Lecture 28: Outtro

Lecture 28: Outtro#

STATS 60 / STATS 160 / PSYCH 10

Concepts and Learning Goals:

  • Overview of what you learned this quarter!

  • tl;dr: three themes

  • What’s next if you’re stats-curious?

Remembering our journey#

Unit 1: Thinking about scale#

In statistics and data science, we are trying to use numbers to

  1. Describe our observations

  2. Quantify how confident we are

Numbers are only meaningful in context.

  • Is $ 10 billion a lot of money?

    Forbes' real-time billionaires' list

GDP heat map, in billions

Unit 1 was about building tools for contextualizing numbers and thinking critically about scale:

  • Three questions for contextualizing numbers:

    1. What type of number is this?

    2. What can I compare this number to? Is it large or small compared to other similar values?

    3. What would I have expected this number to be?

  • Ballpark estimates for estimating a number

    1. Set up a simple model to compute the quantity approximately by break up the estimate into small parts

      • How many visitors go on guided tours at Stanford per year?

        (# visitors / year) = (# days/ year) x (# tours/ day) x (# visitors / tour)

    2. Approximate parts up to a factor of 10

  • Cost-benefit analysis: a simple model helps us make difficult decisions

Unit 2: Probability#

A mathematical framework for modeling uncertain scenarios.

Is an observed pattern meaningful, or just random noise?

The probability we learned was essential for:

  • Hypothesis testing

  • Confidence intervals for estimation

  • Understanding selection bias

Topics covered:

  1. Probabilistic experiments

    • Formalism: sample spaces, outcomes, events, probabilities

At least one heads.

- Modeling almost everything with coinflips, dice, and bags of marbles

    <div style="display: flex; justify-content: center; flex-direction: column; align-items: center;">

Drawing a marble from the bag.