A comparative introduction to statistical inference and hypothesis testing
نویسنده
چکیده
These are some notes on a very simple comparative introduction to four basic approaches of statistical inference—Fisher, Neyman–Pearson, Fisher/Neyman–Pearson hybrid, and Bayes—from a course on Quantitative & Statistical Reasoning at OU in Fall 2016. In particular, I hope to give a rough understanding of the differences between the frequentist and Bayesian paradigms, though they are not entirely disjoint. This is not intended as a practical introduction to how to numerically perform various standard tests. For instance, I won’t explain z-tests, t-tests, F -tests, χ2-tests, or one-sided tests versus two-sided tests. I will only work with small samples of discrete distributions for transparency of computation. My goal is to focus on what I consider more basic conceptual issues in understanding the statistical framework of hypothesis testing. I assume a little familiarity of the notion of a random variable, conditional probabilities, and a working understanding of the binomial distribution B(n, p), but no deeper study of statistics or probability is required.
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