Let $\mathcal B_c$ denote the real-valued functions continuous on the extended real line and vanishing at $-\infty $. Let $\mathcal B_r$ denote the functions that are left continuous, have a right limit at each point and vanish at $-\infty $. Define $\mathcal A^n_c$ to be the space of tempered distributions that are the $n$th distributional derivative of a unique function in $\mathcal B_c$. Similarly with $\mathcal A^n_r$ from $\mathcal B_r$. A type of integral is defined on distributions in $\mathcal A^n_c$ and $\mathcal A^n_r$. The multipliers are iterated integrals of functions of bounded variation. For each $n\in \mathbb N$, the spaces $\mathcal A^n_c$ and $\mathcal A^n_r$ are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to $\mathcal B_c$ and $\mathcal B_r$, respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space $\mathcal A_c^1$ is the completion of the $L^1$ functions in the Alexiewicz norm. The space $\mathcal A_r^1$ contains all finite signed Borel measures. Many of the usual properties of integrals hold: Hölder inequality, second mean value theorem, continuity in norm, linear change of variables, a convergence theorem.
The use of significance tests in social sciences is widespread mainly due to simple computation via statistical packages. Unfortunately the more social scientists use statistical significance estimates for making causal inferences the less they appear to understand about this influential concept. Statistical modelling results are usually presented in terms of their statistical significance and little other information is provided. The goal of this article is to show the limits of using statistical significance as a sole means of making inferences; and to present alternative statistical fit indicators readily available within frequentist approach to statistics: confidence intervals, minimum sample size and power analysis. Multiple working hypotheses are also explored together with two well known information criteria - AIC and BIC. This article provides practical information on how to undertake valid and reliable statistical analyses of social science data., Petr Soukup., and Obsahuje bibliografii a bibliografické odkazy