Manoel Galdino pointed me to a discussion on the Polmeth list on the topic of reporting p-values and regression coefficients. (The polmeth listserv doesn’t seem to have a way to link to threads, but if you go here for March 2009 you can scroll down to the posts on “Displaying regression coefficients.”) I don’t want to go on and on about this, but in the interest of advancing the ball forward just a bit, here are a few thoughts:

1. I like standardized regression coefficients; see here for a full discussion with examples.

2. Discretizing predictors can also be useful. With a good discretization, you can present the equivalent of regression results in a more interpretable way; see here.

3. I agree with everyone on that thread who said that it’s not a good idea to report p-values. Larry Bartels puts it well: “Simply reporting p-values will only be informative to readers who happen to be interested in the null hypothesis that the relevant parameter value is zero, which I [Larry] almost never am.” I would go even further and point out that, in social science, I already know ahead of time before collecting any data that the null hypothesis is false!

4. In medical journals, it is becoming common practice for regression results to be presented graphically. This is definitely the way to go, in my opinion.

5. To avoid a graphs vs. tables flame war, let me try to focus the discussion on the question of what to communicate. Larry’s post quoted by Galdino had the following bit:

When space constraints necessitate a choice my [Larry’s] preference will usually be for the table. . . . if the point is simply to report regression coefficients, graphs are likely to take more space and convey the relevant information much less precisely. . . . accuracy and efficiency should often take precedence over “present[ing] your work in the most compelling visual manner” . . .

For me, the sticking point is the phrase, “simply to report regression coefficients.” It’s rare that this has been my research goal. And, the one time I can say that this clearly was our goal–my 1990 article with Gary estimating the incumbency advantage–it was still better to display the estimates graphically. In another example where we did present estimates of regression coefficients, our most important conclusions were shown by a pair of graphs. These graphs did incorporate fitted regression lines. In yet another case, I really did want some numbers, but (a) they were not raw regression coefficients, and (b) they were best portrayed graphically (in this article, see Figure 4, which I admit is a bit messy; if I were to redo it, I’d make a grid of graphs rather than just two very busy graphs

Finally, when there is a single coefficient or two that are of particular interest, it’s perfectly fine to give the number in the text (for example, “6.3% with a standard error of 2.3%”). No need to have a table with dozens of numbers. You can graph what is important and then supply the key numbers in the text as necessary. I can accept that there may be occasional examples where you really want a table of numbers (for example, a report of economic performance in 24 different industries, where the reader of the article might really want to know that the return on investment in a certain sector is 3.8%, or whatever), but that certainly doesn’t come up much in political science articles, as far as I am aware.

Returning to the above quote: the question is, what is the “accuracy and efficiency” you are looking for? Ultimately it’s about conveying what you found in your research, conveying this to yourself as well as to others. Larry has written a whole bunch of important and influential articles on public opinion and politics, and tables have worked for him as a way of organizing his results. I wouldn’t suggest for one minute that Larry change his ways. For those of us with less of a track record, however, it might be worth thinking a bit about what information we’re trying to convey, and whether the reader–even the scholarly reader–needs to know that the coefficient for “age squared” in your regression is 0,0000213 with a standard error of 0.0000079. Maybe you’re better off just explaining that you controlled for age in your analysis, or displaying the coefficient graphically, along with all the others, after an appropriate standardization. In my opinion, you should display this “0,0000213 (0.0000079)” only if you have a good reason to do so.

6. I’m a reformed sinner myself. See, for example, Figure 1 here. In my defense, nobody ever told me I should’ve graphed it–an excuse nobody has anymore!–but . . . how could I have thought that a reader would want to know, for example, that my posterior distribution for the volume of poorly perfused tissues for patient A in the study had a geometric mean of .649 and a geometric standard deviation of 1.04?? I mean, what was I thinking? I was focusing on the proximate goal–recording the numbers–rather than the ultimate goals of understanding the methods and the fitted model and its implications.

P.S. But it’s good to see an anti-graph backlash. This tells me that the method of displaying research results using graphs–or, more specifically, the idea that graphical display should be the default–is making progress.