A introduction to non-parametric tests

Saudi Board of Preventive Medicine, Riyadh Ministry 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

Outline
• Some common terms
• Difference between parametric and
nonparametric tests
• When to use NPT
• Advantages & disadvantages
• Commonly used NPT
• Take home messages
2Nov 2019

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

Parametric & nonparametric concept
• Most of the statistical methods referred to as parametric
require the use of interval- or ratio-scaled data.
• Nonparametric methods are often the only way to analyze
nominal or ordinal data and draw statistical conclusions.
• Nonparametric methods require no assumptions about the
population probability distributions.
• Nonparametric methods are often called distribution-free
methods.
4Nov 2019

Parametric test procedures
• Involve population parameters (mean)
• Have stringent assumptions (normality)
• Examples: Z test, t test
5Nov 2019

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

Assumptions of t test
• The sampling distribution is normally distributed
– For N <30 if the sample data is normally distributed then
the sampling distribution will also be normal
• The data should come from an interval or ratio scale
• In practice an ordinal scale with 5 or more levels is ok
7Nov 2019

Examples of nonnormal distributions
8Nov 2019

Assumptions of t test (contd.)
• There should not be extreme scores or outliers, because these
have a disproportionate influence on the mean and the
variance
• For the independent samples t test the variance in the two
samples should be approximately equal
– This assumption is more important if sample size < 30 and / or sample
sizes are unequal
– As a rule of thumb, if the variance of one group is 3 or more times
greater than the variance of the other group, then use non-parametric
9Nov 2019

What are nonparametric tests?
• ‘Non-parametric’ tests were developed for these situations
where fewer assumptions have to be made.
• Sometimes called distribution-free tests.
• NP tests can be applied to Normal data but parametric tests
have greater power if assumptions are met.
10Nov 2019

How to check for normality of data?
1. Thumb rules
a) Mean & Range & SD
b) Skewness and 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-Bera test
c) Shapiro-Wilks test
d) Kolmogorov-Smirnov test
e) D’Agostino test
f) Grubbs and Dixon test (for
outliers)
4. Comparing non-parametric
and parametric test results
11Nov 2019

Distribution-free tests
• Distribution-free tests are statistical tests that do not rely on
any underlying assumptions about the probability distribution
of the sampled population.
• The branch of inferential statistics devoted to distribution-free
tests is called nonparametrics.
• Nonparametric statistics (or tests) based on the ranks of
measurements are called rank statistics (or rank tests).
12Nov 2019

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

Rules for NPT
• In general, for a statistical method to be classified as
nonparametric, it must satisfy at least one of the
following conditions.
– The method can be used with nominal data.
– The method can be used with ordinal data.
– The method can be used with interval or ratio data when
no assumption can be made about the population
probability distribution.
14Nov 2019

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-test Mann-Whitney test (Wilcoxon Rank Sum)
One-way Analysis of Variance Kruskal-Wallis
Pearson’s correlation Spearman Rank
Repeated Measures Friedman
… many more … many more
15Nov 2019

Types of NPT
16Nov 2019

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

Disadvantages of nonparametric tests
• May waste information
– Parametric model more efficient if data permit
• Difficult to compute by hand for large samples
• Tables not widely available
• Used only to test hypotheses, not for estimation purposes
18Nov 2019

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

Take home messages
• Fewer assumptions than parametric tests
• So useful when these assumptions not met
• Often used when sample size is small and difficult to tell if
normally distributed
• Ragbag of tests developed over time with no consistent
framework
20Nov 2019

THANK YOU
Kindly email your queries to sarizwan1986@outlook.com
21Nov 2019

A introduction to non-parametric tests

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