I expect developers to be familiar with basic statistics.
Firstly, this isn't a job interview. If someone's been working with you for long enough that they want to discuss a salary adjustment, then shouldn't your assessment of the value that they bring to the table be more informed than looking for "red flags" on the spot?
Secondly, developers are generally not familiar with basic statistics. If it's important to your business that they be better-than-average at stats, then budget some time and money for training.
Thirdly, in the real world, we make decisions from incomplete and biased information all the time. Sometimes, those decisions turn out to be wrong, but on the whole, it still works out better than pretending that we have no information at all. If you're in management and you have access to more complete information, then the smart thing for an employee to do is to have a conversation with you. It makes no sense to fire someone for that.
I have a lot of respect for your technical work, but the management style you're describing so far sounds authoritarian and abusive. I really hope that's not how you'd actually treat your reports, in practice.
I don't know; I've never had to fire anyone yet.
I'll admit that when writing at 1AM I may have let some hyperbole slip into my comments. It's quite possible that my reaction would be "great, your assignment for the next week is to do a rigorous statistical analysis of this data".
On the other hand, as someone else commented, I said "more likely"; and that's probably true. I can't imagine a situation where I'd accept a naive analysis of self-selected self-reporting data as having any substance at all, so I would certainly not give someone a raise based on that.
discuss a salary adjustment
Discussing salary is fine. My point is that bad statistics is worse than nothing in this context.
Actually, even this point is wrong, IMHO. I can easily imagine situations where you get just one data point and correctly infer from it that you're underpaid.
One example is that someone who obviously less competent than you will reveal to you higher salary than you have.
Another example is that someone has access to information will tell you that your salary is low, and you have good reason to trust that person.
I understand that you as an employer naturally don't think that you are or ever will be biased in this way. But it still may happen in the wild.
In any case, I think it was already said, if you still think that bad statistics is worse than none, you should make the information publicly available. It's the similar thing as with rumors.
One data point isn't even bad statistics. It's anecdote. Maybe the other person is being vastly overpaid.
Maybe; but if you think like that, then no sample can give you that information. Because you won't get any absolute reference point either way. In any case, such situation is a good reason to talk about your salary.
So your argument is wrong; the sample size is not important (that doesn't mean it's useless, though!). Either you have some reference point, and then you can judge the fairness of the salary (even from one data point), or you don't have a reference point, and then no sample size will help you get it.
If you get told that a large representative sample of people all get paid far more than you, it suggests that you're the anomaly.
Either you assume a prior distribution of salaries or not. If you don't, then you don't know mean salary, and so group of any size will not tell you if you're anomaly. Because they can all be anomalous as well.
On the other hand, if you assume a prior distribution (which is pretty much what Bayesian statistics does), then even one sample will modify the prior, and you gain information (i.e. "suggestion that you're anomaly or not").
Of course more samples is always better, but if you can make conclusion from multiple samples, then you can make conclusion from one sample.
It seems to me that in the first case, you're saying we cannot assume any prior, but in the second case, you're doing exactly that - assuming that there is a mean - 1st moment of the prior distribution and maybe even other moments - which indicate whether an observation is anomaly or not.
"Hey Coliin, I've been chatting with a couple of people, and I've got a concern about my salary"
"You're fired"
The End
So Colin spoke the truth (as far as I can tell). It is very hard to change a bad culture unless the person at the top is committed to it. I fought a number of injustices and was kicked in the balls many times (metaphorically of course). You learn what you can and can't get away with or end up on the outer - truth be damned. I was often respected for my principles but seen as foolhardy for my commitment to truth. From my experience, gender and race is no basis for judging decent & compassionate management either. I worked with some brutal men and women over the years. It doesn't take Einstein to sort the Wheat from the chaff, people normally knew - although terms like "makes stuff happen", "doesn't take prisoners", "hard ass" were some alternate names for these brutal types. I can't speak for all work environments, but I've seen hundreds of salaries and appraisals over the years. I can not guarantee my experience reflects the broader world of business.
The statement was 'more likely to fire than give a raise'. This does not mean that these are the only two options available. 'More likely' just means the chance is higher overall, whether it's 99% likely to fire or 2% likely to fire.
It's also not what was said - it wasn't "chatting led to a concern", it was "self-reported, self-selecting study says X". That stuff really is a red flag to folks who have a decent grounding in statistics.
Brilliant mansplaining though!
I was actually referencing your underlying understanding for your ridicule, not the joke itself.
Once you do that, I'll try and explain (mansplain if necessary) how a play of 2 lines and 1 act is probably not a very serious response.
What might something like this look like?
In this particular context, the biggest threats to data integrity are probably:
1. People lie, and men probably lie about their salaries more than women,
2. Willingness to divulge salary is highly culture-dependent, and in societies where salary is seen as a sign of social success, can be highly salary-dependent (and probably more so for men than for women).
If you're interested in learning more I suggest looking for information about how national census data is processed; they have lots of experience dealing with these sorts of issues (albeit with different factors influencing response rates and data reliability).