# Statistical Hypothesis Testing

## Hypothesis testing in statistics

^{8} Mann-Whitney U Test

Published: 2019-01-20

Category: { Statistical Hypothesis Testing }

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References:
- What's the difference An Overview of Non-Parametric Tests
- How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Summary: Non-parametric test using ranking

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^{7} Statistical Sign Test

Published: 2019-01-20

Category: { Statistical Hypothesis Testing }

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References:
- The sign test @ inferential statistics

Summary: Statistical test without assuming models

Pages: 5

^{4} Neyman-Pearson Theory

Published: 2022-04-02

Category: { Statistics Hypothesis Testing }

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References:
- Shafer G, Vovk V. A tutorial on conformal prediction. arXiv [cs.LG]. 2007. Available: http://arxiv.org/abs/0706.3188
- Perezgonzalez JD. Fisher, Neyman-Pearson or NHST? A tutorial for teaching data testing. Front Psychol. 2015;6: 223. doi:10.3389/fpsyg.2015.00223
- 26.1 - Neyman-Pearson Lemma. In: PennState: Statistics Online Courses [Internet]. [cited 2 Apr 2022]. Available: https://online.stat.psu.edu/stat415/lesson/26/26.1
- Contributors to Wikimedia projects. Likelihood-ratio test. In: Wikipedia [Internet]. 10 Jun 2021 [cited 2 Apr 2022]. Available: https://en.wikipedia.org/wiki/Likelihood-ratio_test

Summary: The Neyman-Pearson hypothesis testing tests two hypothesis, hypothesis $H$, and an alternative hypothesis $H_A$.
Neyman-Pearson Lemma The Neyman-Pearson Lemma is an very intuitive lemma to understand how to choose a hypothesis. The lecture notes from PennState is a very good read on this topic1.
An example For simplicity, we assume that there exists a test statistic $T$ and $T$ can be used to measure how likely the hypothesis $H$ is true, e.g., the hypothesis $H$ is false, corresponds to $T$ being small.
The reference from Shafer2007 assumes a random variable $T$ to be large if the hypothesis $H$ is false[^Shafer2007]. One example is the ratio of likelihood2,

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^{2} Types of Errors in Statistical Hypothesis Testing

Published: 2019-05-31

Category: { Statistical Hypothesis Testing }

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Summary: We all make mistakes. The question is, what kind of mistakes.

Pages: 5

^{1} Statistical Hypothesis Testing

Published: 2019-01-20

Category: { Statistical Hypothesis Testing }

Tags:

References:
- Schaum's Outline of Theories and Problems of Elements of Statistics II, by Ruth Bernstein and Stephen Bernstein, Chapter 16

Summary: hypothesis testing is about the probability of alternative hypothesis if the null hypothesis is true, or even more general

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