Independent two sample t-test (if you think sample size for women group is large enough), otherwise use its non-parametric version Mann–Whitney U test.
For unequal sample sizes, commonly used test is the Welch's t-test (also known as the unequal variances t-test). Welch's t-test is an adaptation of the independent samples t-test that does not assume equal variances between the groups.
1. Check for Normality and Homogeneity: First, ensure that both groups follow approximately normal distributions. You can use graphical methods (e.g., histograms, Q-Q plots) or statistical tests (e.g., Shapiro-Wilk test) to assess normality. Additionally, test for homogeneity of variances between the groups, for example, using Levene's test.
2. Unequal Sample Sizes: If the sample sizes are unequal, as in your case (12 and 58), you should consider using statistical tests that are robust to unequal sample sizes.
3. Use Welch's t-test: If the assumptions of normality and homogeneity of variances are met, despite the unequal sample sizes, you can use Welch's t-test. Welch's t-test adjusts the degrees of freedom and accounts for unequal variances between the groups. It is available in most statistical software packages.
4. Consider Nonparametric Alternatives: If the assumptions of normality and/or homogeneity of variances are not met, or if you prefer to use nonparametric methods, you can consider the Mann-Whitney U test (also known as the Wilcoxon rank-sum test). The Mann-Whitney U test does not assume normality or equal variances and can be used for comparing two groups with unequal sample sizes.