We have got an unbalanced sample of 151 interviewees, 13 of them belonging to a certain ethnic category and the rest to another. We try to find out whether ethnicity has an influence on entrepreneurship, so to say migrant entrepreneurship. Do you think that this unbalanced sample can be problematic for an ordinal logistic regression? Any ideas how to overcome a possible problem?
Burak,
There are two issues. First, whether sample proportions (balanced or otherwise) represent the those found in the target population. That's a generalizability concern, and tactics such as weighting of cases might be considered. Second, whether your smallest category (13 members) is sufficient to yield a good representation of the behavior of that category in the population. That is a parameter estimation concern as well (related to precision). If you were including other IVs, then the problem of estimation might be even more problematic. If only the one IV (and you can't afford to collect additional data from the less-frequent subgroup), then carry on. You can always show the standard error associated with the estimated regression coefficient for ethnicity, and use it to report a confidence interval.
For me the issue is the lack of statistical power with only 13 in a group - you will be able to say little with certainty unless the .effect is exceptionally large - so I would suggest oversampling that ethnic group if it is a crucial variable for you,
I agree with both Kelvyn and David. The small number of the participants in one ethnic category is related to the statistical power of the analysis, and to the validity of the statistical results. Even the proportion of the different ethnic participants in your sample corresponded to the distribution of the same ethnic groups in the population, and your sample was randomly drawn from the population, 13 observations in one category are just not enough for a quantitative analysis. You may consider chi-square test instead of logistic regression to address the statistical power matter but still have to deal with the results validity issue.
Best
Thank you Kelvyn and Delia for your answers. After a Chi-Squared test which turned out to be significant, I tried the strategy of introducing weights based on the ethnic population of the faculty... It was again 85 to 15, but the results remained to be significant. Thank you for your contributions.
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