Parametric and non parametric

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FACULTY OF SCIENCE & MATHEMATICS
QUANTITATIVE RESEARCH METHOD
SRU 6024
Assignment:
Parametric and Non Parametric Data
Prepared for:
Dr. Che Nidzam binti Che' Ahmad
Prepared by:
Putri Nadia Binti Zulkifli
M20121000113
Submission date:
29th
November 2013
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Parametric and Non Parametric Data
A potential source of confusion in working out what statistics to use in analysing data
is whether your data allows for parametric or nonparametric statistics. The
importance of this issue cannot be underestimated. If researcher get it wrong you it
may risk using an incorrect statistical procedure or it may use a less powerful
procedure.
The basic distinction for paramteric versus nonparametric is:
• If your measurement scale is nominal or ordinal, then you use non
parametric statistics;
• If you are using interval or ratio scales, then you use parametric
statistics.
Nonparamteric statistical procedures are less powerful because they use less
information in their calulation. For example, a parametric correlation uses information
about the mean and deviation from the mean while a nonparametric correlation will
use only the ordinal position of pairs of scores.
There are other considerations which have to be taken into account:
You have to look at the distribution of your data. If your data is supposed
to take parametric statistics, you should check that the distributions are
approximately normal.
The best way to do this is to check the Skew and Kurtosis measures
from the frequency output from SPSS. For a relatively normal distribution:
skew ~= 1.0
kurtosis~=1.0
If a distribution deviates markedly from normality then you take the risk that
the statistic will be inaccurate. The safest thing to do is to use an equivalent non
parametric statistic.
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Data are grouped as Nominal, Ordinal, Interval and Ratio (NOIR) and they are
ordered in their increasing accuracy, powerfulness of measurement, preciseness
and wide application of statistical techniques. Further, the nominal and ordinal data
are qualitative (categorical), whereas interval and ratio data are quantitative
(numerical). There are two broad groups of statistical tests, namely, parametric tests
and nonparametric tests.
Interval and ratio data are parametric, and are used with parametric tools in
which distributions are predictable and often Normal. Nominal and ordinal data are
nonparametric, and do not assume any particular distribution. They are used with
nonparametric tools such as the Histogram.
Parametric data follows particular rules and mathematical algorithms. As a
result detailed conclusions may be drawn about the data. Experiments are thus often
designed to use parametric data. There are very different parametric and non
parametric tests used in analysis, depending on the type of data you chose during
the design.
Parametric tests require measurements equivalent to at least an interval
scale and assume that certain properties of parent population like:
i) observations are from a normally distributed population
ii) the study is based on large sample (>30)
iii) population parameters like mean, variance, etc. are known.
Nonparametric tests do not depend on the shape of the distribution of the
population and hence are known as distributionfree tests. In other words, they do
not depend on any assumptions about properties or parameters of the parent
population. Most nonparametric tests assume nominal or ordinal data. Non
parametric tests require more observations than parametric tests to achieve the
same size of Type I and Type II errors. Nonparametric tests have the relative
advantages that they do not require to satisfy stringent assumptions like that of
parametric tests. In other words, nonparametric tests make minimal demands in
terms of prerequisites. They are also much less cumbersome to use as far ascomputational techniques are concerned. They are most useful when dealing with
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qualitative variables and with data that can be classified in order or as ranks. Some
of the common nonparametric tests are ChiSquareTest, The Sign Test, The Mann
Whitney UTest, The Runs test for Randomness and The KruskalWallis H Test.
As the table below shows, parametric data has an underlying normal
distribution which allows for more conclusions to be drawn as the shape can be
mathematically described.
Parametric Nonparametric
Assumed distribution Normal Any
Assumed variance Homogeneous
Any
Typical data Ratio or Interval Ordinal or Nominal
Data set relationships Independent Any
Usual central measure Mean Median
Benefits Can draw more conclusionsSimplicity;
Less affected by outliers
Tests
Choosing Choosing parametric test
Choosing a nonparametrictest
Correlation test Pearson Spearman
Independent measures,
2 groups
Independentmeasures
ttestMannWhitney test
Independent measures,> 2 groups
Oneway,independentmeasures ANOVA
KruskalWallis test
Repeated measures,2 conditions
Matchedpair ttest Wilcoxon test
Repeated measures,> 2 conditions
Oneway,repeated measures ANOVA
Friedman's test
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The chart below can be use to determine the type of the data (column) and
the purpose of the data analysis (row). Then find the intersection of the relevant row
and column. The appropriate statistical test is shown. This is not an exhaustive list of
statistical tests, but illustrative only.