This time, we continue our discussion around p-values by discussing a common trap that people fall into when analyzing data. Imagine the following: you are interested in the influence of hydrology on the abundance of a particular fish species. Because there are many aspects of the hydrological cycle that might play a role in regulating this species, you perform multiple tests to see if there is a statistically significant relationship between fish abundance and hydrological flow metrics such as summer flow magnitude, timing of flooding, duration of low flows, and more.
Great, time to write up the paper describing how summer flows are important in regulating the abundance of this species, right? Well� hold on a minute. Unfortunately, this would be a textbook example of p-hacking � sorting through numerous statistical tests to determine which aspects of a particular hypothesis e.
Let us consider a hypothetical scenario where we know the null hypothesis, e. Probability of falsely rejecting the null hypothesis red when it is true.
Unfortunately, as we do more and more comparisons, we are more and more likely to get a significant p -value simply by chance alone. For a single statistical test using a significance threshold of 0. With five comparisons using the same significance level, there is only a 0. The chance of finding at least one statistically significant result simply by chance climbs to This is a hazard because, as you might recall from the last installment, it is impossible to differentiate between a truly significant relationship versus simply a weird occurrence.
It just takes some tweaking of predictors and responses. For example, which covariates to focus on, how data is transformed, how many categorical bins to divide data into, and so on.
There are several possibilities for mitigating the hazard of falsely Cottage Garden Paths Pictures Sheet rejecting null hypotheses when making multiple comparisons. This is known as a Bonferroni correction, and it brings the probability of a false rejection over the whole suite of tests in line with the rate you would see if you were only conducting one test.
We often learn that exploratory data analysis should be precursor to statistical analysis. Indeed, checking for erroneous observations and distributional assumptions needs to come before statistical testing. Other forms of exploratory analysis, however, can be conducted after formal hypothesis testing. In the above example, what if the researcher had identified, from previous research, the two strongest hypotheses about how hydrology might impact fish abundance and only formally conducted those two tests.
The scientist would then be free to continue graphing and exploring the data to identify other facets of the hydrological cycle that appear to have a relationship with fish abundance as ideas for future research or to spark new mental models of how the ecological system might be structured.
These ideas and models could then be tested with new, independent data. This leads to the crucial importance of establishing hypotheses and methods, including statistical models from the outset, ideally before data collection even begins. This practice will dissuade you from unintentional p-hacking and from digging too hard for expected results. Consequently, you will fortify your statistical assertions and lend more credence to your science when you follow up with the full results of your analyses.
Hopefully, this has been helpful for being cognizant of p-hacking and will prevent you from being an unintentional p-hacker. The article that accompanies the FiveThirtyEight interactive above is also a great read for how p-hacking is not the end of credible science.
We will be diving into simulations to aid in your statistical analyses. Aschwanden, C. Gelman, A. I am working with E. Consequently, I am posting a series of five blogs that explores statistical thinking, provides methods to train intuition, and instills a healthy dose of skepticism.
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You are commenting using your Google account. You are commenting using your Twitter account. You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. Multiple comparisons can lead to spurious conclusions This time, we continue our discussion around p-values by discussing a common trap that people fall into when analyzing data.
Probability of falsely rejecting the null hypothesis red when it is true Unfortunately, as we do more and more comparisons, we are more and more likely to get a significant p -value simply by chance alone. Avoiding this pitfall There are several possibilities for mitigating the hazard of falsely rejecting null hypotheses when making multiple comparisons. Distinguish between hypothesis testing and exploratory data analysis We often learn that exploratory data analysis should be precursor to statistical analysis.
Establish hypotheses and statistical methodology early This leads to the crucial importance of establishing hypotheses and methods, including statistical models from the outset, ideally before data collection even begins. Sources Aschwanden, C. Share this: Twitter Facebook. Like this: Like Loading Fill in your details below or click an icon to log in:. Email required Address never made public. Name required. Add your thoughts here Email Required Name Required Website. By continuing to use this website, you agree to their use.
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