Statistical Analysis

Lecture 1: Overview of Statistics

Bogdan G. Popescu
bogdan.popescu@johncabot.edu

John Cabot University

Learning Outcomes and Skills

Learning Outcomes

  • Use statistical terminology accurately and interpret descriptive statistics, hypothesis tests, and regressions
  • Organize, clean, and merge datasets using R, and summarize data with numerical and graphical methods
  • Conduct hypothesis tests (z-tests, t-tests) and estimate bivariate and multivariate regression models
  • Distinguish correlation from causation using causal diagrams (DAGs) and apply causal inference methods (RCTs, matching, differences-in-differences)
  • Create effective data visualizations using ggplot2 and produce reproducible reports in Quarto

Skills

  • Interpret data using descriptive statistics
  • Apply hypothesis testing and correlation analysis
  • Create effective data visualizations
  • Generate and present insights from data

Career Applications

  • Data Analyst: clean, visualize, and report data
  • Policy Analyst: evaluate program impact with evidence
  • Market Researcher: survey design and trend analysis
  • Academic Researcher: test theories with statistical models

Logistics

Course Logistics

  • Hours: MW 10:00–11:15 AM
  • Room: F.1.5, Frohring Campus, First Floor
  • Office Hours: TBA
  • Bi-weekly problem sets and two exams
  • Laptops required for lab sessions
  • Programming language: R

Assignment Workflow

  • Work individually first, submit your version
  • Check responses with team members
  • Submit updated responses individually
  • Final grade: average of both submissions
  • Teammates grade your contribution

Sample Grades

Sample grades from a previous semester. Source: Author’s illustration.
Student Assignments Midterm Final Peer Grade Letter
1 92.2 92.5 84.0 100 90.2 B
2 87.1 85.0 95.5 100 89.6 B
3 92.8 97.5 95.0 100 95.2 A-
4 97.4 100.0 95.0 100 97.6 A
5 84.2 82.5 63.5 100 78.3 C

Grading Scale

Numerical to letter grade mapping. Source: Author’s illustration.
Range Letter
97 – 100 A
93 – 96 A-
90 – 92 B+
87 – 89 B
83 – 86 B-
80 – 82 C+
77 – 79 C
73 – 76 C-

Course Schedule

  1. Overview of Statistics
  2. Levels of Data
  3. Descriptive Statistics
  4. Probability I
  5. Probability II
  6. Z-tests & Significance
  7. Correlation & Review
  8. Midterm Exam
  1. Bivariate Regression
  2. Multivariate Regression
  3. RCT Data
  4. OLS Assumptions
  5. Causal Models
  6. Conclusion
  7. Final Exam

Workspace Setup

  • Create a dedicated stats folder
  • Add 15 subfolders: week1 through week15
  • Casing matters: use week1 not Week1

Workspace: Main Folder

Workspace: Weekly Subfolders

Within each week, create lecture and lab subfolders.

Empirical Research

Why Empirical Research?

  • Test theories systematically, not just describe
  • Measure relationships and identify patterns

Key steps:

  • Select appropriate data for analysis
  • Choose an analytical method
  • Apply statistical tools to test hypotheses

Research Question Examples

  • Why do countries democratize?
  • What are long-term effects of colonialism?
  • Who votes and who doesn’t?
  • How do regimes repress human rights?
  • What drives support for foreign involvement?

Discussion

Pick a social outcome (e.g., voter turnout, income, health).

  • What is one factor that might influence it?
  • Which is the independent variable? Dependent?
  • Would you expect a positive or negative relationship?

Concepts versus Variables

Variables vs Constants

  • A variable is a concept with variation
  • A concept without variation is a constant
  • Variation is key to data analysis

Independent and Dependent Variables

  • Independent variable: thought to cause variation
  • Dependent variable: influenced by the independent

Example:

Independent Variable → Dependent Variable

Education → Income

Arrow Diagram: Insurance Example

%%{init: {"theme": "base", "themeVariables": {"primaryColor": "#4a7c6f", "primaryTextColor": "#f9fafb", "primaryBorderColor": "#1e293b", "lineColor": "#334155", "fontSize": "22px"}, "flowchart": {"useMaxWidth": true, "nodeSpacing": 50, "rankSpacing": 80}, "width": 1150, "height": 650}}%%
flowchart LR
    A["Adequacy of<br/>Medical Insurance<br/>(Antecedent)"] --> B["Attitudes toward<br/>Nat. Health Insurance<br/>(Independent Variable)"]
    B --> C["Presidential<br/>Vote<br/>(Dependent Variable)"]
    style A fill:#64748b,stroke:#1e293b,color:#f9fafb
    style B fill:#4a7c6f,stroke:#1e293b,color:#f9fafb
    style C fill:#b44527,stroke:#1e293b,color:#f9fafb

