Test for the significance of the difference between means in two normal populations having unequal variances

Key Points

• To establish and evaluate statistical significance testing for the difference between means in two normal populations that exhibit unequal variances.
• Theoretical formulation and statistical derivation of hypothesis tests comparing sample means drawn from two independent, normally distributed populations with unequal variances.
• Presents statistical criteria to test whether observed differences between group means remain significant when population variances cannot be assumed equal.
• Provides a mathematical framework to resolve inference problems arising from variance heterogeneity between two normal sample distributions.