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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:

  1. 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 Dmax. If Dmax is greater than 0.32 (for n=m=36) then a significant difference exists.

  2. Determine if Dmax is sensitive to bin size by changing the bin size in Excel.

  3. 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, Dmax 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