Conditional probabilities are really confusing because intuitively, even for those with statistical training, it’s easy to flip them around, make mismatched comparisons, or ignore base-rates.  So nobody needs to feel stupid.  :-)  You might create a picture - a cross-tab - where you find 4 numbers about the population: (a) number of working age persons who are deaf who are employed, (b) number of working age persons who are deaf who are not employed, (c) number of working age persons who are hearing who are employed, and (d) number of working age persons who are hearing who are not employed.  Then you could conclude if those who are deaf are disproportionately less likely to be employed.  I would say to focus on working age because those who are deaf might be over-represented in the retirement-age population.  So I definitely agree with your advisor that, as academics, we need to be really careful that we can support the claims we assert.  Oh, and I would also add that you might avoid the comparison with those who have mental health challenges, unless that’s critical to your broader thesis.  Otherwise there is a hint that you might be trying to say one group’s struggles with employment are more serious than the other.  Why make suffering into a zero-sum game?  Moreover, then you would also have to take into account that there are people who are both deaf and have mental health challenges.  Hope this helps some. Best wishes with your dissertation, Kirsten. ~ Kevin

Hi Kirsten,

Don't panic! It's good that you're seeking help from other researchers too! Research work can be distressing because we're keeping to our own thoughts most of the time, and having an outsider's perspective can be extremely helpful when we're stuck.

I attached an image file to help me see the situation more clearly (and maybe give you some ideas!). The whole pie-chart represents the entire population of people who are employed. The shaded region represents those who declared disability. The size of the shaded region is not drawn to scale as it is merely a representation.

So from what I gather, of all persons who: a) are employed and b) declared disability, those who are deaf comprise 7.5% (see blackened region in figure A and B) and those with mental health difficulties comprise 18% (see dotted region in figure B).

Firstly, I must agree with your supervisor (please don't feel discouraged!). In order to claim that deaf people are disproportionately less likely to be employed than those with mental health issues, we must observe a discrepancy between the proportion of them in employment and in the actual population. What if, for whatever reason, the true population prevalence of being deaf (and of legal working age) is 7.5% and the true prevalence for mental health problems (and of legal working age) is 18%? If this is true, then we cannot say deaf persons are less likely to be employed than persons with mental health problems because there are less deaf persons in the world to begin with. I cannot comment on the statistics of these because they are conditional on your (and the census data's) definition of: 1) deafness (type of deafness); and 2) mental health problems (clinical diagnosis? self-reported?). Once you do get those kinds of data, then you can begin to formulate your argument. I am unaware of the inferential statistical procedure to compare sample prevalence with population prevalence. It sounds like you could make that comparison descriptively because you're already comparing it to a known population parameter.

Secondly, I also agree with Dr. Grobman on the potential for these two groups to overlap. Could you provide us with more detail about your project please? It would be nice to get an idea of the premise and objectives of your thesis :)

Hope this helps.

You can not limit the test to the number analysis. Think about what these numbers mean. Every statistic concerning the population has a reason in the theory of economics and human behavior. Look for these causes and associate them with numbers. A comparison to the total population is also necessary, but look for more indicators than absolute numbers. The true value of a scientific study is not the description, but the conclusions and recommendations. Regards.