Statistical Analysis: today’s analysis, I applied two distinct statistical approaches—a two-sample t-test and a comprehensive Monte Carlo simulation—to assess potential age disparities between two groups, one represented by “AgesWhite” and the other by “AgesBlack.” Two-Sample T-Test: The two-sample t-test, a widely recognized statistical method, was utilized to ascertain whether there exists a statistically significant difference in means between the two groups. The results of the t-test are as follows: T-statistic: 19.21 P-value: 2.28e-79 Negative Log (base 2) of p-value: 261.24 The t-statistic value of 19.21 signifies a substantial difference in means between the ‘Black’ and ‘White’ racial groups. The remarkably small p-value (2.28e-79) provides strong evidence against the null hypothesis of no difference. The negative log (base 2) of the p-value accentuates the significance, illustrating that the observed age difference is equivalent to the likelihood of obtaining more than 261 consecutive tails when flipping a fair coin.
Remarkably, none of the 2,000,000 random samples generated in the Monte Carlo simulation produced a difference in means greater than the observed 7.2-year disparity between White and Black individuals. This outcome aligns with the t-test results, providing strong evidence that such a substantial age difference is exceedingly unlikely to occur by random chance if the null hypothesis (no difference in means) were true. Combined Conclusion: Both the two-sample t-test and the Monte Carlo simulation converge on a consistent conclusion. The age difference of 7.2 years between White and Black individuals is highly statistically significant. The t-test presents strong evidence against the null hypothesis, and the Monte Carlo simulation reinforces this by demonstrating the extreme unlikelihood of observing such a significant age difference by random chance. This collective statistical analysis firmly underscores the presence of a genuine and substantial disparity in mean ages between these two demographic groups.
Two-Sample T-Test Results: T-statistic: 7.637258554192298 P-value: 4.715270331488705e-07 Monte Carlo Simulation Results: Observed Age Difference: 9.2 P-value (Monte Carlo): 5e-06