Today’s statistical examination delved into the age disparities between White and Black individuals, leveraging two quantitative methods: the two-sample t-test and a Monte Carlo simulation to scrutinize the potential discrepancies in age between the groups labeled “AgesWhite” and “AgesBlack.”
Two-Sample T-Test: This classic statistical tool compares average values between two distinct groups. The outcomes of the t-test were striking:
– T-statistic: 19.207307521141903
– P-value: 2.28156216181107e-79
– Negative Log (base 2) of p-value: 261.2422975351452
A t-statistic of 19.21 markedly underscores a significant variance in averages between the Black and White cohorts. The minuscule p-value indicates compelling evidence that refutes the null hypothesis, which posits no variance. The negative logarithm of the p-value (base 2) further amplifies this significance, suggesting that the chance of the age difference occurring is as improbable as flipping a coin and getting tails over 261 times in a row, highlighting the statistical prominence of the age disparity.
Monte Carlo Simulation: Acknowledging that the ‘age’ variable deviates from a normal distribution, the t-test’s reliability could be questioned. Thus, a Monte Carlo simulation was implemented, executing 2 million cycles. Each cycle drew random samples from a pooled age distribution representing both groups, mirroring the sample sizes of the ‘White’ and ‘Black’ data.
Remarkably, not a single instance in the 2 million iterations of the Monte Carlo simulation presented an average age difference that surpassed the observed 7.2 years between the White and Black groups. This finding aligns with the t-test and heavily suggests that the probability of such a notable age difference occurring by chance is extremely slim.
Synthesized Conclusion: The integration of results from the two-sample t-test and the Monte Carlo simulation leads to a unanimous inference: the 7.2-year age gap between White and Black individuals stands as statistically significant. The t-test’s indications against the null hypothesis and the Monte Carlo simulation’s reinforcement of these findings collectively affirm a substantial and genuine discrepancy in the mean ages across these demographic divisions.