Parametric vs non-parametric tests:
Generally, parametric tests are more powerful than non-parametric tests.
Parametric tests make the assumption that data is normally distributed. Non-parametric tests do not make this assumption.
Non-parametric tests look at the rank order of the values rather than absolute differences between them.
For the use of a parametric test, they data must be:
1) Normally distributed
2) Data should be of interval or ratio measurement
3) Homogeneity of variance
Homogeneity of variance:
The variance of the two populations that the sample is drawn from must have equal variances check variances of samples.
Guideline - if variance between samples is more than 4 times larger not equal parametric assumption is violated.
“Two-tailed” or “one-tailed” test?. Publications need to state which was used as the two will produce a different p value for the same data set.
One tailed test is more powerful – less likely to commit a type 2 error. Two tailed tests are more conservative and may need a larger treatment effect to get the same level of statistical significance. One-tailed tests are usually used when the direction of the difference is known in advance.
Equivalent Parametric and parametric tests:
Unpaired t-test Mann-Whitney U test
Paired t-test Wilcoxon matched pairs test
One-way ANOVA Kruskall-Wallis
Two-way ANOVA Two-way ANOVA by ranks
Chi square Fisher’s exact test
Pearson’s r Spearman’s r