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For the last 50 years of research in quantitative social sciences, the empirical evaluation of scientific hypotheses has been based on the rejection or not of the null hypothesis. However, more than 300 articles demonstrated that this method was problematic. In summary, null hypothesis testing (NHT) is unfalsifiable, its results depend directly on sample size and the null hypothesis is both improbable and not plausible. Consequently, alternatives to NHT such as confidence intervals (CI) and measures of effect size are starting to be used in scientific publications. The purpose of this article is, first, to provide the conceptual tools necessary to implement an approach based on confidence intervals, and second, to briefly demonstrate why such an approach is an interesting alternative to an approach based on NHT. As demonstrated in the article, the proposed CI approach avoids most problems related to a NHT approach and can often improve the scientific and contextual relevance of the statistical interpretations by testing range hypotheses instead of a point hypothesis and by defining the minimal value of a substantial effect. The main advantage of such a CI approach is that it replaces the notion of statistical power by an easily interpretable three-value logic (probable presence of a substantial effect, probable absence of a substantial effect and probabilistic undetermination). The demonstration includes a complete example.

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