Non-parametric tests

Non-parametric tests
Non-parametric tests
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Non-parametric tests
PART A
QUESTION 1: Reasons for using non-parametric tests over parametric tests
We have parametric and non-parametric tests. The choice of test to be employed in a
given test depends on the distribution of a given data. For example, parametric tests are normally
very sensitive to distribution of data (normality). Therefore it is not appropriate to use a
parametric test in a distribution that is not normal (Dallal, 2012). The simple reason is that a
skewed distribution will greatly affect the measure of central tendency (mean). Thus if a
parametric test is employed in this case, the results will not be accurate. It is therefore necessary
to use a non-parametric test where data is not normally distributed.
Secondly, when the requirements of parametric test about sample size are not met, then a
non-parametric test becomes an alternative. Small sample sizes make it difficult for one to
sometimes determine the distribution. In this case the non-parametric tests come in handy.
Parametric tests are only capable of assessing continuous data which are again not affected by
outliers. However, non-parametric tests can be employed in ordinal and ranked data but not
affected by outliers.
QUESTION 2: Statistical Power in Non-Parametric Tests
According to central limit theorem, samples that appear to be large tend to be normally
distributed as opposed to small sample sizes (Field, 2013). In such cases parametric tests are
employed to conduct various tests Armstrong (2010). The large sample sizes translate to more
power making parametric tests to be considered more powerful than non-parametric tests.
Though calculating the power of tests is not popular with statisticians, (Forman, 2017) asserts
that the power of parametric tests can be calculated using a textbook formulae. However,
according to (Speer, 2006), some non-parametric tests might have more than parametric tests.
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Non-parametric tests
QUESTION 3
The table below shows some parametric tests and their non-parametric equivalents
Parametric test
Non-parametric test
equivalents
Dependent t-test Wilcoxon rank sum test
Independent samples t-test Mann-Whitney U test
Repeated measures ANOVA (one-
variable) Friedman two-way ANOVA
One-way ANOVA (independent) Kruskal-Wallis test
Pearson correlation Spearman correlation
Table1. Source: HealthKnowledge.org.uk (n.d.) and Dallal (2012).
The dependent t-test measures the difference in means of two paired variables.
Independent t-test on the other hand assesses the difference in means of two independent
variables. One way anova tests whether there is difference in the means of three variables.
Pearson correlation measures the extent of relationship between two variables while repeated
measures ANOVA compares variable groups that have been classified into two factors.
PART B
Non-Parametric Version of the Dependent T-test
Table of dependent t-test
Hypothesis
H0: Having undergone the creative course does not lead to higher marks in creative writing.
VERSUS
H1: Having undergone the creative course leads to higher marks in creative writing.
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