The null hypothesis (H₀) is the assumption that there is no effect or no difference in your data, while the alternative hypothesis (H₁ or Hₐ) is the claim that there is a real effect or difference. Every statistical test you run — a t-test, ANOVA, correlation — is really a contest between these two statements. If you've ever stared at your thesis data unsure what you're actually testing, this is the piece that makes it click.
Key Takeaways
- The null hypothesis (H₀) states that any pattern you see in your sample is just random noise — no real effect exists in the population.
- The alternative hypothesis (H₁) states the opposite: there is a genuine effect, difference, or relationship.
- You never "prove" the alternative. You either reject the null (evidence of an effect) or fail to reject it (not enough evidence).
- The p-value decides. If p < .05, you reject the null; if p ≥ .05, you fail to reject it.
- The two hypotheses are mutually exclusive and cover all outcomes — exactly one of them describes reality.
What Is the Null Hypothesis (H₀)?
The null hypothesis is the "nothing is happening" position. It assumes any difference between groups, or any relationship between variables, is due to chance rather than a real effect. Statisticians treat the null as the default truth until the data give strong evidence against it — the same way a court presumes innocence until proven guilty.
For example, if you're testing whether a new study technique improves exam scores, the null hypothesis is: the study technique has no effect on scores. You start by assuming that's true, then check whether your data are surprising enough to overturn it.
The null almost always contains an equals sign, because it states that two things are the same:
- H₀: μ₁ = μ₂ (the two group means are equal)
- H₀: r = 0 (there is no correlation)
What Is the Alternative Hypothesis (H₁)?
The alternative hypothesis is the claim you actually care about — the effect you're hoping to detect. It states that there is a difference, relationship, or effect that isn't explained by chance. When your test lets you reject the null, the alternative is what's left standing.
Using the same example, the alternative hypothesis is: the study technique changes exam scores. This is what your research question is really asking, even though the maths quietly tests the null instead.
The alternative comes in two flavours:
- Two-tailed (non-directional): H₁: μ₁ ≠ μ₂ — the means differ, but you don't predict which is higher.
- One-tailed (directional): H₁: μ₁ > μ₂ — you specifically predict one group scores higher.
Use a two-tailed test unless you have a strong, pre-registered reason to expect a direction. It's the more conservative, defensible choice for most thesis work.
Why Do We Test the Null Instead of the Alternative?
We test the null because it's the only hypothesis specific enough to calculate. "There is no difference" gives us a single, precise value (a difference of exactly zero) to model. "There is a difference" could mean a difference of 2 points, 20 points, or 200 — it's too vague to compute a probability for.
So the logic runs backwards from what feels intuitive: we assume the null is true, calculate how likely our data would be if it were true, and reject it if that likelihood (the p-value) is very small. This is why you'll never see a study "prove the alternative hypothesis" — you can only gather enough evidence to reject the null.
A Worked Example with Real Numbers
Imagine you're testing whether caffeine improves reaction time. You recruit 60 participants: 30 drink caffeinated coffee, 30 drink decaf. You measure reaction time in milliseconds (lower = faster).
Step 1 — State your hypotheses.
- H₀: μ_caffeine = μ_decaf (caffeine has no effect on reaction time)
- H₁: μ_caffeine ≠ μ_decaf (caffeine changes reaction time)
Step 2 — Set your significance level. The standard threshold is α = .05, meaning you accept a 5% risk of wrongly rejecting a true null.
Step 3 — Run the test. An independent-samples t-test compares the two group means. Suppose the caffeine group averages 310 ms and the decaf group 342 ms, and the test returns:
t(58) = 2.47, p = .016, d = 0.64
Step 4 — Make the decision. Because p = .016 is less than .05, you reject the null hypothesis. The 32 ms difference is unlikely to be chance. Cohen's d = 0.64 tells you it's a medium-to-large effect, not just statistically detectable but practically meaningful.
Step 5 — Interpret plainly. Caffeine was associated with faster reaction times, and the effect is large enough to matter. Notice you didn't "prove" caffeine works — you showed the no-effect assumption was implausible given your data.
If you're unsure which test matches your hypotheses, StatRyx picks the correct one from your variables and runs it automatically — no formula-hunting required.
What Counts as "Significant"? Rejecting vs Failing to Reject
Here's the wording that trips up almost every first-time researcher: you either reject the null or fail to reject it. You never "accept" the null.
| Your result | What you say | What it means |
|---|---|---|
| p < .05 | Reject H₀ | Evidence of a real effect; support for H₁ |
| p ≥ .05 | Fail to reject H₀ | Not enough evidence for an effect |
| Never | ~~Accept H₀~~ | Absence of evidence ≠ evidence of absence |
Failing to reject the null doesn't prove there's no effect — it just means your study didn't find strong enough evidence. A small sample can easily miss a real effect. That's why reporting effect sizes and confidence intervals alongside your p-value is now expected in APA 7; the p-value alone doesn't tell the whole story.
How to Report Hypotheses in APA 7 Format
APA 7 doesn't require you to write "H₀" and "H₁" symbolically in your results — you state them in prose in your method or introduction, then report the outcome numerically. For our caffeine study:
An independent-samples t-test showed that participants who consumed caffeine had significantly faster reaction times (M = 310 ms, SD = 41) than those who consumed decaf (M = 342 ms, SD = 48), t(58) = 2.47, p = .016, d = 0.64, 95% CI [6.2, 57.8].
Notice the APA conventions: test statistics and p are italicised, the leading zero is dropped from p (.016, not 0.016), and an effect size and confidence interval accompany the result. Getting this formatting right by hand is fiddly — StatRyx outputs the full APA 7 sentence for you, so you can paste it straight into your dissertation.
Which Test Do I Actually Need for My Hypotheses?
Your hypotheses point to a test, and the test depends on your variables. Two groups and continuous data usually means an independent-samples t-test; three or more groups means a one-way ANOVA; two categorical variables means a chi-square test. If your data aren't normally distributed, you'd swap to a non-parametric version — if you're choosing there, see our guide on the Mann-Whitney U test versus the t-test.
The hypotheses stay the same in spirit (H₀: no difference; H₁: a difference), but the machinery changes. Choosing wrong is one of the most common reasons dissertation