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Data Science

307Defining the Null Hypothesis (H₀)
308Defining the Alternative Hypothesis (H₁ or Hₐ)
309Complementary Nature of Hypotheses
310Writing Hypotheses for Different Parameters
311One-Sided vs Two-Sided Alternatives
312Hypothesis Testing as a Legal Analogy
313Common Pitfalls in Hypothesis Formulation
314What is a Test Statistic?
315Common Test Statistics: Z, t, Chi-Square, and F
316Calculating Test Statistics from Sample Data
317Sampling Distribution of the Test Statistic
318What is a P-Value?
319Calculating P-Values from Test Statistics
320Interpreting P-Values Correctly
321P-Values and the Strength of Evidence
322Exact vs Asymptotic P-Values
323What is a Significance Level (α)?
324Common Significance Levels: 0.05, 0.01, and 0.10
325The Rejection Region
326Critical Values
327Decision Rules: Reject or Fail to Reject
328The Relationship Between α and Confidence Level
329Choosing α Before Analysis
330Understanding Type I Error (False Positive)
331Understanding Type II Error (False Negative)
332The Trade-off Between Type I and Type II Errors
333Consequences of Type I and Type II Errors
334Setting Alpha: Choosing Your Significance Level
335Calculating Type II Error Probability (Beta)
336Visualizing Error Types with Sampling Distributions
337Error Rates in Practice: Multiple Testing
338What is Statistical Power?
339Factors Affecting Power
340Power and Sample Size Relationship
341Effect Size and Power
342Alpha Level Trade-offs
343Calculating Power for Common Tests
344Power Analysis in Study Design
345Directionality in Hypothesis Testing
346Two-Tailed Tests: Testing for Any Difference
347One-Tailed Tests: Testing for a Specific Direction
348P-Value Calculation Differences
349Power Advantages and Trade-offs
350Choosing the Right Tail Configuration

Data Science

307Defining the Null Hypothesis (H₀)
308Defining the Alternative Hypothesis (H₁ or Hₐ)
309Complementary Nature of Hypotheses
310Writing Hypotheses for Different Parameters
311One-Sided vs Two-Sided Alternatives
312Hypothesis Testing as a Legal Analogy
313Common Pitfalls in Hypothesis Formulation
314What is a Test Statistic?
315Common Test Statistics: Z, t, Chi-Square, and F
316Calculating Test Statistics from Sample Data
317Sampling Distribution of the Test Statistic
318What is a P-Value?
319Calculating P-Values from Test Statistics
320Interpreting P-Values Correctly
321P-Values and the Strength of Evidence
322Exact vs Asymptotic P-Values
323What is a Significance Level (α)?
324Common Significance Levels: 0.05, 0.01, and 0.10
325The Rejection Region
326Critical Values
327Decision Rules: Reject or Fail to Reject
328The Relationship Between α and Confidence Level
329Choosing α Before Analysis
330Understanding Type I Error (False Positive)
331Understanding Type II Error (False Negative)
332The Trade-off Between Type I and Type II Errors
333Consequences of Type I and Type II Errors
334Setting Alpha: Choosing Your Significance Level
335Calculating Type II Error Probability (Beta)
336Visualizing Error Types with Sampling Distributions
337Error Rates in Practice: Multiple Testing
338What is Statistical Power?
339Factors Affecting Power
340Power and Sample Size Relationship
341Effect Size and Power
342Alpha Level Trade-offs
343Calculating Power for Common Tests
344Power Analysis in Study Design
345Directionality in Hypothesis Testing
346Two-Tailed Tests: Testing for Any Difference
347One-Tailed Tests: Testing for a Specific Direction
348P-Value Calculation Differences
349Power Advantages and Trade-offs
350Choosing the Right Tail Configuration

← Data Science

Lesson 309 of 2,145·9. Hypothesis Testing FoundationsPro lesson

Complementary Nature of Hypotheses

Explore how null and alternative hypotheses are mutually exclusive and exhaustive, covering all possibilities.

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