Thinking Statistically with Data

When we work with data we are more often than not working with a sample of data, and thus need to think statistically about our data. We do NOT need to always run statistical analyses on our data. Instead we can think about how the data are a sample, what limitations they have, and how that influences what inferences we can draw from the data. Below are some resources for thinking statistically and for running statistical analyses.

STATISTICAL THINKING RESOURCES:

• Teaching Statistics Through Data Investigations MOOC-Ed by The Friday Institute

• The Friday Institute’s Hub for Innovation and Research in Statistics Education. While focused on statistical education there are great insights that we can incorporate into non-statistics classrooms.

STATISTICAL ANALYSES RESOURCES:

• Recording of Kristin’s Mini-Review of Statistics - She discusses the following statistical concepts/analyses in further detail: 

  • Standard Deviation and Standard Error

  • Margin of Error and Confidence Intervals

  • Central Limit Theorem

  • p-value Exploration

  • T-Test

  • Line of Best Fit and Regression

  • Correlation Coefficient (r) and r-Squared Value

  • ANOVA

• Online calculators for statistical analyses: http://facultysites.vassar.edu/lowry/polls/calcs.html

• Discussions regarding limitations of p-values:

  • “The Extent and Consequences of P-Hacking in Science” by Megan L. Head, Luke Holman, Rob Lanfear, Andrew T. Kahn, and Michael D. Jennions

  • “Statistics: P values are just the tip of the iceberg” by Jeffrey T. Leek& Roger D. Peng

• “What’s the most important thing in statistics that’s not in the textbooks?” by Andrew Gelman

• Uncertainty resources:

  • Uncertainty, Error, and Confidence simulation / calculator

  • “References for Visualising Uncertainty” by Andy Kirk

  • “Error Bars Considered Harmful: Exploring Alternate Encodings for Mean and Error” by Michael Correll & Michael Gleicher

  • Alex Krusz’s tool for creating uncertainty visualizations (article explaining it)

• Simulations Galton probability boxes on YouTube

• Donahue, Rafe M.J. Fundamental Statistical Concepts in Presenting Data: Principles for Constructing Better Graphics. A free book available online if you want to dive deeply into statistical thinking and data visualization.