Monthly Archives: June 2017

Two tales about a null result

(See the bottom for a bit of a plot twist.)

Tale 1

A researcher has some intuitions about how to test a theoretical proposition using what appears to be a nice natural experiment. Before discussing things with other colleagues and without putting much more thought into it, the researcher pulls together some data and does some analyses. The idea is just to see whether there are any interesting patterns to pursue further. The researcher tries out different outcome measures. The researcher also tries out different specifications that come to mind based on deeper, iterative reflection on the problem. All results come back noisy, with no clear patterns—it’s a null result. The researcher declares that the either the proposition or the natural experiment has flaws that were not apparent at the outset.

Tale 2

A researcher has some intuitions about how to test a theoretical proposition using what appears to be a nice natural experiment. The researcher discusses the idea with some colleagues who agree that this has potential as a natural experiment and also addresses a question in a research program that draws a lot of interest. The research thinks harder about the theory and the natural experiment, finding some subtleties that make the analysis of the natural experiment more informative about the theoretical proposition. The researcher writes up the theoretical analysis giving rise to the proposition, the various tests that the proposition implies, and the data analysis plan and presents them for comment at workshops and conferences. The researcher receives suggestions and generally positive feedback about the value of pursuing the project. This is somewhat unusual — in the past, ideas have been shot down either at the more inchoate stage or even at workshops based on pre-analysis plans. So the researcher is excited to carry out the analysis. All results come back noisy, with no clear patterns—it’s a null result. The researcher declares that the either the proposition or the natural experiment has flaws that were not apparent at the outset.

Reflections

How do these tales end?

Probably for tale 1, the researcher just abandons the project. Should there be a record available of this? I suppose, insofar as the absence of a record is “file drawering.” But the project was exploratory and informal, so I do not think it is reasonable that a full-on journal publication would be warranted. Rather, what would be nice would be a place to deposit logs of such exploratory analyses along with an abstract and keywords. Then, others interested in the pursuing similar ideas would have a place to search and learn from others attempts. The researcher could add a line to the CV in a section called “research logs.”

Tale 2 is different. It is the process leading up to the null that makes it different. Given the “peer review” in the pre-analysis stage, the findings should be of interest to that community of researchers. The null finding merits a full-on journal publication.

Plot twist

Nothing about the results being “null” in the above affects the logic of the story. Indeed, I focused only on null results here because I wanted a story that shows how we can feel good about a null result. That’s the second tale. However, if we made the results “significant” instead, it does not follow that one should, as a result of that change, now “feel good” in the first tale.

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Notes on multiple comparisons and pre-specifying exploratory analyses

I am part of a few research projects and initiatives involving the development of pre-analysis plans. This includes involvement in the EGAP metaketas (link) as well as some of my own research projects. Some questions that researchers frequently struggle to address include, “what kind of multiple comparisons adjustments do we need?” and “what if we are unsure about the nature of the effects that will arise and we want to allow for exploration?”. Here are some thoughts in relation to these questions:

First, I recommend that you read these two very good blog posts on how to assess multiple comparisons issues by Daniel Laekens (link) and Jan Vanhove (link). The core insight from these posts is that multiple comparisons adjustments are intended to control error rates in relation to the specific judgments that you want to make on the basis of your analysis.

Second, my understanding is that multiple comparisons adjustments and two-sided tests are ways of establishing appropriate standards precisely for exploratory analyses. For example, multiple comparisons adjustments (or index creation — link) can come into play when, ex ante, available information leaves you undecided about which outcomes might reveal an effect, but you are willing, ex post, to take a significant estimate on any outcome as being indicative of an effect. Similarly, two-sided tests come into play when, ex ante, available information leaves you undecided as to whether an effect is positive or negative, but you are willing, ex post, to take a significant negative estimate as indicative of a negative effect and a significant positive estimate as indicative of a positive effect. There is nothing wrong with being honest about such undecidedness in a pre-analysis plan, and there is nothing about pre-specification that precludes such exploration. Rather the prespecification allows you to think through an inferential strategy that is ex post reliable in terms of error rates.

Update (6/5/17):

Some discussions that followed my posting these notes made me think it would be useful to give a toy example that helps to think through some of the issues highlighted above. So here goes:

Suppose that you have a study that will produce hypothesis tests on treatment effect estimates for two outcomes, outcome A and B. So, we have two significance tests. (Most of the points made here would generalize to more tests or groupings of tests.) What kind of multiple testing adjustment would be needed? It depends on the judgments that you want to make. Here are three scenarios:

  1. My primary goal with the experiment is that I want to see if the treatment does anything, and if it does, I will proceed with further research on this treatment, although the direction of the research depends on whether I find effects on neither, A, B, or both. I selected outcomes A and B based on pretty loose ideas about how the treatment might work.
  2. My selection of outcomes A and B is based on the fact that there is a community of scholars quite invested in whether there is an effect on A, and another community of scholars invested in whether there is an effect on B. My research design allows me to test these two things. The conclusion regarding the outcome-A effect will inform how research proceeds on the “A” research program, and, distinct from that, the conclusion regarding the outcome-B effect will inform how research proceeds on the “B” program.
  3. Outcome A is the main outcome of interest. However, depending on whether there is an effect on A, I am also interested in B, as a potential mechanism.

These three scenarios each suggest a different way of treating the multiple outcomes. The judgment in scenario 1 depends on whether A or B is significant, and therefore requires multiple testing adjustment for the two outcomes so as to control this joint error rate. The two judgments in scenario 2 are independent of each other. As such, the error rate for each independent judgment depends on the error rate for each individual test — no multiple comparisons adjustment is called for. The sequence of judgments in scenario three suggests a “sequential testing plan,” along the lines of those discussed by Rosenbaum in Chapter 19 of his Design of Observational Studies. (Hat tip to Fernando Martel @fmg_twtr for this.)

The upshot is that it is not the number of outcomes that matters in and of itself, rather it is the nature of the judgments that one wants to make with tests on these outcomes that determines the adjustment needed. The goal is to control the error rate for the judgment that you are making. I get the sense that the confusion over adjustments comes from confusion over what people want to do with the results of an analysis.

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