- statistics is the study of variation
- R.A. Fisher (father of design of experiments)
"Robert Martin was laid off from his job at Westvaco, Inc. soon after he turned 54 years old. He sued for age discrimination.”
How do we evaluate his claim?
- the ages of other people who were laid off, the ages of people who weren't
- variation in all data
Two Approaches
- what comes naturally: see the threat, find the cause
- we're good at generating causal ideas, but we're not good at considering randomness
- statistical approach:
- define a set of "cases" (e.g. all of employees and their ages)
Muller-Lyer Illusion - Which line is longer?
- the lines appear to be the same size
- analogous to the situation with statistics
- statistics gives us a way of evaluating a claim
- statistics is a tool to help us understand variation more clearly
Connections to Core Concepts
- DGP (data generative process) + data + sampling distributions > statistical model
- what is understanding? more connections
What It Takes to Understand
- for for deep learning, with understanding, students need recurring and sustained opportunities for:
- productive struggle - with important mathematics
- explicit connections - among concepts, procedures, problems, and situations
- deliberate practice - increasing variation and complexity over time
- understanding, like skill, takes deliberate practice
- complex concepts develop over weeks, month, and years
Practicing Connections: What connections to practice?
- core concepts (those that tie the whole domain together)
- distribution triad
- statistical model
- representations (that you can become skilled at using)
- R
- GLM notation
- data visualization
- the world
- the practice of data analysis
- contexts in which statistics can be applied