Overview
This lecture introduces basic categorical data analysis, focusing on understanding and converting between percentages and proportions, especially as used in statistics.
Types of Data
- Data can be categorized as either categorical (descriptive, non-numeric) or quantitative (numeric).
- Categorical data describes traits like location, school, or other identifiers.
Percentages and Proportions
- A percentage represents a part out of 100; "percent" means "per hundred."
- A proportion is the decimal form of a percentage, used widely in statistics.
- In statistics, "proportion" does not refer to the algebraic meaning involving cross-multiplication.
Converting Percentages and Proportions
- To convert a percentage to a proportion, divide by 100 (move the decimal two places left).
- Example: 33.7% → 0.337
- Example: 100% → 1
- Example: 6% → 0.06
- To convert a proportion to a percentage, multiply by 100 (move the decimal two places right), then add the % sign.
- Example: 0.018 → 1.8%
- Example: 0.873 → 87.3%
- Example: 1 → 100%
- Leading zeros before the decimal are standard practice (e.g., 0.06).
Scientific Notation and Small Proportions
- Very small proportions may be represented in scientific notation (e.g., 2.3 × 10^-5).
- Move the decimal left by the exponent to get the standard decimal form (e.g., 0.000023).
- Convert to percentage by multiplying by 100 (e.g., 0.000023 → 0.0023%).
Categorical Data Analysis Basics
- First steps in analyzing categorical data include finding counts or frequencies (number of successes), often denoted by X.
- The total sample size is denoted by n, representing the total number of observations, objects, or trials.
Key Terms & Definitions
- Categorical Data — data described by words or categories, not numbers.
- Percentage — a value out of 100, denoted by the % symbol.
- Proportion — the decimal equivalent of a percentage used in statistics.
- Frequency (Count) — the number of times a particular category appears.
- Sample Size (n) — the total number of observations in the data set.
- Scientific Notation — a way to write very small or large numbers using powers of ten.
Action Items / Next Steps
- Practice converting between percentages and proportions.
- Be able to interpret and convert numbers in scientific notation.
- Review definitions of key terms for categorical data analysis.