Inference for Numerical Data in R

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

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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!

  1. 1

    Bootstrapping for estimating a parameter

    Free

    In this chapter you'll use bootstrapping techniques to estimate a single parameter from a numerical distribution.

    Play Chapter Now
    Welcome to the course!
    50 xp
    Generate bootstrap distribution for median
    100 xp
    Review percentile and standard error methods
    50 xp
    Calculate bootstrap interval using both methods
    100 xp
    Which method more appropriate: percentile or SE?
    50 xp
    Doctor visits during pregnancy
    50 xp
    Average number of doctor's visits
    100 xp
    SD of number of doctor's visits
    100 xp
    Re-centering a bootstrap distribution
    50 xp
    Test for median price of 1 BR apartments in Manhattan
    100 xp
    Conclude the hypothesis test on median
    50 xp
    Test for average weight of babies
    100 xp
  2. 2

    Introducing the t-distribution

    In this chapter you'll use Central Limit Theorem based techniques to estimate a single parameter from a numerical distribution. You will do this using the t-distribution.

    Play Chapter Now
    t-distribution
    50 xp
    When to t?
    50 xp
    Probabilities under the t-distribution
    100 xp
    Cutoffs under the t-distribution
    100 xp
    Estimating a mean with a t-interval
    50 xp
    Average commute time of Americans
    100 xp
    Average number of hours worked
    100 xp
    t-interval for paired data
    50 xp
    t-interval at various levels
    100 xp
    Understanding confidence intervals
    50 xp
    Testing a mean with a t-test
    50 xp
    Estimate the median difference in textbook prices
    100 xp
    Test for a difference in median test scores
    100 xp
    Interpret the p-value
    50 xp
  3. 3

    Inference for difference in two parameters

    In this chapter you'll extend what you have learned so far to use both simulation and CLT based techniques for inference on the difference between two parameters from two independent numerical distributions.

    Play Chapter Now
    Hypothesis testing for comparing two means
    50 xp
    Evaluating the effectiveness of stem cell treatment
    100 xp
    Evaluating the effectiveness of stem cell treatment (cont.)
    100 xp
    Conclusion of the hypothesis test
    50 xp
    Evaluating the relationship between smoking during pregnancy and birth weight
    100 xp
    Bootstrap CI for difference in two means
    50 xp
    Quantifying the relationship between smoking during pregnancy and birth weight
    100 xp
    Median lengths of pregnancies for smoking and non-smoking mothers
    100 xp
    Comparing means with a t-test
    50 xp
    Hourly pay vs. citizenship status
    100 xp
    Estimating the difference of two means using a t-interval
    100 xp
  4. 4

    Comparing many means

    In this chapter you will use ANOVA (analysis of variance) to test for a difference in means across many groups.

    Play Chapter Now
    Vocabulary score vary between vs. (self identified) social class
    50 xp
    EDA for vocabulary score vs. social class
    100 xp
    Comparing many means, visually
    50 xp
    ANOVA
    50 xp
    ANOVA for vocabulary score vs. (self identified) social class
    100 xp
    Conditions for ANOVA
    50 xp
    Checking the normality condition
    50 xp
    Checking the constant variance condition
    100 xp
    Post-hoc testing
    50 xp
    Calculate alpha*
    50 xp
    Compare pairwise means
    100 xp
    Congratulations!
    50 xp

In the following tracks

Statistical InferenceStatistician

Datasets

Chp1-vid1-boot-dist-noaxes-paranthesesChp1-vid1-bootsamp-bootpop.001Chp1-vid1-manhattan-rentsChp1-vid2-boot-dist-withaxesChp1-vid2-perc-method.001Chp1-vid2-perc-method.002Chp1-vid3-boot-test.001Chp3-vid3-hrly-rate-citizen-smallerChp3-vid3-hrly-rate-citizenChp4-vid1-class-barChp4-vid1-wodrsum-histGss moredaysGSS dataManhattan rent dataRunners.001Tdistcomparetonormaldist

Collaborators

Nick CarchediNick Solomon

Prerequisites

Foundations of Inference
Mine Cetinkaya-Rundel Headshot

Mine Cetinkaya-Rundel

Associate Professor at Duke University & Data Scientist and Professional Educator at RStudio

Mine is the Director of Undergraduate Studies and an Associate Professor of the Practice in the Department of Statistical Science at Duke University as well as a Professional Educator at RStudio. Her work focuses on innovation in statistics pedagogy, with an emphasis on computation, reproducible research, open-source education, and student-centered learning. She is the author of three open-source introductory statistics textbooks as part of the OpenIntro project and teaches the popular Statistics with R MOOC on Coursera.
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