Always Conduct the “Simplest Valid Analysis”

This piece was cross-posted on the Transprent Replications blog.

A significant and pretty common problem I see when reading papers in social science (and psychology in particular) is that they present a fancy analysis but don’t show the results of what we have named the “Simplest Valid Analysis” – which is the simplest possible way of analyzing the data that is still a valid test of the hypothesis in question.

This creates two potentially serious problems that make me less confident in the reported results:

1. Fancy analyses impress people (including reviewers), but they are often harder to interpret than simple analyses. And it’s much less likely the reader really understands the fancy analysis, including its limitations, assumptions, and gotchas. So, the fancy analysis can easily be misinterpreted, and is sometimes even invalid for subtle reasons that reviewers, readers (and perhaps the researchers themselves) don’t realize. As a mathematician, I am deeply unimpressed when someone shows me a complex mathematical method when a simple one would have sufficed, but a lot of people fear or are impressed by fancy math, so complex analyses can be a shield that people hide behind.
2. Fancy analyses typically have more “researcher degrees of freedom.” This means that there is more wiggle room for researchers to choose an analysis that makes the results look the way the researcher would prefer they turn out. These choices can be all too easy to justify for many reasons including confirmation bias, wishful thinking, and a “publish or perish” mentality. In contrast, the Simplest Valid Analysis is often very constrained, with few (if any) choices left to the researcher. This makes it less prone to both unconscious and conscious biases.

When a paper doesn’t include the Simplest Valid Analysis, I think it is wise to downgrade your trust in the result at least a little bit. It doesn’t mean the results are wrong, but it does mean that they are harder to interpret.

I also think it’s fine and even good for researchers to include more sophisticated (valid) analyses and to explain why they believe those are better than the Simplest Valid Analysis, as long as the Simplest Valid Analysis is also included. Fancy methods sometimes are indeed better than simpler ones, but that’s not a good reason to exclude the simpler analysis.

Here are some real-world examples where I’ve seen a fancier analysis used while failing to report the Simplest Valid Analysis:

• Running a linear regression with lots of control variables when there is no need to control for all of these variables (or no need to control for more than one or two of the variables)
• Use of ANOVA with lots of variables when really the hypothesis only requires a simple comparison of two means
• Use of a custom statistical algorithm when a very simple standard algorithm can also test the hypothesis
• Use of fancy machine learning when simple regression algorithms may perform just as well
• Combining lots of tests into one using fancy methods rather than performing each test one at a time in a simple way

The problems that can occur when the results of Simplest Valid Analysis aren’t reported was one of the reasons that we decided to include a Clarity Criterion in our evaluation of studies for Transparent Replications. As part of evaluating a study’s Clarity, if it does not present the results of the Simplest Valid Analysis, we determine what that analysis would be, and pre-register and conduct the Simplest Valid Analysis on both the original data and the new data we collect for the replication. Usually it is fairly easy to determine what the Simplest Valid Analysis would be for a research question, but not always. When there are multiple analyses that could be used as the Simplest Valid Analysis, we select the one that we believe is most likely to be informative, and we select that analysis prior to running analyses on the original data and prior to collecting the replication data.

In my view, while it is very important that a study replicates, replication alone does not guarantee that a study’s results reflect something real in the world. For that to be the case, we also have to be confident that the results obtained are from valid tests of the hypotheses. One way to increase the likelihood of that being the case is to report the results from the Simplest Valid Analysis.

My advice is that, when you’re reading scientific results, look for the Simplest Valid Analysis, and if it’s not there, downgrade your trust in the results at least a little bit. If you’re a researcher, remember to report the Simplest Valid Analysis to help your work be trusted and to help avoid mistakes (I aspire always to do so, though there have likely been times I have forgotten to). And if you’re a peer reviewer or journal editor, ask authors to report the Simplest Valid Analysis in their papers in order to reduce the risk that the results have been misinterpreted.