## Individual KS Assignment

### Due on March 1

This assignment is somewhat involved but it should help
you gain practice and experience with the application of
the KS Test.

Each data set has 36 values in it. The data sets represent monthly
rainfall in Eugene from 1973-75, 1983-85, and 1993-95.

Please do this exercise in the following order:

- Determine if the distributions are the same or different
between the data sets (i.e. compare data set 1 with 3, 2 with 3, 1 with 2),
by comparing the respective cumulative frequency distributions and
determining D
_{max}. If D_{max} is greater than
0.32 (for n=m=36) then a significant difference exists.

- Determine if D
_{max} is sensitive to bin size by
changing the bin size in Excel.

- Compare the data sets to model Gaussian distributions using
the procedure we went through in class with Excel. In the
first case compare each data set to a guassian with
mean = 3.5 and standard deviation = 4.0. You should find, in all cases,
this model to be a poor fit to the data. If it is, what can you conclude
about the nature of the data? What aspect of the model seems to not
make any physical sense in comparison to the data?
Now combine all three data sets into one average data set and find
the best fitting Normal Distribution to that data. In this case,
comparing 36 points against a model, D_{max} should be less
than 0.23 for the model to be acceptable.

Here you go.

Data Set 1:
12.8 8.4 12.5 2.5 1.1 0.4 1.4 0.4 0.1 1.6 6.4 9.3
6.9 6.8 7.6 2.9 2.2 0.9 1.2 2.1 0.1 5.7 8.5 7.1
9.8 7.6 6.2 1.9 0.9 0.2 0.4 2.0 1.1 1.9 1.3 1.2
Data Set 2:
6.8 12.3 10.6 3.4 1.8 1.8 1.8 3.2 0.5 1.4 13.1 7.5
2.1 9.6 6.4 5.4 3.9 3.9 0.3 0.1 0.9 6.1 18.7 4.6
0.3 5.1 5.7 0.5 1.5 2.5 1.4 0.1 2.1 4.8 6.3 3.5
Data Set 3:
6.9 2.6 8.6 7.9 6.9 3.7 1.1 1.8 0.1 1.5 2.0 10.8
5.5 5.5 5.5 2.0 1.6 1.1 0.1 0.1 2.1 7.5 9.6 6.1
15.4 3.8 6.4 5.6 2.1 2.3 1.1 1.0 1.1 3.9 9.5 13.4
Guassian Model Data (Generic; Mean = 0 sd = 1):
-1.33 -1.28 -1.21 -1.13 -1.02 -0.91 -0.77 -0.61 -0.44 -0.24 -0.04 0.17 0.39
0.61 0.82 1.01 1.17 1.31 1.41 1.48 1.50 1.48 1.41 1.31 1.17 1.01 0.82 0.61
0.39 0.17 -0.04 -0.24 -0.44 -0.61 -0.77 -0.91 -1.02 -1.13 -1.21 -1.28 -1.33
Gaussian Model Data (Specific Example; Mean = 3.5 sd = 4.0)
-1.83 -1.61 -1.34 -1.00 -0.60 -0.12 0.43 1.05 1.76 2.52 3.34 4.20 5.07
5.93 6.76 7.52 8.19 8.75 9.16 9.41 9.50 9.41 9.16 8.75 8.19 7.52 6.76
5.93 5.07 4.20 3.34 2.52 1.76 1.05 0.43 -0.12 -0.60 -1.00 -1.34 -1.61
-1.83