week2

This week covers:

• More wrangling and plotting in R
• Statistical inference
• Regression
• Overfitting / generalization

Day 1

Combining and reshaping data

• Review combine_and_reshape_in_r.ipynb on joins with dplyr and reshaping with tidyr

Plotting exercises

• Finish up the Citibike plotting exercises in plot_trips.R, including the plots that involve reshaping data

Combining and reshaping exercises

• Read chapters 5 and 19 of the 2nd edition of R for Data Science on reshaping and joins
• Do the following exercises from the 1st edition of R for Data Science in combining-reshaping.R:
  • Section 12.2.1, exercise 2
  • Section 12.3.3 exercises 1 and 3

Rmarkdown

• Read Chapter 27 of the 1st edition of R for Data Science on Rmarkdown
• Do the following exercises from the 1st edition of R for Data Science in diamond-sizes.Rmd:
  • First, install pandoc here (choose the windows file ending in .msi)
  • Section 27.2.1, exercises 1 and 2 (try keyboard shortcuts: ctrl-shift-enter to run chunks, and ctrl-shift-k to knit the document)
    • Note: If you're getting an error that you don't have pandoc installed, try closing/re-opening your VS code!
  • Section 27.3.1 exercise 3
  • Section 27.4.7, exercise 1

Learn more

• Do part 1 of Datacamp's Cleaning Data in R tutorial
• Additional references:
  • The tidyr vignette on tidy data
  • The dplyr vignette on two-table verbs for joins
  • A visual guide to joins

Day 2

Sampling distributions and standard errors

• See the Statistical Inference slides (rendered here)
• Review the "Estimating a proportion" section of the statistical inference Rmarkdown file (preview the output here)
• Read Chapter 4 of an Introduction to Statistical Thinking (With R, Without Calculus) (IST), pdf and html versions available online. Do questions 4.1 and 4.2 in sampling-distributions.R. Feel free to execute code in the book along the way.
• Read Chapter 6 of IST on the normal distribution and do question 6.1 in sampling-distributions.R
• Time permitting, read Chapter 7 of IST on sampling distributions and do exercise 7.1 in sampling-distributions.R

References

• Chapter 1 of the online textbook Intro to Stat with Randomization and Simulation (ISRS)
• Interactive demos:
  • From the Seeing theory site:
    • Random variables
    • Basic probability
    • Central limit theorem
    • Confidence intervals
  • An interactive tutorial on sampling variability in polling
  • Student t-distribution
• Some notes on expected values and variance, with proofs of their properties
  • Expected value, click through on "linearity of expectation" for proof
  • Variance

Day 3

Hypothesis testing

• Review the "Hypothesis testing" section of the statistical inference Rmarkdown file (preview the output here)
• Read Chapter 9 of IST and do exercise 9.1, use hypothesis-testing.R for your work
• Read Chapter 10 of IST and do exercises 10.1 and 10.2, use hypothesis-testing.R for your work
• Also check out the this analysis of the color distribution of M&Ms
• Read Chapter 2 of the online textbook Intro to Stat with Randomization and Simulation (ISRS) and do exercises 2.2 and 2.6
• Read Sections 3.1 and 3.2 of ISRS
• Do exercise 9.2 in IST, use hypothesis-testing.R for your work

References

• See the relevant part of these lecture notes on statistics by simulation
• Statistics for Hackers by VanderPlas (slides, video)
• See section 4 of Mindless Statistics and this article for some warnings on misinterpretations of p-values

Day 4

• Continue working on exercises from yesterday
• Read Chapters 12 and 13 of IST and do exercises 12.1 and 13.1

Power, effect sizes, and the replication crisis

• See this post and the related lecture notes on effect sizes and the replication crisis
• See coin_test.R for a simulated hypothesis test, false positive rate, and power
• See this notebook on statistical vs. practical significance
• There's also an interactive version, play with it and see if you understand what's going on!

References

• Understanding Statistical Power and Significance Testing
• Calculating the power of a test
• The American Statistical Association's statement on p-values by Wasserstein & Lazar
• Inference by eye by Cumming and Finch
• Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations by Greenland et al.
• The Insignificance of Significance Testing by Johnson
• The Insignificance of Null Hypothesis Significance Testing by Gill
• Why Most Published Research Findings Are False
• Felix Schönbrodt's blog post and shiny app on misconceptions about p-values and false discoveries
• Interpreting Cohen's d effect size
• The New Statistics: Why and How by Cummings
• A guide on effect sizes and related blog post

Day 5

Regression

• Review the slides we covered in class
• See this shiny app on model fitting and this tool for visualing least squares (Dan's version here is similar, but requires Flash)
• Read Chapter 5 of Intro to Stats with Randomization and Simulation, do exercises 5.20 and 5.29 in regression.R
• Read Section 3.1 of Intro to Statistical Learning (R version), do Lab 3.6.2 in regression.Rmd (You won't need to write any code, but walk through the file!)
• See the notebook on linear models with the modelr from the tidyverse

References

• Detailed notes on derivations for ordinary least squares regression with multiple predictors
• Chapter 14 of Introduction to Statistical Thinking
• Formula syntax in R
• The "Model Basics" and "Model Building" Chapters in R for Data Science (Chapters 18 and 19 in the print edition, Chapters 23 and 24 online)
• The modelr and tidymodels packages in R
• An animation of gradient descent and a related blog post