Advanced Statistics with Applications in R

Chapter 7Hypothesis testing and confidence intervals

Together with parameter estimation, hypothesis testing and confidence intervals are the backbones of statistical inference. In a way, parameter estimation is essential because once a satisfactory estimator exists, one can use it to test hypotheses or construct confidence intervals. Properties of statistical tests and confidence intervals are studied from two perspectives: (i) small‐sample properties, when the sample size, is finite, and (ii) asymptotic properties, when From a practical standpoint, the latter never takes place – we treat asymptotic results as an approximation. Hypothesis testing and confidence intervals are intrinsically related. We discuss how to test statistical hypotheses, and then turn our attention to interval estimation.

Special attention is given to explanation of major statistical concepts, such as the ‐value, in layman's terms. Often, the work of statisticians is used by nonstatisticians. Therefore, the ability to explain statistics in lay‐language is of paramount importance – this is how our work is judged, and ultimately, paid.

7.1 Fundamentals of statistical testing

We give an intuitive introduction ...