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Statistics I

Make the best decisions with limited information.

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.

Interactive
quizzes

35

Concepts and
exercises

380+
  1. 1

    Intro to Stats

    The essentials of statistical analysis in a nutshell.

    1. Into the Mystic: Hypothesis Testing

      Journey into the core ideas of statistics.

    2. Blue Mars: Sampling & Estimation

      Discover how statisticians make sound judgments with limited data.

    3. Roll the Dice: The Central Limit Theorem

      Learn about the most important statistical tool of all.

  2. 2

    Data Sampling

    Techniques for gathering quality statistical data, and tips for avoiding the pitfalls of bias.

    1. Included with
      Brilliant Premium

      Everyday Stats: Politics & Polls

      Explore one of the most familiar uses of statistics.

    2. Included with
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      Sampling Methods

      Sample some basic methods for collecting good data.

    3. Included with
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      The Sample Mean

      What is a statistic, anyway?

    4. Included with
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      Margin of Error I

      Learn how to judge the results of a statistical analysis.

  3. 3

    The Z-test

    The core ideas of hypothesis testing.

    1. Included with
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      The Z-statistic

      Measure the "extremeness" of your data.

    2. Included with
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      The Z-test

      Apply probability concepts to test a hypothesis.

    3. Included with
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      Understanding p-values

      Explore the essential piece of many popular hypothesis tests.

    4. Included with
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      p-hacking

      Discover how p-values can be misused.

  4. 4

    The Chi-Square test

    A toolbox for testing statistical relationships.

    1. Included with
      Brilliant Premium

      The Chi-Square Statistic I

      Venture into the world of hypothesis testing with chi-square statistics.

    2. Included with
      Brilliant Premium

      The Chi-Square Statistic II

      Apply the chi-square statistic to a goodness of fit test.

    3. Included with
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      Chi-Square Random Variables

      Gain insight into chi-square statistics and their distributions.

    4. Included with
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      Degrees of Freedom I

      Deduce properties of dice from a distance.

  5. 5

    The t-test

    Statistical methods for comparing the means of two populations.

    1. Included with
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      A Tale of Two Cities' Proportions

      Use data to compare the means of two binomially distributed populations.

    2. Included with
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      Intro to t-variables

      Find out how to handle small samples and unknown variances.

    3. Included with
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      Pooled Variance

      Test for changes in population mean over time.

    4. Included with
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      Unpooled Variance

      Compare the means of two normally distributed populations.

  6. 6

    Linear Regression & ANOVA

    The basics of statistical model building and a real-world application.

    1. Included with
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      Why ANOVA?

      Take the first steps towards a test for comparing multiple means.

    2. Included with
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      Linear Regression: The Simplest Model

      Explore the concepts at the heart of linear regression.

    3. Included with
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      Best Fit Lines

      Learn how to find the best possible linear fit to your data.

    4. Included with
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      The Linear Regression F-statistic

      Construct the go-to statistic for linear regression tests.