There are so many things in statistics (and hence in econometrics) that are easily, and frequently, misinterpreted. Two really obvious examples are p-values and confidence intervals.
I've devoted some space in earlier posts to each of these concepts, and their mis-use. For instance, in the case of p-values, see the posts here and here; and for confidence intervals, see here and here.
Today I was reading a great paper by Greenland et al. (2016) that deals with some common misconceptions and misinterpretations that arise not only with p-values and confidence intervals, but also with statistical tests in general and the "power" of such tests. These comments by the authors in the abstract for their paper sets the tone of what's to follow rather nicely:
"A key problem is that there are no interpretations of these concepts that are at once simple, intuitive, correct, and foolproof. Instead, correct use and interpretation of these statistics requires an attention to detail which seems to tax the patience of working scientists. This high cognitive demand has led to an epidemic of shortcut deﬁnitions and interpretations that are simply wrong, sometimes disastrously so - and yet these misinterpretations dominate much of the scientiﬁc literature."
The paper then goes through various common interpretations of the four concepts in question, and systematically demolishes them!
The paper is extremely readable and informative. Every econometrics student, and most applied econometricians, would benefit from taking a look!
Greenland, S., S. J. Senn, K. R. Rothman, J. B. Carlin, C. Poole, S. N. Goodman, & D. G. Altman, 2016. Statistical tests, p values, confidence intervals, and power: A guide to misinterpretations. European Journal of Epidemiology, 31, 337-350.