Statistical significance asks whether an observed difference is unlikely to be due to chance under a null hypothesis. It depends on the difference between group means, variation within groups, and the number of records: a small difference can be significant in a long dataset, while a large difference may not be significant in a short one. A p-value at or below 0.05 is used as the cutoff for rejecting a null hypothesis of equal means. section 7.4.1 section 12.7.2
For comparisons of exactly two groups with continuous data, a t-test evaluates whether the means are essentially equal or different. Start with a clear null hypothesis, calculate the test, compare its p-value with the chosen threshold, and then either reject or fail to reject the null hypothesis. The result turns a visible difference into a more disciplined conclusion about whether chance is a plausible explanation. section 7.4.1 section 1.3
A practical significance-testing workflow is:
- State the null hypothesis. For home and road teams, the starting claim is that their average fouls or free-throw attempts do not differ. section 7.4.1
- Inspect the observed totals and average differences before testing, rather than treating the p-value as the whole story. section 7.4.1
- Run a t-test when comparing two continuous groups, then check whether the p-value is at or below 0.05. section 7.4.1
- Interpret the decision in context: reject the equal-means null when the result clears the threshold; otherwise fail to reject it. section 12.7.2
Home versus road foul calls
During the 2018–19 regular season, road teams averaged about 0.38 more personal fouls per game than home teams. A Welch two-sample t-test returned p = 0.02727, below 0.05, so the equal-means null hypothesis was rejected. The same analysis found home teams attempted about 0.65 more free throws per game, with p = 0.03072. Paired boxplots display the distributions and their mean markers alongside these testable differences. section 7.4.1 section 7.4.1
Salary inequality and championships
A second two-group comparison contrasts Gini coefficients for championship-winning teams and all other teams from 1991–2018. Champions averaged 0.53 versus 0.48 for other teams; the t-test produced p = 0.006245. Because this is below the 5% threshold, the difference in salary distributions is treated as statistically significant rather than merely chance variation. section 12.7.2
options(scipen = 999) t.test(fouls1819reg$pfR, fouls1819reg$pfH) ## ## Welch Two Sample t-test ## ## data: fouls1819reg$pfR and fouls1819reg$pfH ## t = 2.2089, df = 2457.8, p-value = 0.02727 ## alternative hypothesis: true difference in means is not equal to 0 ## 95 percent confidence interval: ## 0.04290002 0.72132763 ## sample estimates: ## mean of x mean of y ## 21.09512 20.71301
This R output shows the full Welch two-sample t-test for road and home personal fouls, including the p-value, confidence interval, and group means used to interpret significance. section 7.4.1
