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Categorical data is all around us. It's in the latest opinion polling numbers, in the data that lead to new breakthroughs in genomics, and in the troves of data that internet companies collect to sell products to you. In this course you'll learn techniques for parsing the signal from the noise; tools for identifying when structure in this data represents interesting phenomena and when it is just random noise.
Inference for a single parameterFree
In this chapter you will learn how to perform statistical inference on a single parameter that describes categorical data. This includes both resampling based methods and approximation based methods for a single proportion.The General Social Survey50 xpExploring consci100 xpGenerating via bootstrap100 xpConstructing a CI100 xpWhy more bootstraps?50 xpInterpreting a Confidence Interval50 xpCIs and confidence level50 xpSE with less data100 xpSE with different p100 xpThe approximation shortcut50 xpCI via approximation100 xpMethods compared50 xp
Proportions: testing and power
This chapter dives deeper into performing hypothesis tests and creating confidence intervals for a single parameter. Then, you'll learn how to perform inference on a difference between two proportions. Finally, this chapter wraps up with an exploration of what happens when you know the null hypothesis is true.Hypothesis test for a proportion50 xpLife after death100 xpGenerating from H0100 xpTesting a claim100 xpMaking a decision50 xpIntervals for differences50 xpDeath penalty and sex100 xpHypothesis test on the difference in proportions100 xpInterpreting the test50 xpHypothesis tests and confidence intervals100 xpStatistical errors50 xpWhen the null is true100 xpWhen the null is true: decision100 xp
Comparing many parameters: independence
This part of the course will teach you how to use both resampling methods and classical methods to test for the indepence of two categorical variables. This chapter covers how to perform a Chi-squared test.Contingency tables50 xpPolitics and Space100 xpUnderstanding contingency tables50 xpFrom tidy to table to tidy100 xpChi-squared test statistic50 xpA single permuted Chi-sq100 xpBuilding two null distributions100 xpIs the data consistent with the model?50 xpAlternate method: the chi-squared distribution50 xpChecking conditions50 xpThe geography of happiness100 xpA p-value two ways100 xpIntervals for the chi-squared distribution50 xp
Comparing many parameters: goodness of fit
The course wraps up with two case studies using election data. Here, you'll learn how to use a Chi-squared test to check goodness-of-fit. You'll study election results from Iran and Iowa and test if Benford's law applies to these datasets.Case study: election fraud50 xpGetting to know the Iran data50 xpWho won?100 xpBreaking it down by province100 xpExtracting the first digit I100 xpGoodness of fit50 xpGoodness of fit test100 xpA p-value, two ways100 xpIs this evidence of fraud?50 xpAnd now to US50 xpGetting to know the Iowa data50 xpExtracting the first digit II100 xpTesting Iowa100 xpFraud in Iowa?50 xpElection fraud in Iran and Iowa: debrief50 xp
In the following tracksStatistical Inference
PrerequisitesFoundations of Inference
Assistant Professor of Statistics at Reed College
Andrew Bray is an assistant professor of statistics at Reed College. His interests are in computing, differential privacy, environmental statistics, and statistics education. He is a co-author of the infer package for tidy statistical inference.