Quantitative Understanding in Biology
Spring 2008

Quantifying a Sample Distribution

Goals

Understand the difference between the standard deviation and the standard error of the mean.
Understand how to convey the essential characteristics of a single distirbution of values, both numerically and graphically.
Install and develop some competence in using the R statistical prackage to perform basic computations and to prepare basic plots.

Homework Project

Get R running on your computer.
Familiarize yourself with R by reviewing any of the on-line tutorials or (for the more motivated) the "Introduction to R" by Venables and Smith (see references below).
Generate the following samples from a normal distribution. Report a mean and confidence interval for each.

Xn <- rnorm(n)	for n = 5, 50, and 1,000,000
Xm.n <- c(rnorm(n), rnorm(n,mean=m))	for n=5, 50, and 1,000,000 and m = 1, 2, and 3

For each case above, present the data in the form that you feel best conveys the data you have generated.
What can you say about the ability to detect a bimodal distribution in an underlying population. How far apart do the means need to be?

For this project, use the first sample you generate; don't keep generating samples until you get one that 'looks good'.

References

Intuitive Biostatistics, H. Motulsky

An Introduction to R, Venables and Smith

R Reference Card, T. Short