Data science interview questions with answers

Very interesting. I wonder in what type of interviews would these answers be considered ideal? Do people at OpenAI ask these sorts of questions, or is this more targeted toward other industries that require data scientists but are not populated by "stats" experts?

For example, consider "What is regression?". The answer given is one way to go, but if the job posting would involve causal analysis or more statistical know-how, for example, it would probably be insufficient. I would want the candidate to speak about linear projections, about sampling assumptions, about probability models underlying the process and so on.

On the other hand, I could imagine that it would not be a good strategy to start to lecture about minute details of regression analysis when applying for a standard data scientist position when sitting on front of "applied data scientists" or even HR folks.

Anyone has any insights?

The quality and depth of answers here is pretty inconsistent. But this in particular is a pet peeve of mine:

> Plot a histogram out of the sampled data. If you can fit the bell-shaped "normal" curve to the histogram, then the hypothesis that the underlying random variable follows the normal distribution can not be rejected.

This is commonly taught in undergrad stats, but you shouldn't do this. I'm of the opinion that normality testing in general is usually a red herring, but this is specifically not a productive way of doing it. Use the other methods. A visual test that relies on how much the histogram approximates a bell curve is very prone to error, because a sample from a variety of other distributions can look visually normal even though it isn't.

More broadly speaking, the reason I don't like this is because it's an example of the kind of formulaic, cargo-culted recipes that are often used in statistics without critical thinking. You should strive to obtain a deep understanding of your data and its distribution, and you should be deeply skeptical if the sample you happen to have looks normal. Nature abhors normality, and the central limit theorem can only promise a tendency towards normality as n approaches infinity. It says nothing about what size sample you'll practically need for your specific data to be able to treat it as normal.

Linear regression does not require errors to be iid, normal, and homoscedastic for it to "work". One of the ways to separate candidates is to push on what (and how) assumptions can be weakened, what the consequences are for estimation and inference, and what sort of corrections can be incorporated for maintaining consistency, improving efficiency, correcting biases, etc. An entry level candidate may not have (nor need to have) a complete understanding of asymptotic theory, but they should know what the purpose of robust standard errors are and how to use them.

Not really sure why your comment is marked dead when it is correct. Maybe it's a new account thing? As you say, the Gauss-Markov conditions are necessary (and sufficient) to make OLS BLUE, but OLS still works fine under a variety of pathological conditions, and many of those conditions can be tested for and adjusted for using common techniques.

> You should strive to obtain a deep understanding of your data and its distribution, and you should be deeply skeptical if the sample you happen to have looks normal.

Although normality testing is useless in many situations, the parent comment somewhat overstates the degree of caution required. In many contexts the exact distribution doesn't matter; sort-of-normal is good enough. For example, the t-test is used ubiquitously. It assumes normality, so we would expect possible non-normality to be a major problem, right? Not so. The t-test is extremely robust to departures from normality given equal sample sizes [1,2,3]. Or you can use a so-called non-parametric test. Rather than investing great effort in specifying exactly what distribution you're dealing with, it's more productive to simply use a test that is robust against your unknowns and move on to pursuing your actual objectives.

It's true that if you are interested in predicting events in the tails of the distribution, you really do need to study the distribution in detail. Predicting rare events is very difficult. But if you're just interested in differences between group means, don't overthink it.

[1] http://www.jerrydallal.com/LHSP/student3.htm [2] Posten, H.O., Yeh, H.C., and Owen, D.B. (1977). Robustness of the two-sample t-test under violations of the homogeneity of variance assumption. Communications in Statistics - Theory and Methods 11, 109–126. [3] Posten, H.O. (1992). Robustness of the two-sample t-test under violations of the homogeneity of variance assumption, part ii. Communications in Statistics - Theory and Methods 21, 2169–2184.