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Data Science

351When to Use a One-Sample t-Test
352The t-Distribution and Degrees of Freedom
353Calculating the t-Statistic
354Setting Up Hypotheses for One-Sample t-Test
355Finding Critical Values and P-Values
356Making Decisions and Stating Conclusions
357Confidence Intervals and t-Tests
358Worked Example: One-Sample t-Test in Practice
359Two-Sample t-Test Overview
360Independent vs. Dependent Samples
361Pooled Variance t-Test
362Welch's t-Test for Unequal Variances
363Testing Equality of Variances
364Degrees of Freedom in Two-Sample Tests
365Conducting Two-Sample t-Tests by Hand
366Two-Sample t-Tests in Python and R
367Interpreting Two-Sample Test Results
368Common Pitfalls and Best Practices
369When to Use a Paired t-Test
370Differences as the Unit of Analysis
371Calculating Paired Differences
372Paired t-Test Statistic and Degrees of Freedom
373Hypotheses for Paired t-Tests
374Assumptions of the Paired t-Test
375Paired t-Test vs Two-Sample t-Test
376The Assumption of Normality in t-Tests
377Testing Normality: Visual Methods
378Testing Normality: Statistical Tests
379The Assumption of Equal Variances (Homoscedasticity)
380Testing Equal Variances: Levene's and Bartlett's Tests
381Independence Assumption and Its Violations
382Robustness of t-Tests to Assumption Violations
383Diagnostic Workflow: When to Proceed or Switch Tests
384What is Effect Size?
385Cohen's d for Standardized Mean Differences
386Effect Size Interpretation Guidelines
387Confidence Intervals for Effect Sizes
388Effect Size in Sample Size Planning
389Reporting Effect Sizes in Practice
390When Parametric Tests Fail: Violations of Assumptions
391The Sign Test for Medians
392Wilcoxon Signed-Rank Test
393Mann-Whitney U Test (Wilcoxon Rank-Sum)
394Interpreting Rank-Based Tests: Medians vs Distributions
395Permutation Tests for Means and Beyond
396Bootstrap Hypothesis Testing
397Power and Efficiency of Non-Parametric Tests
398Choosing Between Parametric and Non-Parametric Tests

Data Science

351When to Use a One-Sample t-Test
352The t-Distribution and Degrees of Freedom
353Calculating the t-Statistic
354Setting Up Hypotheses for One-Sample t-Test
355Finding Critical Values and P-Values
356Making Decisions and Stating Conclusions
357Confidence Intervals and t-Tests
358Worked Example: One-Sample t-Test in Practice
359Two-Sample t-Test Overview
360Independent vs. Dependent Samples
361Pooled Variance t-Test
362Welch's t-Test for Unequal Variances
363Testing Equality of Variances
364Degrees of Freedom in Two-Sample Tests
365Conducting Two-Sample t-Tests by Hand
366Two-Sample t-Tests in Python and R
367Interpreting Two-Sample Test Results
368Common Pitfalls and Best Practices
369When to Use a Paired t-Test
370Differences as the Unit of Analysis
371Calculating Paired Differences
372Paired t-Test Statistic and Degrees of Freedom
373Hypotheses for Paired t-Tests
374Assumptions of the Paired t-Test
375Paired t-Test vs Two-Sample t-Test
376The Assumption of Normality in t-Tests
377Testing Normality: Visual Methods
378Testing Normality: Statistical Tests
379The Assumption of Equal Variances (Homoscedasticity)
380Testing Equal Variances: Levene's and Bartlett's Tests
381Independence Assumption and Its Violations
382Robustness of t-Tests to Assumption Violations
383Diagnostic Workflow: When to Proceed or Switch Tests
384What is Effect Size?
385Cohen's d for Standardized Mean Differences
386Effect Size Interpretation Guidelines
387Confidence Intervals for Effect Sizes
388Effect Size in Sample Size Planning
389Reporting Effect Sizes in Practice
390When Parametric Tests Fail: Violations of Assumptions
391The Sign Test for Medians
392Wilcoxon Signed-Rank Test
393Mann-Whitney U Test (Wilcoxon Rank-Sum)
394Interpreting Rank-Based Tests: Medians vs Distributions
395Permutation Tests for Means and Beyond
396Bootstrap Hypothesis Testing
397Power and Efficiency of Non-Parametric Tests
398Choosing Between Parametric and Non-Parametric Tests

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Lesson 372 of 2,145·10. Hypothesis Tests for MeansPro lesson

Paired t-Test Statistic and Degrees of Freedom

Calculate the t-statistic using the mean and standard error of differences with n-1 degrees of freedom.

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