Win-Vector Blog

Nina Zumel and I ( John Mount ) have been working very hard on producing an exciting new book called “Practical Data Science with R.” The book has now entered Manning Early Access Program (MEAP) which allows you to subscribe to chapters as they become available and give us feedback before the book goes into print.

Please subscribe to our book, your support now will help us improve it. Please also forward this offer to your friends and colleagues (and please ask them to also subscribe and forward). Read more…

Related posts:

1. Setting expectations in data science projects
2. Data Science, Machine Learning, and Statistics: what is in a name?
3. Data science project planning
4. Revisiting Cleveland’s The Elements of Graphing Data in ggplot2
5. Good Graphs: Graphical Perception and Data Visualization

It occurred to us recently that we don’t have any articles about Bayesian approaches to statistics here. I’m not going to get into the “Bayesian versus Frequentist” war; in my opinion, which style of approach to use is less about philosophy, and more about figuring out the best way to answer a question. Once you have the right question, then the right approach will naturally suggest itself to you. It could be a frequentist approach, it could be a bayesian one, it could be both — even while solving the same problem.

Let’s take the example that Bayesians love to hate: significance testing, especially in clinical trial style experiments. Clinical trial experiments are designed to answer questions of the form “Does treatment X have a discernible effect on condition Y, on average?” To be specific, let’s use the question “Does drugX reduce hypertension, on average?” Assuming that your experiment does show a positive effect, the statistical significance tests that you run should check for the sorts of problems that John discussed in our previous article, Worry about correctness and repeatability, not p-values: What are the chances that an ineffective drug could produce the results that I saw? How likely is it that another researcher could replicate my results with the same size trial?

We can argue about whether or not the question we are answering is the correct question — but given that it is the question, the procedure to answer it and to verify the statistical validity of the results is perfectly appropriate.

So what is the correct question? From your family doctor’s viewpoint, a clinical trial answers the question “If I prescribe drugX to all my hypertensive patients, will their blood pressure improve, on average?” That isn’t the question (hopefully) that your doctor actually asks, though possibly your insurance company does. Your doctor should be asking “If I prescribe drugX to this patient, the one sitting in my examination room, will the patient’s blood pressure improve?” There is only one patient, so there is no such thing as “on average.”

If your doctor has a masters degree in statistics, the question might be phrased as “If I prescribe drugX to this patient, what is the posterior probability that the patient’s blood pressure will improve?” And that’s a bayesian question. Read more…

Related posts:

1. Statistics to English Translation, Part 2a: ’Significant’ Doesn’t Always Mean ’Important’
2. Worry about correctness and repeatability, not p-values
3. Statistics to English Translation, Part 2b: Calculating Significance
4. “I don’t think that means what you think it means;” Statistics to English Translation, Part 1: Accuracy Measures
5. How to test XCOM “dice rolls” for fairness

I know I have already written a lot about technicalities in logistic regression (see for example: How robust is logistic regression? and Newton-Raphson can compute an average). But I just ran into a simple case where R‘s glm() implementation of logistic regression seems to fail without issuing a warning message. Yes the data is a bit pathological, but one would hope for a diagnostic or warning message from the fitter. Read more…

Related posts:

1. Newton-Raphson can compute an average
2. How robust is logistic regression?
3. What does a generalized linear model do?
4. Modeling Trick: Impact Coding of Categorical Variables with Many Levels
5. Learn Logistic Regression (and beyond)

A fair complaint when seeing yet another “data science” article is to say: “this is just medical statistics” or “this is already part of bioinformatics.” We certainly label many articles as “data science” on this blog. Probably the complaint is slightly cleaner if phrased as “this is already known statistics.” But the essence of the complaint is a feeling of claiming novelty in putting old wine in new bottles. Rob Tibshirani nailed this type of distinction in is famous machine learning versus statistics glossary.

I’ve written about statistics v.s. machine learning , but I would like to explain why we (the authors of this blog) often use the term data science. Nina Zumel explained being a data scientist very well, I am going to take a swipe at explaining data science.

