MTH 155 Section 1.4, 1.5 cvcc

Chapter 1: Introduction

Organizing Categorical Data

  • Tool for organizing categorical data: Two-way table (contingency table).

  • Summarizes frequencies of individuals in two categories.

  • Can be expanded to varying dimensions (e.g., 2x3, 3x4).

  • Example variables: Seatbelt Usage (Always, Not Always) and Gender (Male, Female).

    • Example table:

      • Categories:

        • Seat Belt: Always, Not Always

        • Gender: Male, Female

      • Frequencies:

        • Male Always: 2

        • Male Not Always: 3

        • Female Always: 3

        • Female Not Always: 7

Calculating Totals

  • Male total: 2 + 3 = 5

  • Female total: 3 + 7 = 10

  • Overall total: 5 males + 10 females = 15 subjects.

  • Percentage of males: 5/15 = 0.333 (33.3%).

  • Percentage of females: 10/15 = 0.666 (66.7%).

Chapter 2: Males Or Females

Risky Behavior Comparison

  • To determine who is more risky:

    • Calculate percentage of males (Not Always Seat Belt): 2/5 = 0.40 (40%).

    • Calculate percentage of females (Not Always Seat Belt): 3/10 = 0.30 (30%).

  • Conclusion: Males are more risky (40% vs 30%).

Working with Percentages and Frequencies

  • Example: 1500 people in an apartment complex; 30% over 50 years old:

    • Calculation: 0.30 * 1500 = 450 (over 50).

  • Calculating total from percentage:

    • If 20% of group has blue eyes = 52 people:

    • Using percent proportion: 20/100 = 52/x, solve for x, where x = 260.

Chapter 3: Anecdotal Study Data

Understanding Percent Proportion

  • Percent proportion formula:

    • Percent/100 = Part/Total

    • The part is not always less than total.

Causality and Anecdotal Studies

  • Causality can only be determined through controlled experiments.

  • Anecdotal studies rely on personal experiences, cannot determine causality due to uncontrolled factors.

  • Lack of a set standard for comparison hinders establishing causality.

Chapter 4: Outside School Hours

Observational Studies

  • Subjects are observed based on conditions; no treatment assignment.

  • Confounding factors can affect results; example involving hours worked outside of school and GPAs.

  • Conclusion: Association between variables exists, but causation cannot be determined.

Chapter 5: Say A Treatment

Controlled Experiments

  • Necessary for determining cause and effect:

    • Key Features:

      1. Random assignment of subjects to treatment/control groups.

      2. Adequate sample size to observe variability.

      3. Double-blind approach: neither subjects nor researchers know group assignments.

      4. Use of placebo to mitigate psychological effects (especially in human subjects).

  • In plant studies, placebo not needed; treatment can be directly applied to observe effects.

Chapter 6: Conclusion

  • Review of key concepts covered in sections 1.1 through 1.3.