Probability and Statistics Chapter 7: Introduction to ...kvansteen/MATH0008-2... · Probability and Statistics Chapter 7: Introduction to Statistical Inference

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

Documents

Probability and Statistics Chapter 7: Introduction to ...kvansteen/MATH0008-2... · Probability and Statistics Chapter 7: Introduction to Statistical Inference