The enduring replication crisis in many scientific disciplines casts doubt on the ability of science to estimate effect sizes accurately, and in a wider sense, to self-correct its findings and to produce reliable knowledge. We investigate the merits of a particular countermeasure—replacing null hypothesis significance testing with Bayesian inference—in the context of the meta-analytic aggregation of effect sizes. In particular, we elaborate on the advantages of this Bayesian reform proposal under conditions of publication bias and other methodological imperfections that are (...) typical of experimental research in the behavioral sciences. Moving to Bayesian statistics would not solve the replication crisis single-handedly. However, the move would eliminate important sources of effect size overestimation for the conditions we study. (shrink)

The origins of testing scientific models with statistical techniques go back to 18th century mathematics. However, the modern theory of statistical testing was primarily developed through the work of Sir R.A. Fisher, Jerzy Neyman, and Egon Pearson in the inter-war period. Some of Fisher's papers on testing were published in economics journals (Fisher, 1923, 1935) and exerted a notable influence on the discipline. The development of econometrics and the rise of quantitative economic models in the mid-20th century made statistical significance (...) testing a commonplace, albeit controversial tool within economics. -/- In the debate about significance testing, methodological controversies intertwine with epistemological issues and sociological developments. Our aim in this chapter is to expound these connections and to show how the use of, and the debate about, significance testing in economics differs from other social sciences, such as psychology. (shrink)

It is widely held that falsification of statistical hypotheses is impossible. This view is supported by an analysis of the most important theories of statistical testing: these theories are not compatible with falsificationism. On the other hand, falsificationism yields a basically viable solution to the problems of explanation, prediction and theory testing in a deterministic context. The present paper shows how to introduce the falsificationist solution into the realm of statistics. This is done mainly by applying the concept of empirical (...) content to statistical hypotheses. It is shown that empirical content is a substitute for ‘power’ as defined by Neyman and Pearson. Since the empirical content of a hypothesis is independent of alternative hypotheses, the proposed theory of statistical testing allows for tests of isolated hypotheses. (shrink)

In a recent note Roger Carlson presented a rather negative appraisal of my treatment of the logic of Fisherian significance testing in [10]. The main issue between us involves Carlson's thesis that, within the limits set by Fisher, standard significance tests are valuable tools of data analysis as they stand, i.e., without modification of the structure of the reasoning they employ. Call this the adequacy thesis. In my paper I argued that the pattern of reasoning employed by tests of significance (...) needs to be justified in spite of its unquestioned acceptance by most researchers, The best justification offered to date—by R. A. Fisher—is seriously defective. Therefore the adequacy thesis is not justified. I proposed some alterations of the pattern of reasoning employed by tests of significance and argued that they guarantee that tests are adequate epistemological tools. (shrink)

According to Fisher, a hypothesis specifying a density function for X is falsified (at the level of significance ) if the realization of X is in the size- region of lowest densities. However, non-linear transformations of X can map low-density into high-density regions. Apparently, then, falsifications can always be turned into corroborations (and vice versa) by looking at suitable transformations of X (Neyman's Paradox). The present paper shows that, contrary to the view taken in the literature, this provides no argument (...) against a theory of statistical falsification. (shrink)