INFERENTIAL STATISTICS NON-PARAMETRIC TESTS Non-parametric Tests When one of the assumptions of a Parametric Test is violated (especially Normality), it is not appropriate to use them anymore; you should use the Nonparametric Statistics instead. Non-parametric Tests are distribution-free and are used when the variables of interest are Categorical. Also note, as established earlier, the less you know about the population, the less certain the results of your analysis become (since the non-parametric tests require less information than the parametric, classical, tests; they are always less precise).
Wilcoxon’s Signed-ranks Test When the dataset is quantifiable but the variables themselves are ordinal or not normally distributed, the non-parametric Wilcoxon Signed-ranks Test may be used to obtain a confidence interval for the difference in population medians.
Wilcoxon’s Signed-ranks Test Hypotheses 1. H : The median difference in the population is equal to zero. 2. H : The median difference in the population is not equal to zero. 0
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Wilcoxon’s Signed-ranks Test Example The table below contains the results of a case–control study on the dietary intake of people with schizophrenia in Scotland. It shows the daily energy intake of two dietary substances for the cases and the controls.
Intake/day
Cases (m=30)
Controls (n=30)
Median difference (95% CI)
Sig.
Protein (g)
84.5 (38.4157.4)
96 (40.5-633)
15.9 (-1.1-32.8)
0.07
Alcohol (g)
0(0-19.4)
4.7 (0-80)
5.4 (1.2-9.9)
0.009
Interpretation: 1. The Protein Intake Median Difference CI includes 0 and p-value/sig. > 0.05: NO Statistically Significant Difference between the cases and the controls is noticed.
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