Understanding Differences of Mean between Two Groups I have a variable test score that is measured for an organization consisting of 2050 people. The goal is to test if men outperform women (or vice versa). Unfortunately, only 50 of the 2050 people are women. I was told that in order to run inference when there is such a disproportion of one group within a sample that I should pursue some sort of matching strategy. 
First, is this true, that if I match on a few characteristics that I can run inference (e.g., ordinary least squares, linear probability models) and be less worried about the fact that there are so few females--since many males will drop out? 
Second, is there anything I can do to compare the groups before the match even as an anecdote?
This is the data:
           Test Score    Test Score
     N        Mean        Variance    Coef. Var.     Gender    
   2000      26.12         10.89         0.13         Male        
     50      56.10         25.01         0.09        Female

 A: This answer will not be very complete.
1) If the performance scores are reliable (in the sense that they do not change considerably when measured repeatedly within worker), then there is absolutely no point in doing statistical inference (i.e. estimates, tests, confidence intervals) about population parameters, because your sample is equivalent to the corresponding population. Your descriptive presentation of means and variances could be complemented by adding medians, quartiles and boxplots etc.
2) If the performance scores are not very reliable, then you could think of a very simple model of the form
$$
\text{Performance} = \alpha + \beta \cdot \text{Gender} + \varepsilon
$$
with Gender = 1 if female and 0 if male. The random error $\varepsilon$ accounts for the fact that performance varies within person (depending on day, mood etc.) and that the true "gender-effect" $\beta$, i.e. the true average overperformance of women, is not exactly $\hat\beta =56.10 - 26.12 = 29.98$ but might change from day to day. With a two-sample t-test (with Welch-correction for unequal variance) you might test whether $\beta \ne 0$. If the p-value is below 5%, you can assert with 95% confidence that women systematically outperform men. (We could now discuss about whether we should pick an other two-sample test or log transform the data etc.)
3) As quite always when men are compared to women, the question of confounding raises: Is the difference really due to gender or can it be explained at least partially by other factors such as age? It's possible that in your company, women are typically older than men, which could already partially explain the difference in performance. One simple way to try to adjust for confounding is to modify the simple model from 2) to
$$
\text{Performance} = \alpha + \beta' \cdot \text{Gender} + \gamma \cdot \text{Age} + \varepsilon
$$
and infer about the age-corrected gender effect $\beta'$ by linear regression.
An alternative to the modelling approach is matching by age followed by a paired t-test (or similar). This also adjusts for potential age-confounding but leads to another estimated "gender-effect" $\hat \beta''$. Depending on the variability of the performance difference between pairs (which is directly linked to the intra-pair correlation) and the difference between $\hat \beta$ and $\hat \beta''$, the power of such test is higher or lower than the two-sample test in 2). 
Summa summarum: Matching leads to inference about a confounder-adjusted effect of gender, whereas the unmatched comparison infers about the "crude" gender effect without considering any confounders. Both parameters might be interesting, so you could easily summarize both of them.
