Use cor.test() in R to test whether the correlation between two numeric variables differs from zero. It reports the correlation estimate, test statistic, degrees of freedom, p-value, confidence interval, and alternative hypothesis. The test formalizes a practical question such as whether NBA team payrolls and regular-season wins have a meaningful relationship. section 10.4.1 section 14.4.2
A typical correlation-testing workflow is:
- Prepare two numeric variables and decide how missing values should be handled before testing. section 10.4.1 section 10.5
- State the null hypothesis as no correlation and use a predefined significance level, commonly 0.05. section 14.4.2
- Run cor.test(x, y), then inspect the p-value alongside the estimated correlation and confidence interval. section 10.4.1 section 14.4.2
- Reject or fail to reject the null hypothesis according to the p-value, while treating statistical association as distinct from causation. section 10.4.1 section 10.5
Testing payrolls against wins
After combining team-season payroll and win data, run cor.test(salaries_cor2$salary, salaries_cor2$wins). The Pearson test returns r = 0.211, t = 4.9844, 533 degrees of freedom, p = 0.0000008417, and a 95% confidence interval from 0.1286 to 0.2906. Because the p-value is below 0.05, reject the no-correlation hypothesis; interpret the result as evidence of association, not proof that payrolls cause wins. section 10.4.1
options(scipen = 999) cor.test(nba_stats$z_wins, nba_stats$z_o_pts) ## ## Pearson's product-moment correlation ## ## data: nba_stats$z_wins and nba_stats$z_o_pts ## t = -12.434, df = 298, p-value < 0.00000000000000022 ## alternative hypothesis: true correlation is not equal to 0 ## 95 percent confidence interval: ## -0.6543987 -0.5046282 ## sample estimates: ## cor ## -0.5844698 cor.test(nba_stats$z_wins, nba_stats$z_pts) ## ## Pearson's product-moment correlation ## ## data: nba_stats$z_wins and nba_stats$z_pts ## t = 10.74, df = 298, p-value < 0.00000000000000022 ## alternative hypothesis: true correlation is not equal to 0 ## 95 percent confidence interval: ## 0.4414140 0.6052828 ## sample estimates: ## cor ## 0.5282497
Compare two executable Pearson tests: one relates wins to points allowed and the other relates wins to points scored, with estimates, confidence intervals, and p-values shown together. section 14.4.2
