Practical vs Statistical Significance

Statistics · Axiom Academy

LESSON Practical vs Statistical Significance Understanding when a statistically significant result actually matters in the real world 1. Statistical Significance: Unlikely Under H₀ Statistical significance tells us whether an observed effect is unlikely to have occurred by chance alone if the null hypothesis were true. It's determined by the p-value. The animation below shows how a hypothesis test evaluates whether sample data falls in the rejection region. 2. Practical Significance: Meaningful Effect Size Practical significance asks: "Is this effect large enough to matter?" It considers the magnitude of the difference, cost-benefit analysis, and real-world impact. The animation illustrates how two effects can both be statistically significant but differ dramatically in practical importance. 3. Why Large Samples Find Tiny Differences With large sample sizes, even trivially small differences become statistically significant. This occurs because standard error decreases as sample size increases. Consider the standard error formula: As n increases, SE decreases, making even small differences from H₀ statistically detectable. 4. Effect Sizes and Confidence Intervals To assess practical significance, we use effect sizes and confidence intervals to quantify and visualize the magnitude of effects. Confidence intervals provide a range of plausible values for the true effect, helping us judge whether the entire range represents practically meaningful values.

This is the written version of the interactive lesson above. See the full Statistics course.