Understanding Descriptive Statistics Basics

Sep 11, 2024

Lecture 4: Descriptive Statistics

Introduction

  • Instructor: Dr. Alvarez
  • Course: Sociology 303 - Social Statistics
  • Topic: Descriptive Statistics
  • Purpose: To describe variables in a sample using descriptive statistics.

Key Concepts

  • Descriptive Statistics: Used for describing variables in a sample.
  • Variables: Characteristics measured in a study (e.g., age, race, political party).
  • Tools for Descriptive Statistics:
    • Frequency Tables
    • Measures of Central Tendency
    • Measures of Dispersion

Goals of Lecture

  1. Understand the use of descriptive statistics.
  2. Demonstrate frequency tables.
  3. Explore measures of central tendency.
  4. Explore measures of dispersion.

Tools for Descriptive Statistics

1. Frequency Tables

  • Purpose: Used for nominal and ordinal variables (categorical variables).
  • Description: Shows how respondents answered questions by listing categories and frequencies.
  • Interpretation: Describe what is in the table and interpret what it means.
  • Example Structure:
    • Response Categories
    • Frequency
    • Valid Percent
    • Cumulative Percent

2. Measures of Central Tendency

  • Types:
    • Mode: Most frequently occurring response.
    • Median: Middle value in a distribution.
    • Mean: Average value of a distribution.
  • Use Cases:
    • Mode and median can be used for ordinal variables.
    • Mean is used for interval/ratio variables.

3. Measures of Dispersion

  • Importance: Shows how spread out the data points are.
  • Main Measure: Standard Deviation
  • Variance: Average of squared deviations from the mean.
  • Standard Deviation: Square root of the variance, preferred because it is in the original units and less sensitive to outliers.

Interpreting Descriptive Statistics

  • Frequency Table: Describe and interpret based on valid percent and cumulative percent.
  • Measures of Central Tendency:
    • Mean vs. Median: Compare to find skewness.
    • Symmetrical Distribution: Mean and median are equal.
    • Skewed Distribution: Mean and median differ (positive or negative skew).
  • Measures of Dispersion:
    • Standard Deviation: Compare relative to the mean to understand dispersion.

Examples

  • Age of Respondent: Symmetrical distribution as mean and median are close.
  • TV Hours: Positive skew indicated by mean higher than median.
  • Internet Use: High positive skew and high dispersion.

Special Distribution: Normal Distribution

  • Properties:
    • 68% of cases fall within ±1 standard deviation.
    • 95% within ±2 standard deviations.
    • 99% within ±3 standard deviations.

Key Takeaways

  • Descriptive statistics provide a foundation for understanding the sample data before further analysis.
  • Always describe and interpret when presenting statistical data.
  • Mode, Median, Mean: Essential for understanding central tendencies.
  • Standard Deviation: Crucial for understanding dispersion.