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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

TestPurposeData TypeCalculation (Basic)Assumptions
Z-TestCompares a single sample mean to a known population meanContinuous, normally distributedPopulation standard deviation (σ\sigmaσ) known, normality
T-Test (Independent Samples)Compares the means of two independent groupsContinuous, 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 groupsContinuous, normally distributed (or large samples)Uses Sum of Squares (SS) & Mean Squares (MS) to compare variance between groups and within groupsNormality (or large samples), equal variances, independence
Chi-Square Test (Goodness-of-Fit)Tests if observed frequencies match expected frequencies in one or more categoriesCategoricalIndependence of observations, minimum expected frequency
Chi-Square Test (Independence)Tests if two categorical variables are independentCategoricalIndependence of observations, minimum expected frequency
Mann-Whitney U TestCompares the medians of two independent groups (non-parametric)Ordinal or continuousUses ranking and calculation of U statisticNo assumptions about normality or equal variances
Wilcoxon Signed-Rank TestCompares the medians of two paired samples (non-parametric)Ordinal or continuousUses ranking of differences between paired samples and calculation of T statisticNo assumptions about normality

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