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Monte Carlo Simulations: Class 3

Independent Study / Spring 2023

Francis L. Huang, PhD

huangf@missouri.edu

@flhuang

https://francish.net

2023.01.30 / Updated 2023-04-22

1 / 3
Simulation stuff
Francis Huang / huangf@missouri.edu

Investigating Student's independent sample t-test assumptions

  • Normally distributed
  • Independent
  • Homogeneity of variance (tested using a F-test; see below)

Source: https://en.wikipedia.org/wiki/Student%27s_t-test

2 / 3
Simulation stuff
Francis Huang / huangf@missouri.edu

NOTE: R, by default, does not run Student's t-test but Welch's t-test

## Default S3 method:
t.test(x, y = NULL,
       alternative = c("two.sided", "less", "greater"),
       mu = 0, paired = FALSE, var.equal = FALSE,
       conf.level = 0.95, ...)
var.equal: 
a logical variable indicating whether to treat the two variances as being equal. 
*If TRUE then the pooled variance is used to estimate the variance otherwise the 
Welch (or Satterthwaite) approximation** to the degrees of freedom is used.

  • Welch's t-test does NOT assume equality of variance

  • Which is better and why?

  • Does it make a difference which test you run?
    • When does it make a difference?
  • Is one more powerful than the other?
  • Is one more robust than the other?
3 / 3
Simulation stuff
Francis Huang / huangf@missouri.edu

Investigating Student's independent sample t-test assumptions

  • Normally distributed
  • Independent
  • Homogeneity of variance (tested using a F-test; see below)

Source: https://en.wikipedia.org/wiki/Student%27s_t-test

2 / 3
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