SAMPLES DISTINCTION BY PARAMETRIC AND NONPARAMETRIC STATISTICS IN SPSS
DOI:
https://doi.org/10.17770/sie2019vol5.3779Keywords:
t-test, independent samples, paired samples, SPSSAbstract
Testing samples distinction is necessary in a wide range of practical tasks. Medicine, sociology, psychology, marketing - this is a short list of industries where it is required to conduct tests that establish effectiveness or inefficiency of a certain technology.
Diversity of situations and techniques applied to sample distinction create a problem for compliance of testing procedures. The problem rises for tests including large and small samples (dependent or independent) with various distributions. The article proposes a list of problems created by testing differences between two samples. Limits of applicability of parametric and non-parametric tests are established based on selected distribution. Informative examples are included based on simulated data.
SPSS software was used for sample distinction tests. It is important to double-check the operation of the machine computing procedure "manually” to understand the nature of tests and in educational purposes. The article provides mathematical illustration for the algorithms used, which can be considered as supplementary information for SPSS help.
Downloads
References
IBM Knowledge Center. https://www.ibm.com/support/knowledgecenter
Gosset [Student, pseud.], W. S. (1908). The probable error of a mean. Biometrika, 6, 1–2.
Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione. Giornale dell’ Istituto Italiano degli Attuari 4, 83–91.
Luke K., Corrine M. and Ismail W. (2012). Strengthening the Experimenter's Toolbox: Statistical Estimation of Internal Validity American Journal of Political Science, Vol. 56, No. 2 , pp. 484-499.
Mann, H. B., and D. R. Whitney. (1947). On a test of whether one of two random variables is stochastically larger than the other. Annals of Mathematical Statistics, 18, 50–60.
Moses, L. E. (1952). Non-parametric statistics for psychological research. Psychological Bulletin, 49, 122-143.
Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin 2, 110–114.
Smirnov, N. V. (1933). Estimate of deviation between empirical distribution functions in two independent samples. Bulletin Moscow University, 2, 3–16.
Sprent, P. and Smeeton, N. (2007). Applied Nonparametric Statistical Methods. 4th ed. Boca Raton, FL: Chapman & Hall/CRC.
Official website SPSS. https://www.ibm.com/products/spss-statistics
Wald, A. and Wolfowitz, J. (1940). On a test whether two samples are from the same population. Ann. Math Statist., 11, 147-162.
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics, 1, 80–83.