Practice Statistical Significance in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A result is statistically significant when the p-value falls below a predetermined threshold (\alpha), typically 0.05, suggesting the observed effect is unlikely due to chance alone.
Statistical significance is a decision rule: before looking at data, you set a threshold (usually 5%). If your p-value is below this threshold, you declare the result 'significant' - meaning unlikely to be just random noise. It's not about importance; it's about confidence that something real is happening.
Example 1
hardA drug trial finds a statistically significant reduction in blood pressure (p = 0.02). The mean reduction was 2 mmHg. Is this result practically significant?
Example 2
hardExplain the difference between a Type I error and a Type II error in hypothesis testing.
Example 3
hardA study with 10,000 participants finds a statistically significant difference in test scores between two teaching methods (p = 0.001), but the difference is only 0.5 points out of 100. Discuss.
Example 4
hardA treatment improves average test scores by 12 points, but the p-value is 0.08. At \alpha = 0.05 is the result statistically significant, and could the effect still be practically important?