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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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