Uploaded December 2012 | Updated September 2026, 43 minutes ago
I introduce the chi-square test of independence and work through an example.
The binge drinking data is from:
Wechsler H, Lee JE, Kuo M, Lee H. (2000). College Binge Drinking in the 1990s: A Continuing Problem — Results of the Harvard School of Public Health 1999 College Alcohol Study. Journal of American College Health. 2000. 48 (10): 199-210.
I introduce the chi-square test of independence and work through an example.
The binge drinking data is from:
Wechsler H, Lee JE, Kuo M, Lee H. (2000). College Binge Drinking in the 1990s: A Continuing Problem — Results of the Harvard School of Public Health 1999 College Alcohol Study. Journal of American College Health. 2000. 48 (10): 199-210.
![An Introduction to the Hypergeometric Distribution
An introduction to the hypergeometric distribution. I briefly discuss the difference between sampling with replacement and sampling without replacement. I describe the conditions required for the hypergeometric distribution to hold, discuss the formula, and work through 2 simple examples.
I also discuss the relationship between the binomial distribution and the hypergeometric distribution, and a rough guideline for when the binomial distribution can be used as a reasonable approximation to the hypergeometric. I finish with a brief example involving the multivariate hypergeometric distribution.
For those using R, here is the R code to find the probabilities for the examples in this video:
The probability of picking exactly 4 red balls when picking 5 balls from a source containing 6 red and 14 yellow.
Without replacement (hypergeometric):
choose(6,4)*choose(14,1)/choose(20,5)
[1] 0.01354489
or
dhyper(4,6,14,5)
[1] 0.01354489
With replacement (binomial):
dbinom(4,5,6/20)
[1] 0.02835
The probability of picking exactly 7 females when randomly sampling from a school with 1100 female and 900 male students.
Without replacement (hypergeometric):
choose(1100,7)*choose(900,3)/choose(2000,10)
[1] 0.1664901
or
dhyper(7,1100,900,10)
[1] 0.1664901
With replacement (binomial):
dbinom(7,10,1100/2000)
[1] 0.1664783
Multivariate hypergeometric, probability of picking exactly 3 Democrats, 2 Republicans, and 1 independent in the sample.
choose(12,3)*choose(24,2)*choose(8,1)/choose(44,6)
[1] 0.06881377
or, with the extraDistr package installed:
dmvrhyper(c(3,2,1),c(12,24,8),6) An Introduction to the Hypergeometric Distribution](https://i.ytimg.com/vi/L2KMttDm3aY/mqdefault.jpg)






![What Factors Affect the Margin of Error? (In a Confidence Interval for One Mean)
A look at the effect of various factors (the standard deviation, the sample size, and the confidence level) on the margin of error of a confidence interval for the population mean.
For those that use R, below I give the R code to find the values given in this video.
Z value for a 90% interval (see my other videos for a more detailed explanation of the rationale):
qnorm(.95)
[1] 1.644854
Z value for a 95% interval:
qnorm(.975)
[1] 1.959964
Z value for a 99% interval:
qnorm(.995)
[1] 2.575829 What Factors Affect the Margin of Error? (In a Confidence Interval for One Mean)](https://i.ytimg.com/vi/NQtcGOhUWB4/mqdefault.jpg)


