An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors

A comparative introduction to statistical inference and hypothesis testing

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 entirel...

Introduction to Hypothesis Testing

Introduction to Hypothesis Testing

Statistical Hypothesis • Null hypothesis (H0): Hypothesis of no difference or no relation (or not guilty) and often has =, ≥, or ≤ notation in the mathematical statement of the hypothesis. A theory about the values of one (or more) population parameter(s). The theory generally represents the status quo, which we accept until it is proven false. Example: H0: μ = 98.6F (average body temperature i...

Introduction to Hypothesis Testing

Suppose we are using a pH meter to test acidity/alkalinity of a solution used in a manufacturing process. The pH of pure water is 7.00. For samples in the pH range from about 5 to 9 the meter gives normally distributed readings with • μ equal to the true pH of the sample and • standard deviation σ = 0.20. The meter is tested each morning to make sure it is operating properly: n = 4 samples of p...

An Introduction to Statistical Spoken Language Understanding

1 Introduction Besides dictation, there are many other practical applications for speech recognition, including command and control, spoken dialog systems [1, 2], speech-to-speech translation [3], and multi-modal interaction [4-6]. The success of these applications relies on the correct recognition of not only what is said, but also what is meant. In contrast to automatic speech recognition (AS...