tests; a genuinely directional hypothesis needs the one-tailed value, which is roughly half the two-tailed p-value for the same test.

Type I and Type II Error

Two ways a hypothesis test can go wrong:

• Type I error: rejecting a true null hypothesis, concluding there’s an effect when there isn’t one. Controlled by your alpha level, conventionally .05.
• Type II error: failing to reject a false null hypothesis, missing a real effect that’s actually there. Controlled by your statistical power, conventionally targeted at .80.

These two error types trade off against each other, and both are exactly what a priori power analysis is designed to balance before you collect any data.

Connecting a Stated Hypothesis to the Correct Statistical Test

A well-formed hypothesis names the variables involved and implies their measurement level, which is most of what you need to identify the correct test. “There is a significant difference in exam scores between two teaching methods” points toward an independent samples t-test. “There is a significant relationship between hours studied and exam score” points toward correlation or regression. See the full SPSS statistical test guide to confirm the exact test your specific hypothesis calls for, and the Chapter 3 statistical analysis plan guide for stating hypotheses correctly in a formal proposal.

Need help formulating your hypotheses or matching them to the right test? Get SPSS assignment help.