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 Survey

Exploring consci

Generating via bootstrap

Constructing a CI

Why more bootstraps?

Interpreting a Confidence Interval

CIs and confidence level

SE with less data

SE with different p

The approximation shortcut

CI via approximation

Methods compared

Inference for a single parameter

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 proportion

Life after death

Generating from H0

Testing a claim

Making a decision

Intervals for differences

Death penalty and sex

Hypothesis test on the difference in proportions

Interpreting the test

Hypothesis tests and confidence intervals

Statistical errors

When the null is true

When the null is true: decision

Proportions: testing and power

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 tables

Politics and Space

Understanding contingency tables

From tidy to table to tidy

Chi-squared test statistic

A single permuted Chi-sq

Building two null distributions

Is the data consistent with the model?

Alternate method: the chi-squared distribution

Checking conditions

The geography of happiness

A p-value two ways

Intervals for the chi-squared distribution

Comparing many parameters: independence

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 fraud

Getting to know the Iran data

Who won?

Breaking it down by province

Extracting the first digit I

Goodness of fit

Goodness of fit test

A p-value, two ways

Is this evidence of fraud?

And now to US

Getting to know the Iowa data

Extracting the first digit II

Testing Iowa

Fraud in Iowa?

Election fraud in Iran and Iowa: debrief

Comparing many parameters: goodness of fit

GSS data

Iowa election data

Iran election data

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.

Foundations of Inference in R

In this course you'll learn how to leverage statistical techniques for working with categorical data.

Inference for Categorical Data in R

Inférence statistique en R

Assistant Professor of Statistics at Reed College

Approximation distributions: normal

Approximation distributions: chi-squared

H-test via approximation

The chi-squared distribution

Let's practice!

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Comparing many parameters: independence - Alternate method: the chi-squared distribution

Alternate method: the chi-squared distribution

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