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Statistics I

via Brilliant

Overview

We make many day-to-day decisions without seeing the big picture. Sometimes things turn out in our favor, sometimes not. Scientists, engineers, and other technically-minded people also make judgments using limited information. However, their fields have exacting standards, so a toolkit for making good conclusions from small data samples is invaluable to them.

This course covers the essential statistical methods that provide a mathematically sound basis for inferring general statements from limited data.
You'll gain hands-on experience designing experiments and framing questions for statistical analysis. You'll also expand your statistics toolkit to include a suite of powerful new hypothesis tests.

Syllabus

  • Intro to Stats: The essentials of statistical analysis in a nutshell.
    • Into the Mystic: Hypothesis Testing: Journey into the core ideas of statistics.
    • Blue Mars: Sampling & Estimation: Discover how statisticians make sound judgments with limited data.
    • Roll the Dice: The Central Limit Theorem: Learn about the most important statistical tool of all.
  • Data Sampling: Techniques for gathering quality statistical data, and tips for avoiding the pitfalls of bias.
    • Everyday Stats: Politics & Polls: Explore one of the most familiar uses of statistics.
    • Sampling Methods: Sample some basic methods for collecting good data.
    • The Sample Mean: What is a statistic, anyway?
    • Margin of Error I: Learn how to judge the results of a statistical analysis.
    • Margin of Error II: Estimate error without the population variance.
    • More on Bias: Become adept at spotting bias.
    • Sample Variance: Count degrees of freedom to resolve a common misconception.
  • The Z-test: The core ideas of hypothesis testing.
    • The Z-statistic: Measure the "extremeness" of your data.
    • The Z-test: Apply probability concepts to test a hypothesis.
    • Understanding p-values: Explore the essential piece of many popular hypothesis tests.
    • p-hacking: Discover how p-values can be misused.
    • Power: Learn to measure the quality of your experiment.
    • Practice: Power & Error: Put your skills to the test with a real-world scenario.
    • Confidence Intervals: Gain confidence in estimating a population's mean.
  • The Chi-Square test: A toolbox for testing statistical relationships.
    • The Chi-Square Statistic I: Venture into the world of hypothesis testing with chi-square statistics.
    • The Chi-Square Statistic II: Apply the chi-square statistic to a goodness of fit test.
    • Chi-Square Random Variables: Gain insight into chi-square statistics and their distributions.
    • Degrees of Freedom I: Deduce properties of dice from a distance.
    • Point Estimates: Learn to estimate population parameters with data.
    • Degrees of Freedom II: Find the right distribution by counting degrees of freedom.
    • Homogeneity Tests: Determine if two samples share the same distribution.
    • Independence Tests: Rule out relationships with chi-square.
  • The t-test: Statistical methods for comparing the means of two populations.
    • A Tale of Two Cities' Proportions: Use data to compare the means of two binomially distributed populations.
    • Intro to t-variables: Find out how to handle small samples and unknown variances.
    • Pooled Variance: Test for changes in population mean over time.
    • Unpooled Variance: Compare the means of two normally distributed populations.
  • Linear Regression & ANOVA: The basics of statistical model building and a real-world application.
    • Why ANOVA?: Take the first steps towards a test for comparing multiple means.
    • Linear Regression: The Simplest Model: Explore the concepts at the heart of linear regression.
    • Best Fit Lines: Learn how to find the best possible linear fit to your data.
    • The Linear Regression F-statistic: Construct the go-to statistic for linear regression tests.
    • Linear Regression ANOVA Tables: Summarize a linear regression analysis like a professional.
    • ANOVA and Mean Comparisons: Compare many means with the F-test.

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