Overview of Hypothesis Testing

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Paired Tests: Difference Two Continuous Outcomes • Exact same idea • Known variance: Z test statistic • Unknown variance: t test statistic • H 0 : μ d =0vs vs. H A : μ d ≠ 0 • Paired Z-test or Paired t-test Z d d = or T = σ / n s / n
2 Samples: Same Variance + Sample Size Calculation Basis • Unpaired - Same idea as paired • Known variance: Z test statistic • Unknown variance: t test t statistic ti ti • H 0 : μ 1 = μ 2 vs. H A : μ 1 ≠μ 2 • H 0 : μ 1 - μ 2 = 0 vs. H A : μ 1 - μ 2 ≠ 0 • Assume common variance Z x − y x − y = or T = σ 1/ n + 1/ m s 1/ n + 1/ m
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Principles of Hypothesis Testing fo
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Objectives • Formulate questions
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Estimation and Hypotheses ‣Infere
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You Use Hypothesis Testing • Desi
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Analysis Follows Design Questions
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Estimation and Hypotheses Inference
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Pictures, Not Numbers • Scatter p
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Like the Washington Post Weather, T
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Distributions • Parametric tests
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Binary Distribution • Binomial di
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Estimation and Hypotheses Inference
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Null Hypothesis • For superiority
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Example Hypotheses • H 0 : μ 1 =
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Use a 2-Sided Test • Almost alway
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Outline Estimation and Hypotheses
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Information at Hand • 1 or 2 samp
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One Sample: Cholesterol l Sample Da
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Situation • May be you are readin
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Cholesterol Sample Data • Populat
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Test Statistic • Basic test stati
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Unknown Truth and the Data Data Tru
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Type II Error (or, 1- Power) • β
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Cholesterol Sample Data • N = 25
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Experiment Develop hypotheses Colle
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Z or Standard Normal Distributionib
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How to test? ‣Rejection interval
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Cholesterol Rejection Interval Usin
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Side Note on t vs. Z • If s = σ
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Z-test: Do Not Reject H 0 Z X −
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Determining Statistical Significanc
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Cholesterol: t-statistic X − μ 2
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How to test? Rejection interval j
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Cholesterol Example • P-value for
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P-value Interpretation Reminders
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Outline Estimation and Hypotheses H
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Cholesterol Confidence Interval Usi
Page 73 and 74: Cholesterol Confidence Interval Usi
Page 75 and 76: Hypothesis Testing and dConfidence
Page 77 and 78: Interpret a 95% Confidence Interval
Page 79 and 80: Take Home: Hypothesis Testing • M
Page 81 and 82: Take Home: CI • Meaning/interpret
Page 83 and 84: Outline Estimation and Hypotheses H
Page 85 and 86: Linear regression • Model for sim
Page 87 and 88: More Than One Covariate • Y i =
Page 89 and 90: Repeated Measures (3 or more time p
Page 91 and 92: Do Not Use Correlation. Use Regress
Page 93 and 94: Outline Estimation and Hypotheses H
Page 95 and 96: Omics • False negative (Type II e
Page 97 and 98: What do you need to think about?
Page 99 and 100: Little Diagnostic Testing Lingo •
Page 101 and 102: Example: Western vs. ELISA • 1 mi
Page 103 and 104: 1% Prevalence • 10980 total test
Page 105 and 106: 10% Prevalence • 99% PPV • 99.9
Page 107 and 108: Prevalence Matters • PPV and NPV
Page 109 and 110: What do you need to think about?
Page 111 and 112: Avoid Common Mistakes: Hypothesis T
Page 113 and 114: Avoid Common Mistakes: Hypothesis T
Page 115 and 116: Comparing A to B • Appropriate
Page 117 and 118: 3 Studies. 3 Answers, Maybe • Stu
Page 119 and 120: Misconceptions • A small p-value
Page 121 and 122: Questions?
Page 123: Do Not Reject H 0 σ 46 220=X > μ
Page 127 and 128: One Sample Binary Outcomes • Exac
Page 129 and 130: Normal/Large Sample Data? No Binomi
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Overview of Hypothesis Testing

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