The paired differences are independent.

Each paired difference comes from a continuous distribution that is symmetric, with the same center of symmetry. Strictly speaking, the population distributions need not be the same for all the paired differences. However, if we want a consistent test, we assume that the paired differences all come from the same continuous, symmetric distribution. (The Wilcoxon signed rank test is a nonparametric test. We need not specify or know what the distribution is, only that all the paired difference follow the same one.)

The paired differences all have the same median. (This median will also be the center of symmetry for the population distribution associated with each paired difference. Moreover, since the mean of a continuous symmetric distribution is equal to its median, this means that the paired differences will also all have the same mean.)

Because the test statistic for the Wilcoxon signed rank is based only on the ranks of the paired differences, the test can be performed when the only data available are those relative ranks for the paired differences.

The two-sample paired signed rank test is equivalent to performing a one-sample signed rank test on the paired differences.

**Ways to detect**before performing the signed rank test whether your data violate any assumptions.**Ways to examine**signed rank test results to detect assumption violations.**Possible alternatives**if your data or signed rank test results indicate assumption violations.

- Brownlee, K. A. 1965.
*Statistical Theory and Methodology in Science and Engineering.*New York: John Wiley & Sons. - Conover, W. J. 1980.
*Practical Nonparametric Statistics.*2nd ed. New York: John Wiley & Sons. - Daniel, Wayne W. 1978.
*Applied Nonparametric Statistics.*Boston: Houghton Mifflin. - Daniel, Wayne W. 1995.
*Biostatistics.*6th ed. New York: John Wiley & Sons. - Hollander, M. and Wolfe, D. A. 1973.
*Nonparametric Statistical Methods.*New York: John Wiley & Sons. - Lehmann, E. L. 1975.
*Nonparametrics: Statistical Methods Based on Ranks.*San Francisco: Holden-Day. - Miller, Rupert G. Jr. 1986.
*Beyond ANOVA, Basics of Applied Statistics.*New York: John Wiley & Sons. - Rosner, Bernard. 1995.
*Fundamentals of Biostatistics.*4th ed. Belmont, California: Duxbury Press. - Sokal, Robert R. and Rohlf, F. James. 1995.
*Biometry.*3rd. ed. New York: W. H. Freeman and Co. - Zar, Jerrold H. 1996.
*Biostatistical Analysis.*3rd ed. Upper Saddle River, NJ: Prentice-Hall.

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