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Probability and Statistics Chapter 7: Introduction to Statistical Inference
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Probability and Statistics Chapter 7: Introduction to Statistical Inference
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Probability and Statistics Chapter 7: Introduction to Statistical Inference
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What can we do with hypothesis testing?
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4.3 Assumptions about hypothesis tests
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Assumptions about the population
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Assumptions about the population
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Assumptions about residuals (see also Chapter 8)
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Assumptions about the nature of the sample
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Assumptions about variables, measurements and models
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4.4Examples
Coca-cola example
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More coca-cola
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Ethnic example
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Politics example
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Decision making
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4.5 Use and abuse of tests
Causes about significance tests
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Practical significance
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Don’t ignore lack of significance
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Interpreting effect size: it is all about context
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The power of a test
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Factors affecting power: size of the effect
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Relation between power, effect size, sample size and significance level
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Don’t panic: There exist alternatives when I cannot get more samples
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Type I and Type II errors
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4.6 Multiple testing
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5 Inference for distributions
5.1 Inference for the mean of a population
Introduction
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When σ is unknown
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Standard deviation s – standard error
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The t-distribution
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Standardizing data before using Table D
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The one-sample t-confidence interval
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The one-sample t-test
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Matched pairs t-procedures
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Robustness
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Power of the t-test
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Inference for non-normal distributions
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Transforming data
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Non-parametric method: the sign test
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5.2 Comparing two means
Comparing two samples
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Two-sample z-statistic
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Two independent samples t-distribution
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Two-sample t-significance test
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Two-sample t-confidence interval
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Common mistake
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Robustness
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Details of the two sample t procedures
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Pooled two-sample procedures
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Which type of test? One sample, two samples, paired samples?
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5.3 Optional topics in comparing distributions
Inference for population spread
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Power of two-sample t-test
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Power calculations using a non-central t-distribution
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6 Inference for proportions
6.1 inference for a single proportion
Sampling distribution of a sample proportion
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Conditions for inference on p
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Large-sample confidence interval for p
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“Plus four” confidence interval for p
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Significance test for p
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Interpretation: magnitude versus reliability of effects
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Sample size for a desired margin of error
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6.2 Comparing two proportions
Comparing two independent samples
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Large-sample confidence interval for two proportions
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“Plus four” confidence interval for two proportions
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Test of significance
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Relative risk
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7 Analysis of two-way tables
7.1 Inference for two-way tables
Hypothesis: no association
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Expected cell count
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The chi-square test
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When is it safe to use a chi-square test?
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Chi-square test versus z-test for two proportions
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7.2 Formulas and models for two-way tables and Goodness-of-fit
Computations for two-way tables
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Computing conditional distribution
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Computing expected counts
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Computing the chi-square statistic
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Finding the p-value with Table F
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Interpreting the chi-square output
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Models for two-way tables
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Comparing several populations
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Testing for independence
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Testing for Goodness-of-fit
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The chi-square goodness-of-fit test
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Cautionary note about software
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8 How to select the appropriate test?
(http://www.graphpad.com/www/book/choose.htm)
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References:
• Mood
• Freeman IPS slides 4