Statistics interview questions

I am looking for some statistics (and probability, I guess) interview questions, from the most basic through the more advanced. Answers are not necessary (although links to specific questions on this site would do well).

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One example: stats.stackexchange.com/questions/4768/… –  radek Dec 14 '10 at 12:01

Not sure what the job is, but I think "Explain x to a novice" would probably be good-

a) because they will probably need to do this in the job

b) it's a good test of understanding, I reckon.

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(+1): I cannot count the times I thought I've understood something, but then I failed to explain it to someone else in easy words. Example: p-value ;) –  steffen Dec 14 '10 at 10:21
"If you can't explain it to a six-year-old, then you probably don't understand it yourself" - Albert Einstein. Maybe not that extreme, but you get the point... :) –  Ｊ. Ｍ. Dec 14 '10 at 13:09
I like "Explain a p-value", with or without the "to a novice" part. –  shabbychef Dec 14 '10 at 17:36
this is why cross-validated is great. lots of "layman" questions and answers. –  Neil McGuigan Dec 15 '10 at 20:17
Really good advice whether you're interviewing or not! –  JMS Jun 6 '11 at 16:56

Standard Q where I work is along the lines of:

Have a look at this output of a multiple logistic regression from a statistical package you claim to have used (preferably one we use too). XXX is the independent variable of principal interest. How woud you interpret the results for a colleague with knowledge of the subject matter but no formal statistical training? (If necessary prompt for separate interpretation of point estimate, CI, p-value).

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In more academic contexts one may also ask: 'have a look at this model output in this paper that you (co-)authored. Tell me what it means.' Underwhelming answers are then fatal because there are no unfamiliarity excuses available, yet dismayingly common. –  conjugateprior Dec 15 '10 at 19:27

You might also want to reflect on whether the interview is the best medium for measuring the construct of interest. If you want to measure prior knowledge of probability or statistics, you might be better off relying more on a written test. You can ask more questions, and thus increase reliability of measurement. It's more standardised both in administration, and in scoring. And once the instrument is developed, it probably uses fewer resources to administer.

You could then use the interview as a more focussed tool looking at factors such as verbal and interpersonal skills.

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This is a good point. I have found in the past that it is very difficult to tell whether a given candidate will work out, unless you have worked with them in the past. –  shabbychef Dec 14 '10 at 17:34

1) You fit a multiple regression to examine the effect of a particular variable a worker in another department is interested in. The variable comes back insignificant, but your co-worker says that this is impossible as it is known to have an effect. What would you say/do?

2) You have 1000 variables and 100 observations. You would like to find the significant variables for a particular response. What would you do?

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Could you post the answers as well? For 1) I assume, there might be some dependent variables causing the problem. For 2) I would probably go for χ² (chi-squared) statistic test –  Rishi Dua Jan 19 '14 at 14:37
There are many reasonable responses to both, here are my quick thoughts: 1) the regression model is from a sample, this sample has random variation and therefore the model is only an estimate and can result in type 1 or type 2 errors. There could also be heavy collinearity among the predictors. For 2) it's the big P vs small N problem. There are many techniques to handle this situation, such as reducing the dimensions and Lasso. –  Glen Jan 19 '14 at 19:03
Thanks @Glen this is helpful! –  Rishi Dua Jan 19 '14 at 19:35

Here is a big data set. What is your plan for dealing with outliers? How about missing values? How about transformations?

Can they deal with real-world data?

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Dear anonymous user, please don't use edit for comments (it is not for you, Neil). –  mbq Jun 10 '11 at 13:06

I was asked once how I would explain the relevance of the central limit theorem to a class of freshmen in the social sciences that barely have knowledge about statistics.

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How do you numericize something that is not numerical?

Rationale: Can they figure out how to analyze something statistically that is not already in a big table?

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How do you prevent over-fitting when you are creating a statistical model?

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I often ask "how would you define/explain what forecasting is?"

Answer to that type of very general question helps me to see if people are connected to a particular case of forecasting. There is not a right answer but answering this synthetically during an interview is not always easy:)

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For an observational data context:

Consider this regression model applied to this substantive problem. What, if anything, in it can be interpreted causally? [Further probe] What would you need to learn to change your opinion?

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Here is a TinkerToy set. Show me how Euclidean distance works in three dimensions. Now show me how multiple regression works.

Can they explain how statistics works in the physical world?

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Doesn't multiple regression with $N$ observations require an $N$-dimensional TinkerToy set though? –  onestop Dec 15 '10 at 21:31
if you want to scatter plot two variables with 100 observations, you only need 2 dimensions, not 100 :), and so on –  Neil McGuigan Dec 19 '11 at 18:48

How will you count the number of sandal wood trees in Bangalore ?

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Is that meant as a kind of Fermi question? –  Thies Heidecke Jun 6 '11 at 15:47
Good question. I've used a version of this in class (trees in a park). They get the idea of sampling, but tend to miss the need for operational definition: when do you start calling it a tree? –  zbicyclist Oct 5 '11 at 0:49

We are running a customer service centre. We are getting 1 million calls per month. How do we reduce it to ten thousand ?

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remove 99% of your phones! –  shabbychef Feb 11 '11 at 17:46
Stop paying the phone bill. –  Glen Feb 11 '11 at 18:30
Incur a fee for the call. (a 900-number in the US...) –  gWaldo Apr 7 '11 at 19:50
This question is about 80–20 rule. It is a common rule of thumb in business; e.g., "80% of your sales come from 20% of your clients". Microsoft noted that by fixing the top 20% most reported bugs, 80% of the errors and crashes would be eliminated. So it would mean set up an FAQ to identify address these 20% of the problems –  Rishi Dua Jan 19 '14 at 14:55

While doing the variance analysis of quantitative variable, sometimes it found that frequency of the variable are very high (>5) then we use the Fisher's exact test to find independence of the variable.

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This would probably be subsumed under Chris's answer. –  Ｊ. Ｍ. Dec 14 '10 at 14:13
Does the correct answer to this one include knowing that there is a controversy about whether fixed marginals make sense and having an informed opinion on the subject? –  Ben Bolker Dec 14 '10 at 15:37