Monte Carlo Simulation

Date: Feb 27

Overview

Monte Carlo simulation is a powerful computational method that uses repeated random sampling to solve complex problems. Starting from the simple idea that a computer can estimate probabilities by trying things many times, we build up to sophisticated research design applications. Along the way, we explore the fascinating history — from a math feud in 1905 Russia to the Manhattan Project — that gave rise to these methods.

Topics

• Solving Probability with Computers: From coin flips to chess pieces — building intuition for random sampling and the Law of Large Numbers.
• A Math Feud That Changed Everything: The Markov vs. Nekrasov debate, Markov chains, and dependent events.
• From Solitaire to the Atomic Bomb: Ulam’s insight, the Manhattan Project, and the birth of the Monte Carlo method.
• Building Simulations: Generating data, creating relationships, and understanding sampling variability.
• Research Design Applications:
  • Sample Size Determination
  • Minimum Detectable Effect
  • Statistical Power Analysis

Slides

View Class Slides

Homework

Assignment #5: Conduct Monte Carlo simulation study and interpret statistical power using Mplus. Due next week.

Readings

Required

• Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural equation modeling, 9(4), 599-620.
• Durlak, J. A. (2009). How to select, calculate, and interpret effect sizes. Journal of pediatric psychology, 34(9), 917-928.

Supplemental

• Mooney, C. Z. (1997). Monte Carlo simulation (Vol. 116). Sage Publications. [Chapters 1, 2, 3]
• Muthén, B. O., & Curran, P. J. (1997). General longitudinal modeling of individual differences in experimental designs: A latent variable framework for analysis and power estimation. Psychological methods, 2(4), 371.
• Kraemer, H. C., & Blasey, C. (2015). How many subjects? Statistical power analysis in research. Sage Publications. [Chapters 1, 2]