We (the authors on this blog) label many of our articles as being about data science because we want to emphasize that the various techniques we write about are only meaningful when considered parts of a larger end to end process. The process we are interested in is the deployment of useful data driven models into production. The important components are learning the true business needs (often by extensive partnership with customers), enabling the collection of data, managing data, applying modeling techniques and applying statistics criticisms. The pre-existing term I have found that is closest to describing this whole project system is data science, so that is the term I use. I tend to use it a lot, because while I love the tools and techniques our true loyalty is to the whole process (and I want to emphasize this to our readers).

The phrase “data science” as in use it today is a fairly new term (made popular by William S. Cleveland, DJ Patil, and Jeff Hammerbacher). I myself worked in a “computational sciences” group in the mid 1990′s (this group emphasized simulation based modeling of small molecules and their biological interactions, the naming was an attempt to emphasize computation over computers). So for me “data science” seems like a good term when your work is driven by data (versus driven from computer simulations). For some people data science is considered a new calling and for others it is a faddish misrepresentation of work that has already been done. I think there are enough substantial differences in approach between traditional statistics, machine learning, data mining, predictive analytics, and data science to justify at least this much nomenclature. In this article I will try to describe (but not fully defend) my opinion. Read more…

Related posts:

1. A Personal Perspective on Machine Learning
2. Setting expectations in data science projects
3. The differing perspectives of statistics and machine learning
4. Data science project planning
5. On Being a Data Scientist

When finishing Worry about correctness and repeatability, not p-values I got to thinking a bit more about what can you actually check when reading a paper, especially when you don’t have access to the raw data. Some of the fellow scientists I admire most have a knack for back of the envelope calculations and dimensional analysis style calculations. They could always read a few facts off a presentation that the presenter may not have meant to share. There is a joy in calculation and figuring, so I decided it would be a fun challenge to see if you could check any of the claims of “Association between muscular strength and mortality in men: prospective cohort study,” Ruiz et. al. BMJ 2008;337:a439 from just the summary tables supplied in the paper itself. Read more…

Related posts:

1. Worry about correctness and repeatability, not p-values
2. Statistics to English Translation, Part 2b: Calculating Significance
3. Statistics to English Translation, Part 2a: ’Significant’ Doesn’t Always Mean ’Important’
4. “I don’t think that means what you think it means;” Statistics to English Translation, Part 1: Accuracy Measures
5. The differing perspectives of statistics and machine learning

In data science work you often run into cryptic sentences like the following:

Age adjusted death rates per 10,000 person years across incremental thirds of muscular strength were 38.9, 25.9, and 26.6 for all causes; 12.1, 7.6, and 6.6 for cardiovascular disease; and 6.1, 4.9, and 4.2 for cancer (all P < 0.01 for linear trend).

(From “Association between muscular strength and mortality in men: prospective cohort study,” Ruiz et. al. BMJ 2008;337:a439.)

The accepted procedure is to recognize “p” or “p-value” as shorthand for “significance,” keep your mouth shut and hope the paper explains what is actually claimed somewhere later on. We know the writer is claiming significance, but despite the technical terminology they have not actually said which test they actually ran (lm(), glm(), contingency table, normal test, t-test, f-test, g-test, chi-sq, permutation test, exact test and so on). I am going to go out on a limb here and say these type of sentences are gibberish and nobody actually understands them. From experience we know generally what to expect, but it isn’t until we read further we can precisely pin down what is actually being claimed. This isn’t the authors’ fault, they are likely good scientists, good statisticians, and good writers; but this incantation is required by publishing tradition and reviewers.

We argue you should worry about the correctness of your results (how likely a bad result could look like yours, the subject of frequentist significance) and repeatability (how much variance is in your estimation procedure, as measured by procedures like the bootstrap). p-values and significance are important in how they help structure the above questions.

The legitimate purpose of technical jargon is to make conversations quicker and more precise. However, saying “p” is not much shorter than saying “significance” and there are many different procedures that return p-values (so saying “p” does not limit you down to exactly one procedure like a good acronym might). At best the savings in time would be from having to spend 10 minutes thinking which interpretation of significance is most approbate to the actual problem at hand versus needing a mere 30 seconds to read about the “p.” However, if you don’t have 10 minutes to consider if the entire result a paper is likely an observation artifact due to chance or noise (the subject of significance) then you really don’t care much about the paper.

