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Inference for Numerical Data in R

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Updated 05/2025

In this course you'll learn techniques for performing statistical inference on numerical data.

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RProbability & Statistics4 hours15 videos49 Exercises3,650 XP13,279Statement of Accomplishment

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Course Description

In this course, you'll learn how to use statistical techniques to make inferences and estimations using numerical data. This course uses two approaches to these common tasks. The first makes use of bootstrapping and permutation to create resample based tests and confidence intervals. The second uses theoretical results and the t-distribution to achieve the same result. You'll learn how (and when) to perform a t-test, create a confidence interval, and do an ANOVA!

Prerequisites

Foundations of Inference in R

1

Bootstrapping for estimating a parameter

Welcome to the course!

Generate bootstrap distribution for median

Review percentile and standard error methods

Calculate bootstrap interval using both methods

Which method more appropriate: percentile or SE?

Doctor visits during pregnancy

Average number of doctor's visits

SD of number of doctor's visits

Re-centering a bootstrap distribution

Test for median price of 1 BR apartments in Manhattan

Conclude the hypothesis test on median

Test for average weight of babies

2

Introducing the t-distribution

t-distribution

Probabilities under the t-distribution

Cutoffs under the t-distribution

Estimating a mean with a t-interval

Average commute time of Americans

Average number of hours worked

t-interval for paired data

t-interval at various levels

Understanding confidence intervals

Testing a mean with a t-test

Estimate the median difference in textbook prices

Test for a difference in median test scores

Interpret the p-value

3

Inference for difference in two parameters

Hypothesis testing for comparing two means

Evaluating the effectiveness of stem cell treatment

Evaluating the effectiveness of stem cell treatment (cont.)

Conclusion of the hypothesis test

Evaluating the relationship between smoking during pregnancy and birth weight

Bootstrap CI for difference in two means

Quantifying the relationship between smoking during pregnancy and birth weight

Median lengths of pregnancies for smoking and non-smoking mothers

Comparing means with a t-test

Hourly pay vs. citizenship status

Estimating the difference of two means using a t-interval

4

Comparing many means

Vocabulary score vary between vs. (self identified) social class

EDA for vocabulary score vs. social class

Comparing many means, visually

ANOVA for vocabulary score vs. (self identified) social class

Conditions for ANOVA

Checking the normality condition

Checking the constant variance condition

Post-hoc testing

Calculate alpha*

Compare pairwise means

Congratulations!

Inference for Numerical Data in R

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