Statistics: Collecting Data

Chapter 3 – Statistics: Collecting Data

Introduction to Collecting Data

  • Importance of Taking Control of Your Life

    • Ability to evaluate daily data and claims is essential

    • Distinguishing good from faulty reasoning is crucial to avoid manipulation

    • Statistics provide tools necessary for intelligent reactions to information

    • Statistics is considered one of the most important subjects to study

Claims and Examples

  • Various claims that illustrate the relevance of statistics:

    1. 4 out of 5 dentists recommend Dentyne

    2. Tobacco-related lung cancers: 85% in men; 45% in women

    3. Condom effectiveness: 94% effectiveness rate

    4. Street crossing accidents among Native Americans: significantly more likely to be hit

    5. Persuasiveness: Increased when speakers maintain direct eye contact and speak loudly and quickly

    6. Gender wage gap: Women earn 75 cents for every dollar earned by men for the same job

    7. Egg whites and lifespan: A surprising study suggesting a positive correlation

    8. Baseball batting average: Low probability of another player exceeding .400 average

    9. Birthday paradox: 80% chance that in a room of 30, at least two people share the same birthday

    10. COVID-19 Vaccine: Pfizer-BioNTech vaccine was 95% effective based on clinical trials

    11. Joke statistic: 79.48% of all statistics are made up on the spot

Statistical Claims Across Various Domains

  • Claims represent diverse subjects—psychology, health, law, sports, business, etc.

  • Statistics are often used to add credibility to arguments or advice

  • Be cautious: many presented statistics are not from careful analysis and can be misleading

The Importance of Learning Statistics

  • Learning about statistics is essential for informed decision-making and autonomy

  • While statistics help guard against manipulation, they also aid in recognizing valid claims

  • Understanding statistics involves questioning the sources, numbers, and procedures behind claims

Examples Highlighting Statistical Misinterpretation

  1. Advertisement Effectiveness Case:

    • A claim states a 30% increase in ice cream sales due to a new advertisement

    • Flaw: Ice cream sales generally rise in warmer months (historical effect)

    • Misinterpretation of causal relationships due to a third variable (time of year)

  2. Churches and Crime Rates:

    • Claim: More churches lead to more crime

    • Flaw: Both are correlated to city population growth

    • Misleading causal inference due to the third-variable problem (population)

  3. Interracial Marriages Statistics:

    • Claim: 75% increase in interracial marriages indicates societal acceptance

    • Flaw: Lacks historical context; the sheer percentage does not indicate the overall rate

    • Insufficient data to support robust conclusions about societal trends

The Value of Critical Thinking

  • Important to begin questioning the statistics encountered daily

  • Quotation from Benjamin Disraeli: “There are three kinds of lies — lies, damned lies, and statistics.”

  • This reflects the necessity of understanding and applying statistical concepts well

Recognizing Proper Use of Statistics

  • Learning to identify valid statistical evidence supporting claims

  • Examples of constructive use of statistics:

    • Research teams demonstrate drug efficacy based on trials

    • Statistics reveal racial bias in jury selections in historical contexts

    • Statistics are prevalent, but their application can vary in integrity

Learning Objectives

3.1 Basic Concepts

  • Identify the population of a study

  • Distinguish between statistics (calculated from a sample) and parameters (calculated from a population)

  • Classify data types as either categorical (qualitative) or quantitative

3.2 Sampling Methods

  • Recognize various sampling techniques

  • Select appropriate sampling methods

  • Identify common sources of bias in sampling

3.3 Experiments

  • Identify characteristics of well-structured experiments

  • Distinguish different methods of experimentation

  • Identify experiments that effectively control for placebo effects

Attributions

  • Content adapted from:

    • David Lippman, “Math In Society, 2nd Edition.” Licensed under CC BY-SA 4.0.

    • Robert Foth, Math Faculty, Pima Community College, 2021.

Links to Previous and Next Sections

  • Previous Section: 2.5 Expected Value

  • Next Section: 3.1 Basic Concepts