Researcher Degrees of Freedom

April 9, 2012

Another good piece on common misuses of statistics (full details at the bottom of the post) – this one demonstrating (among other things) that listening to different types of music will change your age:

Using the same method as in Study 1, we asked 20 University of Pennsylvania undergraduates to listen to either “When I’m Sixty-Four” by The Beatles or “Kalimba.” Then, in an ostensibly unrelated task, they indicated their birth date (mm/dd/yyyy) and their father’s age. We used father’s age to control for variation in baseline age across participants. An ANCOVA revealed the predicted effect: According to their birth dates, people were nearly a year-and-a-half younger after listening to “When I’m Sixty-Four” (adjusted M = 20.1 years) rather than to “Kalimba” (adjusted M = 21.5 years), F(1, 17) = 4.92, p = .040

The gag here, of course, is that if you have enough data, and you analyse it in enough different ways, you’ll be able to find a statistically significant result almost anywhere. The authors of the paper reproduce this same passage later, with some additional phrases added to give a fuller account of the data collection and analysis process:

Using the same method as in Study 1, we asked 20 34 University of Pennsylvania undergraduates to listen only to either “When I’m Sixty-Four” by The Beatles or “Kalimba” or “Hot Potato” by the Wiggles. We conducted our analyses after every session of approximately 10 participants; we did not decide in advance when to terminate data collection. Then, in an ostensibly unrelated task, they indicated only their birth date (mm/dd/yyyy) and how old they felt, how much they would enjoy eating at a diner, the square root of 100, their agreement with “computers are complicated machines,” their father’s age, their mother’s age, whether they would take advantage of an early-bird special, their political orientation, which of four Canadian quarterbacks they believed won an award, how often they refer to the past as “the good old days,” and their gender. We used father’s age to control for variation in baseline age across participants. An ANCOVA revealed the predicted effect: According to their birth dates, people were nearly a year-and-a-half younger after listening to “When I’m Sixty-Four” (adjusted M = 20.1 years) rather than to “Kalimba” (adjusted M = 21.5 years), F(1, 17) = 4.92, p = .040. Without controlling for father’s age, the age difference was smaller and did not reach significance (Ms = 20.3 and 21.2, respectively), F(1, 18) = 1.01, p = .33.

The authors dub this sort of problem “researcher degrees of freedom”. It is a form of data mining.

In the course of collecting and analyzing data, researchers have many decisions to make: Should more data be collected? Should some observations be excluded? Which conditions should be combined and which ones compared? Which control variables should be considered? Should specific measures be combined or transformed or both?

It is rare, and sometimes impractical, for researchers to make all these decisions beforehand. Rather, it is common (and accepted practice) for researchers to explore various analytic alternatives, to search for a combination that yields “statistical significance,” and to then report only what “worked.” The problem, of course, is that the likelihood of at least one (of many) analyses producing a falsely positive finding at the 5% level is necessarily greater than 5%.

The authors propose a set of guidelines for researchers to follow that will limit “researcher degrees of freedom” -

1. Authors must decide the rule for terminating data collection before data collection begins and report this rule in the article

2. Authors must collect at least 20 observations per cell or else provide a compelling cost-of-data collection justification.

3. Authors must list all variables collected in a study.

4. Authors must report all experimental conditions, including failed manipulations.

5. If observations are eliminated, authors must also report what the statistical results are if those observations are included.

6. If an analysis includes a covariate, authors must report the statistical results of the analysis without the covariate.

These solutions are oriented towards psychology, and many of them relate to the data collection/creation process and its reporting. I don’t know how one might effectively limit “researcher degrees of freedom” in a discipline like economics, where often the data is already public, and the “researcher degrees of freedom” can lie in analytic choices alone.

Joseph P. Simmons, Leif D. Nelson, and Uri Simonsohn, “False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant” Psychological Science, XX(X) 1–8, 2011 [pdf!]

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One Response to “Researcher Degrees of Freedom”


  1. [...] variables while testing, especially in the softer sciences. With so many “researcher degrees of freedom, tests can be run with dozens, or even hundreds of specifications and modifications [...]


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