Uploaded July 2013 | Updated September 2026, 2 hours ago
A discussion of the assumptions of pooled-variance t tests and confidence intervals for the difference in means. The assumptions are briefly discussed, and the effects of different violations of the normality assumption are investigated through simulation. The quick summary: Pooled-variance t procedures are more robust to violations of the normality assumption than their one-sample counterparts.
A discussion of the assumptions of pooled-variance t tests and confidence intervals for the difference in means. The assumptions are briefly discussed, and the effects of different violations of the normality assumption are investigated through simulation. The quick summary: Pooled-variance t procedures are more robust to violations of the normality assumption than their one-sample counterparts.
![An Introduction to the Geometric Distribution
An introduction to the geometric distribution. I discuss the underlying assumptions that result in a geometric distribution, the formula, and the mean and variance of the distribution. I work through an example of the calculations and then discuss the cumulative distribution function.
For those using R, here is the R code for the example in this video:
NB R uses a different definition of the random variable than I do here. I define the random variable X to be the number of trials required to get the first success. R defines the random variable to be the number of *failures* before getting the first success (lets call this Y). Then Y = X - 1, and well have to make this adjustment when using dgeom, pgeom, or rgeom. Some might find this confusing, and if you do, dont use these functions.
Sampling from a large population where 30% have CPR training until we get the first person with CPR training.
Finding the probability that it happens on the sixth person sampled:
(.3)*(.7)^5
[1] 0.050421
or
dgeom(6-1,.3)
[1] 0.050421
Finding the probability that it happens on or before the third person sampled:
.3+.3*.7+.3*.7^2
[1] 0.657
or
1-.7^3
[1] 0.657
or
pgeom(3-1,.3)
[1] 0.657 An Introduction to the Geometric Distribution](https://i.ytimg.com/vi/zq9Oz82iHf0/mqdefault.jpg)