In our opinion “p-values” have degenerated from a useful jargon into a secretive argot. We are going to discuss thinking about significance as “worrying about correctness” (a fundamental concern) instead of as a cut and dried statistical procedure you should automate out of view (uncritically copying reported p’s from fitters). Yes “p”s are significances, but there is no reason to not just say what sort of error you are claiming is unlikely. Read more…

Related posts:

1. Level fit summaries can be tricky in R
2. How to test XCOM “dice rolls” for fairness
3. A bit more on sample size
4. Statistics to English Translation, Part 2a: ’Significant’ Doesn’t Always Mean ’Important’
5. What does a generalized linear model do?

In our article What is a large enough random sample? we pointed out that if you wanted to measure a proportion to an accuracy “a” with chance of being wrong of “d” then a idea was to guarantee you had a sample size of at least:

This is the central question in designing opinion polls or running A/B tests. This estimate comes from a quick application of Hoeffding’s inequality and because it has a simple form it is possible to see that accuracy is very expensive (to halve the size of difference we are trying to measure we have to multiply the sample size by four) and the cheapness of confidence (increases in the required confidence or significance of a result cost only moderately in sample size).

However, for high-accuracy situations (when you are trying to measure two effects that are very close to each other) suggesting a sample size that is larger than is strictly necessary (as we are using an bound, not an exact formula for the required sample size). As a theorist or a statistician we like to error on the side of too large a sample (guaranteeing reliability), but somebody who is paying for each entry in a poll would want a smaller size.

This article shows a function that computes the exact size needed (using R). Read more…

Related posts:

1. What is a large enough random sample?
2. Level fit summaries can be tricky in R
3. Don’t use correlation to track prediction performance
4. Setting expectations in data science projects
5. The cranky guide to trying R packages

Using correlation to track model performance is “a mistake that nobody would ever make” combined with a vague “what would be wrong if I did do that” feeling. I hope after reading this feel a least a small urge to double check your work and presentations to make sure you have not reported correlation where R-squared, likelihood or root mean square error (RMSE) would have been more appropriate.

It is tempting (but wrong) to use correlation to track the performance of model predictions. The temptation arises because we often (correctly) use correlation to evaluate possible model inputs. And the correlation function is often a convenient built-in function. Read more…

Related posts:

1. Correlation and R-Squared
2. Level fit summaries can be tricky in R
3. Modeling Trick: Masked Variables
4. Your Data is Never the Right Shape
5. What does a generalized linear model do?

I was flipping through my copy of William Cleveland’s The Elements of Graphing Data the other day; it’s a book worth revisiting. I’ve always liked Cleveland’s approach to visualization as statistical analysis. His quest to ground visualization principles in the context of human visual cognition (he called it “graphical perception”) generated useful advice for designing effective graphics [1].

I confess I don’t always follow his advice. Sometimes it’s because I don’t agree with him, but also it’s because I use ggplot for visualization, and I’m lazy. I like ggplot because it excels at layering multiple graphics into a single plot and because it looks good; but deviating from the default presentation is often a bit of work. How much am I losing out on by this? I decided to do the work and find out.

Details of specific plots aside, the key points of Cleveland’s philosophy are:

• A graphic should display as much information as it can, with the lowest possible cognitive strain to the viewer.
• Visualization is an iterative process. Graph the data, learn what you can, and then regraph the data to answer the questions that arise from your previous graphic.

Of course, when you are your own viewer, part of the cognitive strain in visualization comes from difficulty generating the desired graphic. So we’ll start by making the easiest possible ggplot graph, and working our way from there — Cleveland style.

Read more…

Related posts:

1. Good Graphs: Graphical Perception and Data Visualization
2. Your Data is Never the Right Shape
3. My Favorite Graphs
4. The cranky guide to trying R packages
5. Please stop using Excel-like formats to exchange data

A bit more on the ROC/AUC

The receiver operating characteristic curve (or ROC) is one of the standard methods to evaluate a scoring system. Nina Zumel has described its application, but we would like to emphasize out some additional details. In my opinion while the ROC is a useful tool, the “area under the curve” (AUC) summary often read off it is not as intuitive and interpretable as one would hope or some writers assert. Read more…

Related posts:

1. “I don’t think that means what you think it means;” Statistics to English Translation, Part 1: Accuracy Measures
2. My Favorite Graphs
3. What does a generalized linear model do?
4. Learn Logistic Regression (and beyond)
5. Setting expectations in data science projects