Non-parametric tests

This document provides an overview of non-parametric tests, including their advantages over parametric tests and their equivalents. It also discusses the statistical power of non-parametric tests and provides examples of their application in different scenarios.

Non-parametric tests
Non-parametric tests
Student name:
Instructor:
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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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Non-parametric tests
Source: Author
Table 2
The dependent t-test made us conclude that there was a major statistical difference in the
means of the two variables (scores before creative writing course and scores after creative
writing course). The null hypothesis asserts that the writing course does not translate into
increased scores for creativity. This means that the mean mark of creative writing after the
training course remain almost the same. The alternative hypothesis asserts that the writing course
did translate into increased scores for creativity. From table 2 above, it can be observed that
mean difference of the two variables is 0.2. The p-values calculated (0.508 and 0.708) are all
greater than the level of significance which is 0.05. The decision therefore is that the null
hypothesis is not rejected. The conclusion of the test is that having undergone the creative course
does not lead to higher marks in creative writing. It can therefore be concluded that the non-
parametric equivalent of dependent t-test (Wilcoxon rank sum test) suggests that the null
hypothesis should be accepted. Thus there are no differences in conclusion.
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Non-parametric tests
Non-Parametric Version of the Independent T-test
Hypothesis
H0: Creativity score for the two tests are not independent.
VERSUS
H1: Creativity score for the two tests are independent.
Source: Author
Table 3
The table above represents the results of the Mann-Whitney test which is the counterpart
of the independent t-test. The null hypothesis states that the two variables are dependent while
the alternative hypothesis states that the two variables are independent. From the table above, it
can be observed that the p-value calculated is 0.1 while the significance level is 0.05. The p-
value is less compared to the level of significance. This therefore means that the null hypothesis
is rejected. It is concluded therefore that creativity score for the two tests are independent. The
independent t-test results are t (78) = -1.595, p=0.115. Thus the conclusion from the two tests is
the same.
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Non-parametric tests
Non-Parametric Version of the Single Factor ANOVA
Hypothesis
H0: The mean Systolic BP and Diastolic BP recorded at each location of the population.
VERSUS
H1: At least one mean is different.
Ranks
Setting N Mean Rank
Systolic Blood Pressure
Home (control) 10 14.25
Doctor's office 10 22.80
Classroom 10 9.45
Total 30
Diastolic Blood Pressure
Home (control) 10 15.75
Doctor's office 10 16.30
Classroom 10 14.45
Total 30
Source: Author
Test Statisticsa,b
Systolic Blood
Pressure
Diastolic Blood
Pressure
Chi-Square 11.851 .237
df 2 2
Asymp. Sig. .003 .888
a. Kruskal Wallis Test
b. Grouping Variable: Setting
Source: Author
Table 4
The table above represents the results of the Kruskal Wallis test which is the counterpart
of the anova test. The null hypothesis state that the three variables have the same mean while the
alternative hypothesis states that at least one variable has a different mean. From the table above,
it can be observed that the p-value calculated is 0.003 while the significance level is 0.05. The p-
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Non-parametric tests
value is less compared to the level of significance. This therefore means that the null hypothesis
is rejected. It is concluded therefore that at least one mean is different. The anova test results are
F (2, 27) = 9.964, p=0.001. Thus the conclusion from the two tests is the same.
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References
Field, A. (2013). Discovering statistics using IBM SPSS statistics. Washington D.C.:
SagePublications, Inc.
Speer, J. (2016). Comparison of parametric and nonparametric tests for differences in
distribution. Proceedings of the NCUR 2016
Armstrong, R. (2010). Sample size estimation and statistical power analysis
HealthKnowledge.org.uk (n.d.). Parametric and non-parametric tests for comparing two or more
groups. Retrieved from https://www.healthknowledge.org.uk/public-health-textbook/research-
methods/1b-statistical-methods/parametric-nonparametric-tests
Dallal, G.E. (2012, May 22). Nonparametric statistics. Retrieved from
http://www.jerrydallal.com/lhsp/npar.htm
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Appendix
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Non-parametric tests
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