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Summary from last time:
Refer to document on dispersions for more detail.
For instance:
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).
Seattle | Eugene |
---|---|
mean = 51.5 inches | mean = 39.5 inches |
dispersion = 8.5 | dispersion = 7.0 |
On average, does it rain significantly more in Eugene than Seattle?
Here is the wrong way to do this problem:
12 inches is 12/8 = 1.5 dispersion units and therefore not significant.
But this is not the correct procedure to use when comparing two
separate distributions.
It is only the correct procedure to use
when comparing one data point to the rest of the same distribution.
Seattle | Eugene |
---|---|
mean = 51.5 inches | mean = 39.5 inches |
dispersion = 8.1 | dispersion = 7.0 |
N = 25 | N = 25 |
error in mean = 8.1/5 | error in mean = 7.0/5 |
error in mean = 1.6 | error in mean = 1.4 |
The difference in mean rainfall between Seattle and Eugene is (51.5 - 39.5) = 12 inches which is 12/1.6 = 7.5 dispersion units difference in the mean value.
Thus there is a highly significant difference in the mean annual rainfall between Eugene and Seattle.
Note this method is only an approximation. A more exact and proper way to compare two sample means will be given later.
Another way to look at this rainfall comparison is as follows:
We have already determined that 65 inches is not a significant amount
of rainfall in Eugene compared to the normal value of 51.5 inches.
Would 65 inches be a significant amount of rain in Seattle?