What counts as a successful or failed replication?

Let’s say that some theory states that people in psychological state A1 will engage in behavior B more than people in psychological state A2. Suppose that, a priori, the theory allows us to make this directional prediction, but not a prediction about the size of the effect.

A researcher designs an experiment — call this Study 1 — in which she manipulates A1 versus A2 and then measures B. Consistent with the theory, the result of Study 1 shows more of behavior B in condition A1 than A2. The effect size is d=0.8 (a large effect). A null hypothesis significance test shows that the effect is significantly different from zero, p<.05.

Now Researcher #2 comes along and conducts Study 2. The procedures of Study 2 copy Study 1 as closely as possible — the same manipulation of A, the same measure of B, etc. The result of Study 2 shows more of behavior B in condition A1 than in A2 — same direction as Study 1. In Study 2, the effect size is d=0.3 (a smallish effect). A null hypothesis significance test shows that the effect is significantly different from zero, p<.05. But a comparison of the Study 1 effect to the Study 2 effect (d=0.8 versus d=0.3) is also significant, p<.05.

Here’s the question: did Study 2 successfully replicate Study 1?

My answer is no. Here’s why. When we say “replication,” we should be talking about whether we can reproduce a result. A statistical comparison of Studies 1 and 2 shows that they gave us significantly different results. We should be bothered by the difference, and we should be trying to figure out why.

People who would call Study 2 a “successful” replication of Study 1 are focused on what it means for the theory. The theoretical statement that inspired the first study only spoke about direction, and both results came out in the same direction. By that standard you could say that it replicated.

But I have two problems with defining replication in that way. My first problem is that, after learning the results of Study 1, we had grounds to refine the theory to include statements about the likely range of the effect’s size, not just its direction. Those refinements might be provisional, and they might be contingent on particular conditions (i.e., the experimental conditions under which Study 1 was conducted), but we can and should still make them. So Study 2 should have had a different hypothesis, a more focused one, than Study 1. Theories should be living things, changing every time they encounter new data. If we define replication as testing the theory twice then there can be no replication, because the theory is always changing.

My second problem is that we should always be putting theoretical statements to multiple tests. That should be such normal behavior in science that we shouldn’t dilute the term “replication” by including every possible way of doing it. As Michael Shermer once wrote, “Proof is derived through a convergence of evidence from numerous lines of inquiry — multiple, independent inductions all of which point to an unmistakable conclusion.” We should all be working toward that goal all the time.

This distinction — between empirical results vs. conclusions about theories — goes to the heart of the discussion about direct and conceptual replication. Direct replication means that you reproduce, as faithfully as possible, the procedures and conditions of the original study. So the focus should rightly be on the result. If you get a different result, it either means that despite your best efforts something important differed between the two studies, or that one of the results was an accident.

By contrast, when people say “conceptual replication” they mean that they have deliberately changed one or more major parts of the study — like different methods, different populations, etc. Theories are abstractions, and in a “conceptual replication” you are testing whether the abstract theoretical statement (in this case, B|A1 > B|A2) is still true under a novel concrete realization of the theory. That is important scientific work, but it differs in huge, qualitative ways from true replication. As I’ve said, it’s not just a difference in empirical procedures; it’s a difference in what kind of inferences you are trying to draw (inferences about a result vs. inferences about a theoretical statement). Describing those simply as 2 varieties of the same thing (2 kinds of replication) blurs this important distinction.

I think this means a few important things for how we think about replications:

1. When judging a replication study, the correct comparison is between the original result and the new one. Even if the original study ran a significance test against a null hypothesis of zero effect, that isn’t the test that matters for the replication. There are probably many ways of making this comparison, but within the NHST framework that is familiar to most psychologists, the proper “null hypothesis” to test against is the one that states that the two studies produced the same result.

2. When we observe a difference between a replication and an original study, we should treat that difference as a problem to be solved. Not (yet) as a conclusive statement about the validity of either study. Study 2 didn’t “fail to replicate” Study 1; rather, Studies 1 and 2 produced different results when they should have produced the same, and we now need to figure out what caused that difference.

3. “Conceptual replication” should depend on a foundation of true (“direct”) replicability, not substitute for it. The logic for this is very much like how validity is strengthened by reliability. It doesn’t inspire much confidence in a theory to say that it is supported by multiple lines of evidence if all of those lines, on their own, give results of poor or unknown consistency.