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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 non-parametric 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 non-parametric 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.

Non-paramteric 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 non-parametric 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 non-parametric 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

non-parametric, and do not assume any particular distribution. They are used with

non-parametric 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.

Non-parametric  tests do not depend on the shape of the distribution of the

population and hence are known as distribution-free tests. In other words, they do

not depend on any assumptions about properties or parameters of the parent

population. Most non-parametric 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. Non-parametric tests have the relative

advantages that they do not require to satisfy stringent assumptions like that of

parametric tests. In other words, non-parametric tests make minimal demands in

terms of pre-requisites. 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 non-parametric tests are Chi-SquareTest, The Sign Test, The Mann-

Whitney U-Test, The Runs test for Randomness and The Kruskal-Wallis 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  Non-parametric 

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 non-parametrictest 

Correlation test Pearson  Spearman 

Independent measures,

2 groups

Independent-measures

t-testMann-Whitney test  

Independent measures,> 2 groups

One-way,independent-measures ANOVA

Kruskal-Wallis test

Repeated measures,2 conditions

Matched-pair t-test   Wilcoxon test

Repeated measures,> 2 conditions

One-way,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.