Hypothesis Testing Methods

Hypothesis testing methods help us make decisions based on data by assessing differences and relationships. These techniques, like Z-tests and T-tests, guide us in understanding whether observed patterns are statistically significant or just due to chance.

1. Z-test

   • Used to determine if there is a significant difference between sample and population means when the population variance is known.
   • Assumes that the sample data is normally distributed or the sample size is large (n > 30).
   • Commonly applied in hypothesis testing for large samples.

2. T-test (one-sample, two-sample, paired)

   • One-sample T-test: Compares the sample mean to a known population mean.
   • Two-sample T-test: Compares means from two independent groups to see if they are significantly different.
   • Paired T-test: Compares means from the same group at different times (e.g., before and after treatment).

3. Chi-square test

   • Assesses the association between categorical variables by comparing observed frequencies to expected frequencies.
   • Commonly used in contingency tables to test independence.
   • Requires a minimum sample size and expected frequency in each category.

4. F-test

   • Used to compare two variances to determine if they are significantly different.
   • Often applied in the context of ANOVA to test the equality of means across multiple groups.
   • Assumes that the data is normally distributed and independent.

5. ANOVA (one-way, two-way)

   • One-way ANOVA: Tests for differences in means among three or more independent groups based on one factor.
   • Two-way ANOVA: Examines the effect of two factors on a dependent variable and their interaction.
   • Helps to identify if at least one group mean is different from the others.

6. Regression analysis (simple and multiple)

   • Simple regression: Analyzes the relationship between two variables (one independent and one dependent).
   • Multiple regression: Involves two or more independent variables predicting a dependent variable.
   • Used to understand relationships and make predictions based on data.

7. Likelihood ratio test

   • Compares the goodness of fit of two models: a null model and an alternative model.
   • Based on the ratio of the maximum likelihoods of the two models.
   • Commonly used in logistic regression and other complex models.

8. Wilcoxon rank-sum test

   • A non-parametric test that compares two independent samples to assess whether their population distributions differ.
   • Does not assume normality and is used when data is ordinal or not normally distributed.
   • Useful for small sample sizes or when data does not meet T-test assumptions.

9. Kolmogorov-Smirnov test

   • A non-parametric test that compares the cumulative distributions of two samples to determine if they come from the same distribution.
   • Can also be used to compare a sample distribution to a known distribution.
   • Sensitive to differences in both location and shape of the empirical cumulative distribution functions.

10. Bootstrap methods

    • A resampling technique used to estimate the distribution of a statistic by repeatedly sampling with replacement from the data.
    • Useful for estimating confidence intervals and standard errors when traditional assumptions are violated.
    • Provides a way to assess the stability of statistical estimates without relying on parametric assumptions.