STAT200 Lecture 1 Notes
Introduction to Statistics: Overview of the importance of statistics in data analysis, research, and decision making.
Types of Data: Understanding qualitative vs. quantitative data, discrete vs. continuous variables.
Page 7: Understanding Data and Data Sets
Data: Refers to facts/figures that are collected and analyzed.
Data Set: All data gathered from a specific study.
Page 8: Elements, Variables, and Observations
Elements: Entities from which data is collected.
Variables: Characteristics of interest related to the elements.
Observations: The measurements gathered for each element.
Data Set Composition: A data set with ( n ) elements contains ( n ) observations.
Page 9: More on Elements and Observations
Data Values: Total number of data values in a data set is calculated as:
( \text{Number of elements} \times \text{Number of variables} )
Page 10: Scales of Measurement
Categories:
Numeric
Categorical
Data Types: Non-numeric vs. numeric data
Page 11: Classifying Data
Categorical Data:
Can be numeric or non-numeric.
Used for labeling attributes (no arithmetic operations).
Quantitative Data:
Always numeric.
Discrete (how many) vs. continuous (how much).
Arithmetic operations are relevant.
Page 12: Overview of Measurement Scales
Types of Scales:
Nominal
Ordinal
Interval
Ratio
Significance: The scale in use determines data summarization techniques and appropriate statistical analyses.
Page 13: Nominal Scale
Definition: Data as labels or names representing attributes.
Uses non-numeric or numeric coding.
Examples:
Classifying students by major or using numeric codes (e.g., 1 for Economics).
Page 14: Ordinal Scale
Characteristics: Combines nominal properties with meaningful order/rank.
Examples:
Classifying students by class standing, with possible numeric labels.
Page 15: Interval Scale
Features: Differences are meaningful; no true zero.
Examples: SAT scores and temperature in Celsius.
Operations: - Addition and subtraction are valid, but multiplication/division offer no meaningful insights.
Page 16: More on Interval Scale
Example:
SAT scores of 1985 vs. 1880, indicating differences clearly.
Page 17: Ratio Scale
Definition: Possesses all interval properties with meaningful ratios and a true zero.
Example: Price comparisons of a book showing clear ratios.
Page 18: The Four Levels of Measurement (NOIR)
Nominal: Useful for categorization
Ordinal: Enables ranking of categories
Interval: Interval measures provide equal distances.
Ratio: Includes a meaningful zero.
Page 19: Classification by Time of Data Collection
Cross-Sectional Data: Collected at a single time point.
Time Series Data: Collected across multiple time periods.
Combination: Possible to follow a single group over time.
Page 20: Example of Cross-Sectional Data
Data Example: State gas price averages from various states showing current prices.
Page 21: Example of Time Series Data
Data Example: U.S. gasoline prices over several years depicted in a graph.
Page 22: Data Sources
Common Sources:
Internal records
Business databases (e.g., Dow Jones & Co.)
Government resources (e.g., BLS, Census Bureau)
Internet resources.
Page 23: Observational Studies in Statistics
Definition: Non-experimental studies focusing on passive data collection.
Example: Surveys comparing smokers and nonsmokers without controlling who belongs to either group.
Page 24: Experimental Studies in Statistics
Process: Identify a variable of interest, and control others to see their impacts.
Reference Example: The Salk polio vaccine study as a significant historical experiment.