Statistical Tests and Regression Methods for Data Analysis

Bartlett's Test

Tests if the variances (spread of data) in different groups are equal.

Use case of Bartlett's Test

You use it when you're comparing multiple groups (e.g., three or more) and you need to know if their variability is similar before using certain statistical tests (like ANOVA).

Key idea of Bartlett's Test

Assumes data is normally distributed. If variances are unequal, you might need a different test.

Levene's Test

Also checks if the variances in different groups are equal, but it's more robust than Bartlett's test and can handle situations where the data isn't perfectly normal.

Use case of Levene's Test

Similar to Bartlett's test, but you'd use Levene's test if you think your data might be skewed or not follow a normal distribution.

Welch's ANOVA

A variation of the regular ANOVA (Analysis of Variance), but it is used when the assumption of equal variances is violated.

Use case of Welch's ANOVA

If you're comparing means between three or more groups and the groups have different variances, this test is a better choice than regular ANOVA.

Key idea of Welch's ANOVA

More robust when groups have unequal variances.

Kruskal-Wallis Test

A non-parametric test that compares the medians of more than two groups (instead of means).

Use case of Kruskal-Wallis Test

Use this when the data is not normally distributed and you need to compare more than two groups. It's the non-parametric alternative to one-way ANOVA.

Key idea of Kruskal-Wallis Test

Focuses on ranks, not the actual data values, making it less sensitive to outliers.

Cook's Distance

Identifies influential data points that have a large impact on the results of your regression analysis.

Use case of Cook's Distance

If you're doing a regression analysis, you might use Cook's Distance to detect if any data points are 'outliers' or significantly affecting the results.

Key idea of Cook's Distance

Helps you spot data points that might disproportionately affect the model's results.

Two-Way ANOVA with Interaction

Tests the effect of two different independent variables on a dependent variable, and whether there's an interaction between those independent variables.

Use case of Two-Way ANOVA with Interaction

Use it when you want to see if two factors (e.g., time and treatment type) affect the outcome, and if their effect depends on each other.

Key idea of Two-Way ANOVA with Interaction

Looks at both individual and combined effects of two variables.

One-Way ANOVA

Tests whether there are any statistically significant differences between the means of three or more independent groups.

Use case of One-Way ANOVA

Use it when you want to compare the means of more than two groups (e.g., comparing test scores across three different teaching methods).

Key idea of One-Way ANOVA

Assumes normal distribution and equal variances.

Two-Sample t-test

Compares the means of two independent groups to see if they are different.

Use case of Two-Sample t-test

Use it when you want to compare two groups (e.g., comparing test scores between men and women).

Key idea of Two-Sample t-test

Assumes normal distribution and equal variances (though you can adjust for unequal variances with Welch's version).

Two-Sample Permutation Test

A non-parametric test that compares two groups by calculating the difference between them in all possible ways (permutations) and then checking if the observed difference is unusual.

Use case of Two-Sample Permutation Test

Use it when you don't want to assume a normal distribution or any specific distribution for your data.

Key idea of Two-Sample Permutation Test

More flexible than the t-test because it doesn't require normality assumptions.

Logistic Regression

Models the relationship between a binary dependent variable (e.g., yes/no, 0/1) and one or more independent variables (which can be continuous or categorical).

Use case of Logistic Regression

Use it when you have a binary outcome (e.g., predicting whether a customer will buy a product or not based on their age, income, etc.).

Key idea of Logistic Regression

Outputs probabilities, not direct predictions.

ANCOVA (Analysis of Covariance)

Combines ANOVA and regression. It compares means across groups while adjusting for other continuous variables (covariates).

Use case of ANCOVA

Use it when you want to compare groups (like in ANOVA) but also need to control for variables that could affect the outcome (like age or income).

Key idea of ANCOVA

Controls for additional variables to get a cleaner comparison of group means.

Best Subsets Regression

A method for selecting the best combination of independent variables (predictors) for a regression model.

Use case of Best Subsets Regression

When you have many potential predictors and you want to find the most important ones to use in your model.

Key idea of Best Subsets Regression

Looks at all possible combinations of predictors and chooses the best one based on a criteria (e.g., minimizing error).