Lecture+9

Lecture Overview

• Course: POSC 201: Political Research Design

• Instructor: Lewis Luartz, Chapman University

• Lecture Number: 9

• Semester: Spring 2025

Content Summary

• Overview of lecture topics:

  • Correlation Coefficients

  • The Basics of Sampling

  • Quantitative Methods I

  • Randomized Experiments

  • Observational/Cross-Section Designs

  • Longitudinal/Time-Series Designs

Announcements and Reminders

• Homework 3: Due on Tuesday, March 11, 2025 by 11:59 PM (PST).

• Syllabus Update: Qualitative Research moved to post-Spring Break, focusing more on quantitative methods first.

• R Practice: A practice R script will be provided for tasks related to data cleaning and estimating correlation coefficients, along with an answer key for feedback.

• Midterm Exam: Study guide to be released on the next Tuesday; Midterm scheduled for March 20, 2025.

• Resources: Example posters and papers will be available on Canvas (pending student consent).

• Important Reminders: Bring a computer for R classes and practice R scripts at home to ensure proficiency for projects.

Different Correlation Coefficients

• Pearson Correlation:

  • **Assumptions: **

    • Data must be continuous (interval or ratio).

    • Data should be linear; avoid parabolic or non-parametric shapes.

    • No outliers should be present as they can skew results.

    • Data must be normally distributed; assess using skew and kurtosis or through histograms.

• Spearman Correlation:

  • Evaluates relationships involving at least one ordinal variable and two quantitative variables under partial linearity.

• Kendall’s Tau-b:

  • Used for two qualitative (or categorical) ordinal variables.

  • In R, use: add , method = "type") where type is pearson, spearman, or kendall.

The Basics of Sampling

• Definition of Samples:

  • Samples provide information about a population, defined as any well-defined set of units.

  • A population can refer to a variety of entities, not just people (counties, businesses, etc.).

• Population Example: All adult citizens (18+) in the USA in 2018.

  • Direct interviews with the entire population are impractical.

  • Sampling involves selecting a subset for investigation.

• Significance of Sampling: The sample size and selection method impact the accuracy and reliability of inferences about the whole population.

Sample Statistics and Population Parameters

• After gathering samples, researchers measure characteristics of interest to approximate population parameters.

• Sample statistics provide estimates for population parameters, which will typically not match exactly but should be close under appropriate sampling procedures.

• Goal of Statistical Inference: To conjecture unknown population characteristics based on sample statistics; crucial is the concept of sampling distribution.

Sampling Distribution

• Example with Presidential Approval:

  • If we interview ten adult Americans about Trump’s performance and find 80% approval rate, whereas the real population parameter is 50%, this difference is termed sampling error.

  • Each sample could yield different approval statistics due to sample size limitations.

• Continuous Sampling: Taking multiple samples leads to varied estimates, but the average may converge closer to the true population parameter.

  • For instance, averaging different samples may yield values approaching the actual parameter.

• Normal Distribution Appearances: As more samples accumulate, a bell-shaped normal distribution emerges, where the mean correlates with the population parameter.

Sampling Methods

Definition of Elements and Sampling Frame

• Element: A unit of analysis; in the presidential approval study, it's an individual American adult.

• Sampling Frame: A comprehensive list from which sampling units are drawn, essential for accurate representation of the population.

Types of Samples

• Probability Sample: Each element has a known probability of selection, providing robustness.

• Non-Probability Sample: Each element has an unknown probability of being selected, which can introduce bias.

• Probability samples are generally preferred because they promote representativeness.

Simple Random Samples

• Characteristics: Involve equal chances for each element in the population to be included, ideally using a complete sampling frame.

  • Advantages: Ensures a representative sample with larger sizes.

  • Disadvantages: May be challenging to achieve a perfect sampling frame.

  • Important note: All samples have potential for error, and no sample accurately captures the entire population.

Randomized Experimental Designs

• Posttest Design: A classical experimental design without a pretest, relying on random assignment and large sample sizes to infer causal relations.

  • Researchers must establish that treatment occurs before measuring dependent variables to support causal inferences.

  • Random assignment mitigates the impact of pre-experiment differences across groups, but researchers can't fully ascertain the magnitude of differences with this approach.