Interpreting Conclusions

Learn confidence-level interpretation, type i errors and multiple testing.

Lesson 3 of 32 parts Practice Flashcards

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Confidence-Level Interpretation

Objective: Explain confidence-level interpretation, apply the stated method, and check its conditions.

A valid 95% confidence procedure covers a fixed true parameter in 95% of repeated samples in the long run. Once an interval is computed, frequentist coverage does not assign a 95% probability to the fixed parameter lying in that particular interval. Coverage depends on design and assumptions. Confidence refers to the repeated procedure, not a probability assigned to a fixed parameter.

Formulas

Long-run coverage = confidence level

Worked examples

Try itIn a simulation of 700 intervals from a valid 95% confidence procedure, what is the expected number covering a fixed true parameter?Show answer

Step 1: The confidence level describes the long-run procedure. Step 2: Use 0.95·700. Step 3: The expected count is 665; actual simulations vary.

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Confidence-Level Interpretation

Objective: Explain confidence-level interpretation, apply the stated method, and check its conditions.

Formulas

Long-run coverage = confidence level

Worked examples

Try itIn a simulation of 700 intervals from a valid 95% confidence procedure, what is the expected number covering a fixed true parameter?Show answer

Step 1: The confidence level describes the long-run procedure. Step 2: Use 0.95·700. Step 3: The expected count is 665; actual simulations vary.

Type I Errors and Multiple Testing

Objective: Explain type i errors and multiple testing, apply the stated method, and check its conditions.

A Type I error rejects a true null. Across many true-null tests, expected false rejections sum their individual Type I error probabilities. Multiple testing raises the chance of at least one false positive under common conditions, so study design and adjustments matter. A nominal single-test error rate does not control an entire collection automatically.

Formulas

E[false rejections]=Σαᵢ for true-null tests

Worked examples

Try itIf 700 true-null tests each have Type I error probability 0.05, find the expected number of false rejections.Show answer

Step 1: Expected counts add even without assuming independence. Step 2: Use 700·0.05. Step 3: The expected count is 35; repeated testing can create many false positives.

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