Null Hypothesis

Definition

The null hypothesis is the default statement assumed to be true in a hypothesis test until the data provide sufficient evidence against it. It typically asserts no effect, no difference, or no association (for example, that two population means are equal). It is denoted H₀ and serves as the benchmark against which sample evidence is evaluated.

Why It Matters

Framing a clear null hypothesis is the foundation of falsification in science. Without it, there is no standard against which to measure evidence, and p-values lose their meaning. A well-specified null hypothesis also forces researchers to articulate exactly what they are trying to disprove, which clarifies study design and strengthens the logical basis for conclusions.

Example

A pharmaceutical company tests whether a new painkiller reduces recovery time after surgery. The null hypothesis states that the mean recovery time for the drug group is equal to the mean recovery time for the placebo group (H₀: μ_drug = μ_placebo). The alternative hypothesis states that the means differ (H₁: μ_drug ≠ μ_placebo). If the data yield a sufficiently small p-value, the researchers reject the null in favour of the alternative.

Related Terms

• Alternative Hypothesis (the complement to the null; not a separate page on staging but worth mentioning)
• P-Value
• Statistical Significance
• Type I Error
• Type II Error
• Hypothesis Testing

Software Notes

• SPSS: The null hypothesis is implicit in all test procedures. For custom contrasts, use Analyze > General Linear Model > Univariate > Contrasts or LMATRIX in syntax.
• R: The null hypothesis is built into test functions. For custom null values in t-tests: t.test(x, mu = 100) tests H₀: μ = 100.
• Stata: ttest y == 100 tests a one-sample null. ttest y, by(group) tests equality of group means.