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Kolmogorov -Smirnov Test

Kolmogorov -Smirnov Test. Methodology One Sample KS Test In the one sample KS Test, a given set of data is compared with a theoretical distribution or reference probability. Two Sample KS Test The two sample KS Test compares two sets of data collected under the same or similar conditions.

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Kolmogorov -Smirnov Test

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  1. Kolmogorov-Smirnov Test Methodology One Sample KS Test In the one sample KS Test, a given set of data is compared with a theoretical distribution or reference probability. Two Sample KS Test The two sample KS Test compares two sets of data collected under the same or similar conditions. In each test, the sample data is graphed using a cumulative fraction function. The maximum vertical deviation between either the data and the theoretical distribution or the two data sets is labeled D. If this D value is greater than a critical value (obtained from a table) then the data does not reflect the hypothesis or the two sets of data do not corrolate. Limitations Although this test is not subject to parameters or changes in scale, it has three important limitations Non-continuous distributions do not work The KS test is more accurate in the middle of the data set than near the ends The distribution must be fully specified and not an estimate of the data Overview The Kolmogorov-Smirnov test is designed as a nonparametric test of accuracy and precision. It can reflect either the accuracy of one set of data and a theoretical data distribution, or the precision of two sets of data. Examples One Sample Say we are theorizing a distillation curve and shown is our theoretical (red) and experimental (blue) data. If the D value (the black arrow) is above a certain number, then our theoretical curve is inaccurate, and we must recalibrate. If not, our idealized curve is sufficient. Two Sample In this example, we are examining the number of bees to two different kinds of flowers and how long they stay there. If the D value in this case is above the critical value, there is no correlation. If the D value is below the critical value, they correlate. Note: There are more elegant formulas to describe the Kolmogorov-Smirnov Test. They are worth looking into References http://www.itl.nist.gov/div898/handbook/eda/section3/eda35g.htm http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Kolmogorov-Smirnov_test.html http://www.physics.csbsju.edu/stats/KS-test.html

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