What are the types of hypothesis testing?

Hypothesis Testing

There are several main types of hypothesis testing, each suited to analyzing different kinds of data and research questions. Here’s a breakdown of some common types:

Parametric Tests:

These tests rely on the assumption that the data follows a specific probability distribution (like normal distribution).
- Z-test: Used to compare the mean of one sample to a known value or compare the means of two independent groups when the sample sizes are small, and the population standard deviations are known to be equal.
- T-test: Similar to a z-test but used when the population standard deviation is unknown, or the sample sizes are small (often used with estimates from the data itself). There are different variations of t-tests for different scenarios (e.g., one-tailed vs. two-tailed, paired vs. independent samples).
- ANOVA (Analysis of Variance): Compares the means of more than two groups and helps determine if there’s a significant difference between them.

Non-Parametric Tests:

These tests make fewer assumptions about the underlying data distribution and can be used with non-normal data or ordinal data (ranked data).
Examples:
- Chi-Square Test: Used to assess the relationship between two categorical variables or test if observed frequencies differ significantly from expected frequencies in a single categorical variable.
- Mann-Whitney U Test: Compares the medians of two independent groups and is a non-parametric alternative to the two-tailed t-test.
- Wilcoxon Signed-Rank Test: Compares the medians of two related samples (paired data) and is a non-parametric alternative to the paired t-test.

Choosing the Right Test:

The type of hypothesis test you choose depends on your specific research question and data characteristics:

Data Type: Consider if your data is continuous (e.g., height, weight) or categorical (e.g., hair color, job category).
Sample Size: Some tests, like z-tests, have specific assumptions about sample size.
Number of Groups: Are you comparing two groups, multiple groups, or a single sample to a known value?
Normality: Is your data normally distributed, or is it skewed or non-normal?

Statistical Tests

Test	Purpose	Data Type	Calculation (Basic)	Assumptions
Z-Test	Compares a single sample mean to a known population mean	Continuous, normally distributed		Population standard deviation (σ\sigmaσ) known, normality
T-Test (Independent Samples)	Compares the means of two independent groups	Continuous, normally distributed (or large samples)		Normality (or large samples), equal variances
T-Test (Paired Samples)	Compares the means of two related samples (paired data)	Continuous, normally distributed (or large samples)		Normality (or large samples)
ANOVA (One-Way)	Compares the means of more than two independent groups	Continuous, normally distributed (or large samples)	Uses Sum of Squares (SS) & Mean Squares (MS) to compare variance between groups and within groups	Normality (or large samples), equal variances, independence
Chi-Square Test (Goodness-of-Fit)	Tests if observed frequencies match expected frequencies in one or more categories	Categorical		Independence of observations, minimum expected frequency
Chi-Square Test (Independence)	Tests if two categorical variables are independent	Categorical		Independence of observations, minimum expected frequency
Mann-Whitney U Test	Compares the medians of two independent groups (non-parametric)	Ordinal or continuous	Uses ranking and calculation of U statistic	No assumptions about normality or equal variances
Wilcoxon Signed-Rank Test	Compares the medians of two paired samples (non-parametric)	Ordinal or continuous	Uses ranking of differences between paired samples and calculation of T statistic	No assumptions about normality

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