Final Class Statistics Fallacies and Exam Review 2

Lies, Damned Lies, and Statistics

Statistics

  • Statistics persuade through authority of science.

  • Numbers are perceived as precise and unbiased.

Mean, Median & Mode

  • Mean: Add all values and divide by the number of values.

  • Median: Arrange values from highest to lowest and select the middle value.

  • Mode: Identify the most frequently occurring value.

Playing with the Numbers

  • Example with houses:

    • Values: $100K, $125K, $140K, $150K, $160K, $160K, $400K

    • Mean: $176,428.57

    • Median: $150,000

    • Mode: $160,000

Annual Income Example

  • Town A: 99 people earn $80K, 1 earns $5M

    • Mean: $129,020

    • Mode: $80,000

  • Town B: 51 earn $100K, 50 earn $140K

    • Mean: $119,800

    • Mode: $100,000

Other Examples

  • Average person has 1 testicle due to population ratio.

  • Death Valley Avg Temp: 25°C (range from 0°C to 57°C).

  • Wealth in a room averages $350M, but includes low-income individuals.

Faulty Polling & Misuse of Statistics

  • Beware of flawed correlations and misleading visualizations.

  • Common types of data misuse include selective bias and small sample sizes.

Unknowable Statistics

  • Resulting from reluctance to report socially unacceptable behaviors; estimates may be needed.

  • Critical analysis advised for data sources and estimations.

Flawed Correlations

  • Distinguish true correlation from coincidental relationships (e.g., bear attacks and car accidents).

Fallacies

  • Post Hoc Fallacy: Correlation does not imply causation.

    • Example: A's occurrence doesn’t always cause B's result.

Deception by Omission

  • Omission can skew perception.

  • Statistics may mislead if context is ignored (e.g., percentage increases without context).

Questions to Ask When Considering Statistical Data

  • How were statistics obtained? Is the data representative? Are statistics relevant? What information is missing?

Fallacies in Generalization

  • Hasty Generalization: Drawing conclusions from non-representative facts.

    • Example: Generalizing from a small sample or singular event to a broad conclusion.

Statistical Trends & Changes

  • Present diverse representations of the same data can distort understanding.

  • Understanding context and methodology behind data visualization is key.

Common Arguments Fallacies

  • Confusion of Cause & Effect: Distinguishing influence vs. result in causal relationships.

  • Neglecting Common Causes: Understanding external influences affecting behaviors.

Statistical Fallacies

  • Ad Hominem: Attacking the individual not the argument.

  • Straw Person Argument: Misrepresenting opponent’s view to attack it easily.

Exam Info and Preparation

  • Exam Date: December 14, 6 PM, University Centre.

  • Arrive at least 15 mins early.

Exam Requirements

  • Bring photo ID, no personal items on tables.

  • Latecomers cannot start if more than 15 mins late; contact instructor if missed.

Writing the Exam

  • Focus on instructions, sections weighted 60 marks (Sections I & II) and 40 marks (Section III).

  • Manage time wisely; plan time allocation per section.

Strategies for Learning Material

  • Organize, elaborate, and connect concepts.

  • Visualize new information to enhance retention.

Section Topics for Exam Review

  • Include topics on critical thinking, logical reasoning, and fallacies.

  • Apply concepts from lectures on memory and writing skills.