Many statistical tests assume that the data used are drawn from a normal population.
The principle of the method involves comparing the sample cumulative distribution function with the cumulative distribution function of the hypothesised distribution.
If the experimental data depart substantially from the expected distribution, the two functions will be widely separated.
If, however, the data are closely in accord with the expected distribution, the two functions will never be very far apart.
The test statistic is given by the maximum difference between the two functions (Dx)exp and is compared in the usual way with a set of tabulated values (D)crit.
The data are next transformed by using the above equation and then the Kolmogorov–Smirnov method is applied.
This test is illustrated in the example given in “Statistical Treatment of Analytical Data - One-Sample t-test in Chemical Analysis” using SPSS.
The Kolmogorov–Smirnov test in SPSS shows that the data tested are normally distributed at the 95% confidence level (Figure I.1) The same data are tested below using an online Normal Distribution Calculator (Kolmogorov-Smirnov test).
The data are inserted or copied in the yellow-labeled cells and the confidence level is selected from the drop-down list (in this case 95%).
The median, 15% trimmed mean, mean, standard deviation, # of data, Dexp, Dcrit and the Result is calculated (Fig. The result is consistent with the SPSS test showing that the tested data are normally distributed.
A first indication of normally distributed data is given by the fact that mean≈ median ≈ 15% trimmed mean.
S system, which was developed at Bell Laboratories by John Chambers et al. The term “environment” is intended to characterize it as a fully planned and coherent system, rather than an incremental accretion of very specific and inflexible tools, as is frequently the case with other data analysis software.