Statistics [16]: Summary of Statistical Tests

Cheat sheet of statistical tests.

Purpose of Statistical Tests

Statistical tests are used to:

1. determine whether a predictor variable has a statistically significant relationship with an outcome variable.
2. estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then a statistically significant relationship between the predictor and outcome variables can be inferred. Otherwise, no statistically significant relationship could be inferred.

Parametric Statistical Tests

Comparison Tests

T-tests are used when comparing the means of precisely two groups (e.g. the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups.

	Predictor Variable	Outcome Variable
Independent test	Categorical; 1 predictor	Quantitative; Groups from the same population
Paired test	Categorical; 1 predictor	Quantitative; Groups from different populations
ANOVA	Categorical; 1 or more predictor	Quantitative; 1 outcome
MANOVA	Categorical; 1 or more predictor	Quantitative; 2 or more outcomes

Regression Tests

Regression tests look for cause-and-effect relationships. They can be used to estimate the effect of one or more continuous variables on another variable.

Correlation Tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship. These can be used to test whether two variables used in a multiple regression test are autocorrelated.

	Variables
Pearson’s	2 continous variables

Variance Homogeneity Test

	Requirements
Hartley test	Number of the independent tests under levels are the same
Bartlett test	Number of the independent tests under levels don’t not need to be the same

Non-Parametric Statistical Tests

	Predictor Variable	Outcome Variable	Use In Place Of …
Spearman’s	Quantitative	Quantitative	Pearson’s
test of independence	Categorical	Categorical	Pearson’s
Sign test	Categorical	Quantitative	One-sample -test
Kruskal–Wallis	Categorical; groups	Quantitative	ANOVA
ANOSIM	Categorical; groups	2 or more outcome variables	MANOVA
Wilcoxon Rank-Sum test	Categorical; 2 groups	Quantitative; groups from different populations	Independent test
Wilcoxon Signed-rank test	Categorical; 2 groups	Quantitative; groups from the same population	Paired test

Flow Chart

Flowchart from Scribbr.

Table of Contents

• Probability vs Statistics
• Shakespear’s New Poem
• Some Common Discrete Distributions
• Some Common Continuous Distributions
• Statistical Quantities
• Order Statistics
• Multivariate Normal Distributions
• Conditional Distributions and Expectation
• Problem Set [01] - Probabilities
• Parameter Point Estimation
• Evaluation of Point Estimation
• Parameter Interval Estimation
• Problem Set [02] - Parameter Estimation
• Parameter Hypothesis Test
• t Test
• Chi-Squared Test
• Analysis of Variance
• Summary of Statistical Tests
• Python [01] - Data Representation
• Python [02] - t Test & F Test
• Python [03] - Chi-Squared Test
• Experimental Design
• Monte Carlo
• Variance Reducing Techniques
• From Uniform to General Distributions
• Problem Set [03] - Monte Carlo
• Unitary Regression Model
• Multiple Regression Model
• Factor and Principle Component Analysis
• Clustering Analysis
• Summary