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The Kolmogorov-Smirnov test (KS-test) tries to determine if two datasets differ significantly. The KS-test has the advantage of making no assumption about the distribution of data. In other words it is non-parametric and distribution free. The method is explained here and makes use of an Excel tool called "Real Statiscs". The tests were made using the raw data and distributions, both methods had similar results except for the 100Bytes Packet that had a great difference in the results. The results using raw data says both samples does not come from the same distribution with a significant difference, however if we use distributions the result says that only the 1000Bytes packet does not come from the same distribution. Bellow you will find the graphs for the distributions that were created and the cumulative frequency in both cases plotted one above other (in order to see the difference between the distributions).
| Raw data - 100 Packets | Distribution - 100 Packets | Raw data - 1000 Packets | Distribution - 1000 Packets | |
|---|---|---|---|---|
| D-stat | 0.194674 | 0.039323 | 0.205525 | 0.194379 |
| P-value | 4.57E-14 | 0.551089 | 2.07E-14 | 7.32E-14 |
| D-crit | 0.0667 | 0.067051 | 0.0667 | 0.067051 |
| Size of Raspberry | 816 | 816 | 816 | 816 |
| Size of Pinger | 822 | 822 | 822 | 822 |
| Alpha | 0.05 | |||
If D-stat is greater than D-crit the samples are not considerated from the same distribution with a (1-Alpha) of accuracy. Remember that D-stat is the maximum difference between the two cumulative frequency curves.
Source: http://www.real-statistics.com/non-parametric-tests/two-sample-kolmogorov-smirnov-test/