Null Hypothesis Testing Overview

Overview

This lecture introduces the foundations of null hypothesis significance testing using an example study on progeria and pulse wave velocity (PWV). It covers setting up hypotheses, the logic of statistical testing, calculation of test statistics, decision rules, and the use of one-tailed vs. two-tailed tests.

Research Example: Progeria and PWV

• Hutchinson-Guilford Progeria syndrome causes rapid aging and high arterial stiffness in children.
• PWV (pulse wave velocity) is measured to assess vascular stiffness; normal children have PWV ≤ 6.6 m/s.
• Research question: Is PWV in progeria children different from that of normal children?

Setting Up Hypotheses

• The outcome measure is PWV (in m/s).
• Alternative hypothesis (H1): Progeria children have higher average PWV than 6.6 m/s.
• Null hypothesis (H0): Progeria children have the same average PWV as 6.6 m/s (no difference).
• Hypotheses can be written in words or symbols (using μ for population mean).

Null Hypothesis Significance Testing (NHST)

• NHST involves sampling variability; test whether sample mean differs from population mean.
• Two competing hypotheses (H0 and H1); the test provides probabilistic, not absolute, conclusions.
• Use one-tailed test for directional hypotheses, two-tailed when the direction is not specified.

Calculating Test Statistics

• Use sample mean and standard deviation to standardize difference from population mean.
• When population SD (σ) is unknown, use sample SD and t distribution (with degrees of freedom = n-1).
• The t distribution is similar to normal but has heavier tails, especially for small samples.

Decision Rules: Significance and P-value

• Calculate t statistic: t = (sample mean – 6.6) / (SD/√n).
• Compare t statistic to critical t (t_crit) at significance level α = 0.05.
• P-value: probability of observing a result as extreme as the sample, under the null hypothesis.
• If P < α (typically 0.05), reject the null hypothesis; otherwise, fail to reject it.

One-tailed vs. Two-tailed Testing

• One-tailed test: only considers deviation in one direction (e.g., greater than).
• Two-tailed test: considers deviation in both directions (different from).
• It is generally safer to use two-tailed tests unless there’s a strong directional prediction.

Making Statistical Decisions

• Reject H0 if P-value < 0.05 or if |t| > t_crit.
• Failing to reject H0 means insufficient evidence for a difference, not proof of equality.
• Always report decisions as "reject/fail to reject H0" (not "accept H1").

Key Terms & Definitions

• Null Hypothesis (H0) — states there is no effect or no difference.
• Alternative Hypothesis (H1) — states there is an effect or difference.
• P-value — probability of observing the data (or more extreme) if H0 is true.
• Alpha (α) — significance level, typically set at 0.05.
• t Distribution — probability distribution used when population SD is unknown.
• Critical t (t_crit) — cutoff value defining the rejection region for H0.
• One-tailed Test — hypothesis test for effect in one direction.
• Two-tailed Test — hypothesis test for any difference, regardless of direction.

Action Items / Next Steps

• Install and familiarize yourself with the Jamovi software and the "distraction" module.
• Practice setting up null and alternative hypotheses for different research questions.
• Review how to calculate and interpret t statistics and P-values.
• Prepare for next lecture on selecting appropriate test statistics for different contexts.