Source: Author’s illustration

Arrow Diagram: Education Example

%%{init: {"theme": "base", "themeVariables": {"primaryColor": "#4a7c6f", "primaryTextColor": "#f9fafb", "primaryBorderColor": "#1e293b", "lineColor": "#334155", "fontSize": "22px"}, "flowchart": {"useMaxWidth": true, "nodeSpacing": 40, "rankSpacing": 70}, "width": 1150, "height": 650}}%%
flowchart LR
    A["Formal<br/>Education<br/>(Independent)"] --> B["Sense of<br/>Civic Duty<br/>(Intervening)"]
    A --> C["Knowledge of<br/>Candidates' Positions<br/>(Intervening)"]
    B --> D["Voter<br/>Turnout<br/>(Dependent)"]
    C --> D
    style A fill:#4a7c6f,stroke:#1e293b,color:#f9fafb
    style B fill:#b7943a,stroke:#1e293b,color:#1e293b
    style C fill:#b7943a,stroke:#1e293b,color:#1e293b
    style D fill:#b44527,stroke:#1e293b,color:#f9fafb

Source: Author’s illustration

Associations

What Are Associations?

  • Two variables are associated if one predicts the other

Example: Life Expectancy and Urbanization

Life Expectancy

  • Indicator of overall health and well-being
  • Studied by health researchers and economists
  • We examine data for 214 countries
  • Does urbanization affect life expectancy?

Our World in Data

Source: ourworldindata.org

The Data

  • Each row is a country (unit)
  • Two variables measured per unit
  • Variables vary across units

What Explains Life Expectancy?

  • What explains variation in life expectancy?
  • Traits of longer-lived countries?
  • Traits of shorter-lived countries?
  • Key correlates: income, education, urbanization

Correlates of Life Expectancy

Longer Life Expectancy

  • Higher incomes and more schooling
  • Better public services
  • More urbanized

Shorter Life Expectancy

  • Lower incomes and less schooling
  • Weaker public services
  • Less urbanized

Source: Author’s illustration

Scatterplot: Life Expectancy vs. Urbanization

Figure 1

With Trend Line

Figure 2

Italy Highlighted

Figure 3

Italy and USA Highlighted

Figure 4

All Countries Labeled

Figure 5

Associations vs Causal Relationships

Association and Prediction

  • Associated variables help predict each other

Predictions from our data:

  • Middle-income countries: longer life expectancy
  • More urbanized countries: longer life expectancy

Causal Relationships

A causal relationship requires three elements:

  • X and Y must covary (be associated)
  • Change in X must precede change in Y
  • Association not due to chance or other factors

Causal claims are formalized as hypotheses.

Hypotheses

What is a Hypothesis?

  • Explicit statement about expected relationships
  • Formalizes the researcher’s informed guess
  • Links variables with a predicted direction

Good Hypothesis Characteristics

  • Empirical: testable with observable evidence
  • Grounded in theory or logic
  • Specifies direction of the relationship
  • Concepts consistent with measurement
  • Feasible to test with available data
  • Specifies the unit of analysis

Hypothesis Examples

  • More education → higher income (IV, DV, +)
  • Higher urbanization → longer life expectancy (+)
  • More campaign spending → more votes (+)
  • Higher unemployment → lower trust in government (-)

Your Turn

Write a hypothesis with:

  • A clear independent variable
  • A clear dependent variable
  • A predicted direction (positive or negative)

Defining Concepts

Good concept definitions should be:

  • Clear
  • Accurate
  • Precise
  • Informative

Balance between specific and abstract.

Populations and Samples

  • Population: full set of units of interest
  • Sample: subset we actually study
  • Sampling: selecting a subset from the population
  • We use samples to estimate population characteristics

Sampling: Key Points

  • Good samples should be representative
  • First, clearly define the population
  • Probability sampling: known chance of selection
  • Reduces bias, enables unbiased estimation

Representative Samples

  • Goal: draw conclusions about the population
  • Representative sample reflects population traits
  • Repeated sampling yields population-matching features

Conclusion

What We Covered

  • Variables, associations, and causal claims
  • Hypotheses link an IV to a DV with direction
  • Association does not imply causation

Next week: Levels of data – nominal, ordinal, interval, ratio – and why measurement type determines your analysis.