Both in science and business, we often experience difficulties collecting enough data to test our hypotheses, either because target groups are small or hard to access, or because data collection entails prohibitive costs.
Such obstacles may result in data sets that are too small for the complexity of the statistical model needed to answer the questions we’re really interested in.
This unique book provides guidelines and tools for implementing solutions to issues that arise in small sample studies. Each chapter illustrates statistical methods that allow researchers and analysts to apply the optimal statistical model for their research question when the sample is too small.
This book will enable anyone working with data to test their hypotheses even when the statistical model required for answering their questions are too complex for the sample sizes they can collect. The covered statistical models range from the estimation of a population mean to models with latent variables and nested observations, and solutions include both classical and Bayesian methods. All proposed solutions are described in steps researchers can implement with their own data and are accompanied with annotated syntax in R.
We can’t just throw data into machines and expect to see any meaning […], we need to think [about this]. I see a strong trend in the practitioners community to just automate everything, to just throw data into a black box and expect to get money out of it, and I really don’t believe in that.
All pictures below are slides from the above video.
My summary / interpretation
Lucas highlights an example he has been working on at Booking.com, where they seek to predict which searching activities on their website are for family trips.
What happens is that people forget to specify that they intend to travel as a family, forget to input one/two/three child travellers will come along on the trip, and end up not being able to book the accomodations that come up during their search. If Booking.com would know, in advance, that people (may) be searching for family accomodations, they can better guide these bookers to family arrangements.
The problem here is that many business processes in real life look and act like a funnel. Samples drop out of the process during the course of it. So too the user search activity on Booking.com’s website acts like a funnel.
People come to search for arrangements
Less people end up actually booking arrangements
Even less people actually go on their trip
And even less people then write up a review
However, only for those people that end up writing a review, Booking.com knows 100% certain that they it concerned a family trip, as that is the moment the user can specify so. Of all other people, who did not reach stage 4 of the funnel, Booking.com has no (or not as accurate an) idea whether they were looking for family trips.
Such a funnel thus inherently produces business data with selection bias in it. Only for people making it to the review stage we know whether they were family trips or not. And only those labeled data can be used to train our machine learning model.
And now for the issue: if you train and evaluate a machine learning model on data generated with such a selection bias, your observed performance metrics will not reflect the actual performance of your machine learning model!
Actually, they are pretty much overestimates.
This is very much an issue, even though many ML practitioners don’t see aware. Selection bias makes us blind as to the real performance of our machine learning models. It produces high variance in the region of our feature space where labels are missing. This leads us to being overconfident in our ability to predict whether some user is looking for a family trip. And if the mechanism causing the selection bias is still there, we could never find out that we are overconfident. Consistently estimating, say, 30% of people are looking for family trips, whereas only 25% are.
Fortunately, Lucas proposes a very simple solution! Just adding more observations can (partially) alleviate this detrimental effect of selection bias. Although our bias still remains, the variance goes down and the difference between our observed and actual performance decreases.
A second issue and solution to selection bias relates to propensity (see also): the extent to which your features X influence not only the outcome Y, but also the selection criteria s.
If our features X influence both the outcome Y but also the selection criteria s, selection bias will occur in your data and can thus screw up your conclusion. In order to inspect to what extent this occurs in your setting, you will want to estimate a propensity model. If that model is good, and X appears valuable in predicting s, you have a selection bias problem.
Via a propensity model s ~ X, we quantify to what extent selection bias influences our data and model. The nice thing is that we, as data scientists, control the features X we use to train a model. Hence, we could just use only features X that do not predict s to predict Y. Conclusion: we can conduct propensity-based feature selection in our Y ~ X by simply avoiding features X that predicted s!
Still, Lucas does point that this becomes difficult when you have valuable features that predict both s and Y. Hence, propensity-based feature selection may end up cost(ing) you performance, as you will need to remove features relevant to Y.
These so-called “honest” forests seem a great technique to identify opportunities for personalized actions: think of marketing, HR, medicine, healthcare, and other personalized recommendations. Note that an experimental setup for data collection is still necessary to gather the right data for these techniques.
Propensity score matching (wiki) is a statistical matching technique that attempts to estimate the effect of a treatment (e.g., intervention) by accounting for the factors that predict whether an individual would be eligble for receiving the treatment. The wikipedia page provides a good example setting:
Say we are interested in the effects of smoking on health. Here, smoking would be considered the treatment, and the ‘treated’ are simply those who smoke. In order to find a cause-effect relationship, we would need to run an experiment and randomly assign people to smoking and non-smoking conditions. Of course such experiments would be unfeasible and/or unethical, as we can’t ask/force people to smoke when we suspect it may do harm. We will need to work with observational data instead. Here, we estimate the treatment effect by simply comparing health outcomes (e.g., rate of cancer) between those who smoked and did not smoke. However, this estimation would be biased by any factors that predict smoking (e.g., social economic status). Propensity score matching attempts to control for these differences (i.e., biases) by making the comparison groups (i.e., smoking and non-smoking) more comparable.
Lucy D’Agostino McGowan is a post-doc at Johns Hopkins Bloomberg School of Public Health and co-founder of R-Ladies Nashville. She wrote a very nice blog explaining what propensity score matching is and showing how to apply it to your dataset in R. Lucy demonstrates how you can use propensity scores to weight your observations in such a way that accounts for the factors that correlate with receiving a treatment. Moreover, her explainations are strenghtened by nice visuals that intuitively demonstrate what the weighting does to the “pseudo-populations” used to estimate the treatment effect.
This WordPress blogger I came across — let’s call him “John” for now — has a very peculiar way of testing out his looks. Using dating-apps like Tinder, John conducted A/B-tests to find out whether people would prefer him romantically with or without a beard.
Via a proper experimental setup, John found out that bearded John receives much more attention in the form of Tinder matches. However, not from girls whom John characterized as being asian, that group seemed to prefer shaven John.
While the sample size was not too large (Nbearded = 500; Nshaven = 500) and the response rate even lower (Nbearded = 64; Nshaven = 30), this seems like a fun way to make your look more data-driven!
I wrote about Emily Robinson and her A/B testing activities at Etsy before, but now she’s back with a great new blog full of practical advice: Emily provides 12 guidelines for A/B testing that help to setup effective experiments and mitigate data-driven but erroneous conclusions: