Chapter 19: Content and Pedagogical Knowledge For Teaching Confidence Intervals in a Post p < 0.05 World

The term, inference, as used by statisticians, describes the set of statistical techniques through which conclusions about a population are made from information provided by a sample selected from that population. Unlike scientific inferencing, frequentist statistical inference, especially as taught in the statistics and probability strand of the Common Core State Standards, is quite formulaic with a well-defined series of steps:

In contrast to statistical inference, scientific inference cannot be reduced to a “series of allegedly neat and tidy methodological steps whose dutiful observance renders the output ‘science’” (Hubbard et al., 2019, p. 95). Hubbard and colleagues (2019) described scientific inferencing as the development of the best explanation for the available facts: Scientists study observable behavior and propose theories about the causal mechanisms that generate the observed behavior. The frequentist statistical methods use the information limited to the sample collected and provide only probabilistic conclusions about the population. As Wild (2009) said in his plenary talk at the U.S. Conference on Teaching Statistics, using a sample to make conclusions about a population is like viewing reality through wavy glass and guessing what is on the other side. In contrast, Bayesian statistical methods, which have become more popular as access to computational power has increased, use all available information to continually update probability distributions used to model the population.