3.1 Probabilistic Reasoning

Learning Goals

[Link to PlayPosit]

[Link to instructional video]

More details

After this lesson, students should

1. Recognize that every proposition comes with a degree of uncertainty.
2. Learn to value and defend scientific expressions of uncertainty.
3. Understand that because every proposition comes with a degree of uncertainty:
   1. Partial and probabilistic information still has value.
   2. Back-up plans are important since no information is absolutely certain.
   3. One’s attitude should be more directed towards accurately assigning confidence levels rather than being overinvested in being “right.”
   4. Scientific culture primarily uses a language of probabilities, not certain facts.
   5. Even correctly-done science will obtain incorrect results some of the time.

Definitions

• Credence

  Level of confidence that a claim is true, from 0 to 1.

• Confidence

  Essentially a synonym for credence, as in “level of confidence,” instead of colloquial meaning, “state of having a lot of confidence.”

• Accuracy

  How frequently one is correct; proximity to a true value.

• Calibration

  How closely confidence and accuracy correspond; that is, how accurate a person or system is at estimating the probability that they are correct.

Examples

• Weather forecasts.
• Using polls to predict elections.
• You might decide your credence level that your crush will say yes if you ask them to the dance, and use that to decide whether to ask or not.
• Credence levels predicting the probabilities of natural disasters within specific time frames (earthquakes, floods, wildfires etc.), and using these to make decisions about disaster preparation.
• Use credence levels about getting into various colleges to decide what to use as a safety school.
• Using credence levels about passing tests to decide whether to study more.
• Saul's story of a physicist who cancelled a lecture five minutes in because the presenter wasn't sure how his error bars were calculated.

Common Misconceptions

• My aunt still caught COVID even after taking the vaccine, therefore it’s not true that the vaccine prevents COVID.

  When phrased in terms of risks, the effectiveness of a vaccine is understood as the reduced probability that one would contract the disease after taking the vaccine, rather than total protection. Partial, probabilistic, improvements still have tangible causal consequences.

Context

[Explanation of how the current topic into the larger context of the course by explaining how the previous topic(s) relate to the current topic and leaving cliffhangers for future topics where relevant throughout the lesson]

Before

X.X Lesson Name

Explanation.

• Itemized explanation.

After

X.X Lesson Name

Explanation.

• Itemized explanation.

Recommended Outline

Before Class

• [Any essential logistical things that need to be done for this class]
• Prepare a seating chart.
• Review PlayPosit and discussion questions and ask faculty, Gabriel, or Emlen any questions you have.
• (Optional) Prepare a presentation.

During Class

• (5 min) Come up with some fun way to assign the roles of spokesperson and notetaker (e.g. earliest birthday in the year, lives furthest from campus). Remind them of the responsibilities of these roles.
• ([#] min) [Description of some module from #Lesson Content]
• (5 min) Collect questions for plenary.

After Class

• [Any essential logistical things that need to be done as followup for this class]
• Collect answers from notetakers for the forum / plenary.

Lesson Content

Clicker Question

Question

1. First option
2. Second option
3. Third option
4. Fourth option

Activity 1: Name

[Brief description of and motivation for the activity]

Discussion Questions

1. Question 1
   1. Subquestion a

   2. Subquestion b

Collect Questions for Plenary

(5 min) Collect remaining questions from the students for faculty in plenary (can be questions for clarification, extension, discussion, etc.), and add [ here].