Uploaded June 2014 | Updated September 2026, 3 hours ago
A discussion of the effect of violations of the normality assumption on confidence intervals for the ratio of variances. The effects of different violations of the normality assumption are investigated through simulation. The quick summary: These procedures are very sensitive to violations of the normality assumption, and often perform very poorly when the normality assumption is violated.
This video is very similar in content and results to my video that investigates the effect of violations of the normality assumption on inference procedures for a single variance.
A discussion of the effect of violations of the normality assumption on confidence intervals for the ratio of variances. The effects of different violations of the normality assumption are investigated through simulation. The quick summary: These procedures are very sensitive to violations of the normality assumption, and often perform very poorly when the normality assumption is violated.
This video is very similar in content and results to my video that investigates the effect of violations of the normality assumption on inference procedures for a single variance.
![Standardizing Normally Distributed Random Variables
I discuss standardizing normally distributed random variables (turning variables with a normal distribution into something that has a standard normal distribution). I work through an example of a probability calculation, and an example of finding a percentile of the distribution. It is assumed that you can find values from the standard normal distribution, using either a table or a computer.
The mean and variance of adult female heights in the US is estimated from data found in a National Health Statistics Report:
McDowell MA, Fryar CD, Ogden CL, Flegal KM. Anthropometric reference data for children and adults: United States, 2003-2006. National health statistics re- ports; no 10. Hyattsville, MD: National Center for Health Statistics. 2008.
For those using R, here is the R code for the examples used in this video:
American female heights example (approximately normally distributed with a mean of 162.2 and a standard deviation of 6.8).
Finding the probability that a randomly selected female is taller than 170.5 cm.
Easiest way:
1-pnorm(170.5,162.2,6.8)
[1] 0.111121
Standardizing route:
1-pnorm((170.5-162.2)/6.8,0,1)
[1] 0.111121
The default in Rs pnorm is the standard normal distribution (mean=0, SD=1), so the mean and SD can be left out when dealing with the standard normal.
1-pnorm((170.5-162.2)/6.8)
[1] 0.111121
Finding the probability that a randomly selected female has a height between 150.5 and 170.5.
Easiest way:
pnorm(170.5,162.2,6.8)-pnorm(150.5,162.2,6.8)
[1] 0.8462162
Standardizing route:
pnorm((170.5-162.2)/6.8)-pnorm((150.5-162.2)/6.8)
[1] 0.8462162
10th percentile of heights of adult American females.
Easiest:
qnorm(.1,162.2,6.8)
[1] 153.4854
Alternatively, via the standard normal distribution:
qnorm(.1)
[1] -1.281552
Thats the 10th percentile of the standard normal distribution. Converting to the distribution of heights,
-1.281552*6.8+162.2
[1] 153.4854 Standardizing Normally Distributed Random Variables](https://i.ytimg.com/vi/4R8xm19DmPM/mqdefault.jpg)









