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When researchers carry out a null hypothesis significance test, it is tempting to assume that a statistically significant result lowers Prob(H0), the probability of the null hypothesis being true. Technically, such a statement is meaningless for various reasons: e.g., the null hypothesis does not have a probability associated with it. However, it is possible to relax certain assumptions to compute the posterior probability Prob(H0) under repeated sampling. We show in a step-by-step guide that the intuitively appealing belief, that Prob(H0) is low when significant results have been obtained under repeated sampling, is in general incorrect and depends greatly on: (a) the prior probability of the null being true; (b) type-I error rate, (c) type-II error rate, and (d) replication of a result. Through step-by-step simulations using open-source code in the R System of Statistical Computing, we show that uncertainty about the null hypothesis being true often remains high despite a significant result. To help the reader develop intuitions about this common misconception, we provide a Shiny app (https://danielschad.shinyapps.io/probnull/). We expect that this tutorial will help researchers better understand and judge results from null hypothesis significance tests.
The organisation of legislative chambers and the consequences of parliamentary procedures have been among the most prominent research questions in legislative studies. Even though democratic elections not only lead to the formation of a government but also result in an opposition, the literature has mostly neglected oppositions and their role in legislative chambers. This paper proposes to fill this gap by looking at the legislative organisation from the perspective of opposition players. The paper focuses on the potential influence of opposition players in the policy-making process and presents data on more than 50 legislative chambers. The paper shows considerable variance of the formal power granted to opposition players. Furthermore, the degree of institutionalisation of opposition rights is connected to electoral systems and not necessarily correlated with other institutional characteristics such as regime type or the size of legislative chambers.