Tuesday, June 02, 2009

Paired t-test assumption of normality

It is important to remember that paired t-test is valid if the differences of pairs of variables are normally distributed. It appears that the variables itself do not need to be normally distributed, as paired t-test only operates on the differences. This observation is based on [Bland2000, p. 161 and 260].

Normality of a sample can be evaluated using Q-Q plots [Bland2000, ch. 7.5]. However, the problem with these plots is that they are not objective, i.e. for one person a sample is normally distributed, for other person the same sample may be only approximately normally distributed while for the third person it is not normally distributed. For that reason quantitative methods are better. One of such methods is Shapiro-Wilk test. The other method is Kolmogorov-Smirnov test. For small samples (i.e. 50) Shapiro-Wilk is generally more accurate [Marques2003 p.157].

If sample was found to be non Normal, Wilcoxon signed-rank test (called also Wilcoxon matched pairs test) can be used [Bland2000, ch.12.3].

All the above tests can be performed easily in SPSS.

Bland, Martin. An Introduction to Medical Statistics 3th ed, Oxford University Press, 2000
J. P. Marques de Sá Applied statistics: using SPSS, STATISTICA, and MATLAB, Springer, 2003

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