Comparing Means and Deviations

# ENVS 202 On-line Access

## Comparing Sample Means - What is Significance?

Summary from last time:

• The Sample Mean - Numerical measure of the average or most probable value in some distribution. Can be measured for any distribution knowing the mean value alone for some sample is not very meaningful.

• The Sample Distribution - Plot of the frequency of occurrence of ranges of data values in the sample. The distribution needs to be represented by a reasonable number of data intervals (counting in bins). Refer to the Rainfall Distribution example or for another example of histograms and distributions go here

• The Sample Dispersion - Numerical measure of the range of the data about the mean value. Defined such that +/- 1 dispersion unit contains 68% of the sample, +/- 2 dispersion units contains 95% and +/- 3 dispersion units contains 99.7%. This is schematically shown below:

Refer to document on dispersions for more detail.

In general, we map dispersion units on to probabilities

For instance:

• The Probability that some event will be greater than 0 dispersion units above the mean is 50%
• The Probability that some event will be greater than 1 dispersion units above the mean is 15%
• The Probability that some event will be greater than 2 dispersion units above the mean is 2%
• The Probability that some event will be greater than 3 dispersion units above the mean is 0.1% (1 in 1000)

The calculation of dispersion in a distribution is very important because it represents a uniform way to determine probabilities and therefore to determine if some event in the data is expected (i.e. probable) or is significantly different than expected (i.e. improbable).