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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 336 of 2,145·9. Hypothesis Testing FoundationsPro lesson

Visualizing Error Types with Sampling Distributions

Use overlapping null and alternative distributions to visualize the rejection region and both error types.

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