A introduction to non-parametric tests

A introduction to non-parametric tests

1. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Non-parametric tests
An introduction
Dr. S. A. Rizwan, M.D.,
Public Health Specialist,
Saudi Board of Preventive Medicine,
Riyadh, Kingdom of Saudi Arabia.
1Nov 2019

2. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Outline
•Some common terms
•Difference between parametric and
nonparametric tests
•When to use NPT
•Advantages & disadvantages
•Commonly used NPT
•Take home messages
2Nov 2019

3. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Introduction
•Parametric methods
–They are based in means, standard deviations or
parameters of distributions
•The Normal distribution is not always appropriate
–To study variables with a few observations
–Non-symmetrical distributions
3Nov 2019

4. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Parametric & nonparametric concept
•Mostofthestatisticalmethodsreferredtoasparametric
requiretheuseofinterval-orratio-scaleddata.
•Nonparametricmethodsareoftentheonlywaytoanalyze
nominalorordinaldataanddrawstatisticalconclusions.
•Nonparametricmethodsrequirenoassumptionsaboutthe
populationprobabilitydistributions.
•Nonparametricmethodsareoftencalleddistribution-free
methods.
4Nov 2019

5. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Parametric test procedures
•Involve population parameters (mean)
•Have stringent assumptions (normality)
•Examples: Z test, t test
5Nov 2019

6. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Nonparametric test procedures
•Do not involve population parameters
•Data measured on any scale (ratio or interval, ordinal or
nominal)
•Example: Wilcoxon rank sum test
6Nov 2019

7. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Assumptions of t test
•Thesamplingdistributionisnormallydistributed
–ForN<30ifthesampledataisnormallydistributedthen
thesamplingdistributionwillalsobenormal
•Thedatashouldcomefromanintervalorratioscale
•Inpracticeanordinalscalewith5ormorelevelsisok
7Nov 2019

8. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Examples of nonnormaldistributions
8Nov 2019

9. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Assumptions of t test (contd.)
•Thereshouldnotbeextremescoresoroutliers,becausethese
haveadisproportionateinfluenceonthemeanandthe
variance
•Fortheindependentsamplesttestthevarianceinthetwo
samplesshouldbeapproximatelyequal
–Thisassumptionismoreimportantifsamplesize<30and/orsample
sizesareunequal
–Asaruleofthumb,ifthevarianceofonegroupis3ormoretimes
greaterthanthevarianceoftheothergroup,thenusenon-parametric
9Nov 2019

10. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
What are nonparametric tests?
•‘Non-parametric’testsweredevelopedforthesesituations
wherefewerassumptionshavetobemade.
•Sometimescalleddistribution-freetests.
•NPtestscanbeappliedtoNormaldatabutparametrictests
havegreaterpowerifassumptionsaremet.
10Nov 2019

11. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
How to check for normality of data?
1.Thumb rules
a)Mean & Range & SD
b)Skewnessand kurtosis
c)Compare mean, median &
mode
d)Trimmed mean
e)Outliers
2.Graphs
a)Histogram with theoretical
normal curve
b)QQ plot
c)Box plot and outlier
detection
d)Stem and leaf plot
3.Formal statistical tests
a)W/S test
b)Jarque-Beratest
c)Shapiro-Wilkstest
d)Kolmogorov-Smirnov test
e)D’Agostinotest
f)Grubbs and Dixon test (for
outliers)
4.Comparing non-parametric
and parametric test results
11Nov 2019

12. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Distribution-free tests
•Distribution-freetestsarestatisticalteststhatdonotrelyon
anyunderlyingassumptionsabouttheprobabilitydistribution
ofthesampledpopulation.
•Thebranchofinferentialstatisticsdevotedtodistribution-free
testsiscallednonparametrics.
•Nonparametricstatistics(ortests)basedontheranksof
measurementsarecalledrankstatistics(orranktests).
12Nov 2019

13. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Ranks
•Practical differences between parametric and NP are that NP
methods use the ranks of values rather than the actual values
•E.g.
–1,2,3,4,5,7,13,22,38,45 -actual
–1,2,3,4,5,6,7,8,9,10 -rank
13Nov 2019

14. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Rules for NPT
•Ingeneral,forastatisticalmethodtobeclassifiedas
nonparametric,itmustsatisfyatleastoneofthe
followingconditions.
–Themethodcanbeusedwithnominaldata.
–Themethodcanbeusedwithordinaldata.
–Themethodcanbeusedwithintervalorratiodatawhen
noassumptioncanbemadeaboutthepopulation
probabilitydistribution.
14Nov 2019

15. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Parametric / Nonparametric tests
Parametric Tests Non-parametric Tests
Single sample t-test Wilcoxon-signed rank test
Paired sample t-test Paired Wilcoxon-signed rank
2 independent samples t-testMann-Whitney test (Wilcoxon Rank Sum)
One-way Analysis of VarianceKruskal-Wallis
Pearson’s correlation Spearman Rank
Repeated Measures Friedman
…many more …many more
15Nov 2019

16. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Types of NPT
16Nov 2019

17. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Advantages of nonparametric tests
•Used with all scales
•Easier to compute, developed originally before wide
computer use
•Make fewer assumptions
•Need not involve population parameters
•Results may be as exact as parametric procedures
17Nov 2019

18. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Disadvantages of nonparametric tests
•Maywasteinformation
–Parametricmodelmoreefficientifdatapermit
•Difficulttocomputebyhandforlargesamples
•Tablesnotwidelyavailable
•Usedonlytotesthypotheses,notforestimationpurposes
18Nov 2019

19. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Limitations of nonparametric methods
•Converting ratio level data to ordinal ranked data entails a loss
of information
•This reduces the sensitivity of the non-parametric test
compared to the parametric alternative in most circumstances
–sensitivity is the power to reject the null hypothesis, given that it is
false in the population
–lower sensitivity gives a higher type 2 error rate
•Many parametric tests have no non-parametric equivalent
–e.g. Two way ANOVA, where two IV’s and their interaction are
considered simultaneously
19Nov 2019

20. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
Take home messages
•Fewerassumptionsthanparametrictests
•Sousefulwhentheseassumptionsnotmet
•Oftenusedwhensamplesizeissmallanddifficulttotellif
normallydistributed
•Ragbagoftestsdevelopedovertimewithnoconsistent
framework
20Nov 2019

21. Saudi Board of Preventive Medicine, RiyadhMinistry of Health, KSA
Dr. S. A. Rizwan, M.D.Demystifying statistics series: Meta-analysis course
THANK YOU
Kindly email your queries to [email protected]
21Nov 2019