I am studying the potential of DCT and FFT coefficients extracted from a signal to classify the different objects that emit the signal. I applied the Shapiro-Wilk to confirm that data was not normally distributed and proceeded with non-parametric testes (Kruskall-Wallis and Mann-Whitney). However, I see that the range of each variable (coefficient 1, coefficient 2, etc) is very wide, with small values (1) and very large (3000). Besides, I obtain p-value values such e-218, which makes me wonder if this is the correct approach or if any additional procedures must be conducted. This is my first work involving statistical analysis, any suggestion? I can't seem to find much procedures on such type of data in the literature.

Mann Whitney and Kruskall Wallis are appropriate tests to run if you are comparing two or multiple groups respectively of independent data that is not normally distributed. The range of values is irrelevant because these tests work with ordinal data as well as scale data. Low significance values with the Shapiro Wilk test indicate non-normality. Low significance values with the Mann Whitney and Kruskal Wallis tests indicate a significant difference between the distribution of groups.

It is widely believed, but not true, that we check data for normality before analysis. The assumptions for comparing means across groups apply to the residuals -- that they are homogeneous, normal, and independent. See for example Sokal and Rohlf 2011, 4th Edition. We have to obtain the residuals in order to evaluate the assumptions.

The statistical literature warns against statistical tests to evaluate assumptions and advocates graphical tools to evaluate the residuals (Montgomery & Peck 1992; Draper & Smith 1998, Quinn & Keough 2002). See also (Chatfield 1998; Gelman, Pasarica & Dodhia 2002). La¨a¨ ra¨ (2009) gives several reasons for not applying preliminary tests for normality, including: most statistical techniques based on normal errors are robust against violation; for larger data sets the central limit theory implies approximate normality; for small samples the power of the tests is low; and for larger data sets the tests are sensitive to small deviations (contradicting the central limit theory).

If you are comparing means across groups, run the ANOVA, obtain the residuals, and examine these. This can be done with a histogram or with what is called a QQplot.