Hypothesis Testing A-Z Cheatbook

Rupak (Bob) Roy - II
3 min readMar 8, 2023

Listing all the hypotheses available sorted in one place.

Hi everyone likewise real quick today I will bring you all the hypothesis testing in one place sorted straight from my notebook so that we don't have to go everywhere to look for the appropriate hypothesis test.

Do excuse me if u feel sometimes the definitions are short, as i m writing this article straight from my note :)

Let’s get started with

1. Normality Test

Parametric Test: as we know it refers to those tests that have assumptions. This is the drawback of the parametric tests however they have higher confidence levels.

1.1 Likelihood Ratio Test (LRT) /One-Dimensional Wald Test

1.2 Wald Test — an asymptotic level test

1.3 T-test: t-test is based on a non-asymptotic distribution for the average rescaled by the sample std.

1.4 Neyman Pearson Lemma Test

Non: Parametric Test: refers to the test not bounded by any assumptions.

1.5 Kolmogorov Smirnov(K-S) Test: is a non-parametric (Goodness of Fit) test.

1.6 Anderson Darling K-Sample Test: It is a modification of the Kolmogorov-Smirnov (K-S) test and gives more weight to the tails than the K-S test.

1.7 Carmer-Von Mises: uses empirical distribution function.

1.8 Kolmogrov Lillifors Test

1.9 Chi-square Test (Gof): Discrete distribution

1.10 Shapiro Wilk Tets

1.11 Jarque-Beta test is also an another GOF(Goodness of Fit) test

2. Hypothesis Test

Parametric tests: are those statistical test that assumes the data approximately follows a normal distribution

2.1 One Sample t-test

2.2 Unpaired t-test

2.3 One-way ANOVA

2.4 Pearson’s Coefficient: gives the magnitude of linear correlation

Non-Parametric: are those statistical tests that do not assume anything about the distribution followed by the data.

2.5 Wilcoxon Signed Rank

2.6 Mann-Whitney U

2.7 Kruskal Wallis H

2.8 Friedman Test

2.9 Spearman’s Coefficient: gives the magnitude of non-linear correlation. Alternative to pearson’s coefficient

3. Stationary Test

3.1 Augmented Dickey-Fuller test

3.2 Kwiatkowski-phillips-schmidt-shin (kpss) test

4. Correlation Test

4.1 Pearson’s Correlation Coefficient

4.2 Spearman’s Rank Correlation

4.3 Kendall’s Rank Correlation

4.4 Chi-Squared Test: for Binary Categorical values

4.5 One-way ANOVA & Krushall Wallis H test: for categorical/Mixed Categorical & Continuous: Assumptions required data normally distributed, same variance.

4.6 Logistic Regression: preferred because assumptions like the same variance are not required.

4.7 Dubin Watson: also used for autocorrelation

5. Correlation Test (Ordinal Association)

5.1 Spearman Rank Correlation

5.2 Goodman Krushal’s Gamma

5.3 Kendall’s Tau

5.4 Somer’s D

6. Correction Test

correction test guarantees that you’re type 1 error(False Positive) is actually the right one.

6.1 Bonferroni Test — Non-asymptotic test

6.2 Holm Bonferroni Correction

6.3 Benjamin Hochberg Correction

6.4 Different Protection Levels — a) Family Wise Error Rate(FWER)

b) False Discovery Rate (FDR)

the list will be updated from time to time.

Dn’t yell at me, once again this is a rough note of putting all the tests sorted so that we don't get confused about what is where?

The links below are my other articles that talks about the definitions

Article 1: https://bobrupakroy.medium.com/non-parametric-hypothesis-t-test-f8dccde15eb2

Article 2: https://bobrupakroy.medium.com/normality-tests-in-11-ways-57776095413d

I hope you find this article useful for your machine learning and statistical use cases. Likewise, i will try to bring new ways across with the motto “curiosity leads to innovation” :)

Thanks again, for your time, if you enjoyed this short article there are tons of topics in advanced analytics, data science, and machine learning available in my medium repo. https://medium.com/@bobrupakroy

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Also available on Quora @ https://www.quora.com/profile/Rupak-Bob-Roy

Let me know if you need anything. Talk Soon.



Rupak (Bob) Roy - II

Things i write about frequently on Medium: Data Science, Machine Learning, Deep Learning, NLP and many other random topics of interest. ~ Let’s stay connected!