Abstract
Building on the distinction between sample and population, this chapter covers the process of testing hypotheses about population parameters. Here, substantive hypotheses of interest are transformed into a statistical formulation consisting of a mutually exclusive pair of alternative and null hypotheses. Deciding between these two hypotheses is possible based on the result of a significance test. In this context, we introduce the logic underlying such decisions using a simulation, including concepts such as significance level and p-value. The logic described here will also be the cornerstone for almost all statistical tests discussed in this book.
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Notes
- 1.
We will return to the distinction between dependent and independent samples in Sect. 5.3.
- 2.
Considering the probability of observing either the measured value for D or more extreme values is useful and sometimes necessary for several reasons. For instance, if we had fine-grained measurements, the probability of a particular outcome is necessarily small (in case of continuous variables it is even 0), so that we cannot draw meaningful conclusions from the probability of a particular event. However, because more extreme—here: larger—values would also speak against the H0, we assess the probability of the observed value or even more extreme data instead.
- 3.
An approximation for this probability is provided by so-called Bayesian statistics. We will discuss the basics of these approaches in Chap. 12.
References
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Renkewitz, F., & Sedlmeier, P. (2007). Forschungsmethoden und Statistik in der Psychologie. Pearson.
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Janczyk, M., Pfister, R. (2023). Hypothesis Testing and Significance. In: Understanding Inferential Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66786-6_4
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