What Are Non Parametric Methods!

5/28/2018 What Are Non Parametric Methods!

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Non Parametricethods


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What are Non Parametric Methods?

A commonly used method in statistics wheresmall sample sizes are used to analyze nominal data. Non-parametric method is used when the researcher does not

know anything about the parameters of the sample chosenfrom the population.

his method is sometimes referred to as parameter-free ordistribution-free method.


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Types of Non-parametric Methodshe two commonly used non-parametric correlations are !

"pearman#s $ank %orrelation

&endall#s au


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Spearman's Rank Correlation'n statistics( Spearman's rank correlation

or Spearman's rho( named after %harles "pearman andoften denoted by the )reek letter *rho+ or as ( is a non-

parametric measure of statistical dependence betweentwo ,ariables.

't assesses how well the relationship between two,ariables can be described using a monotonic function.

'f there are no repeated data ,alues( a perfect "pearmancorrelation of or / occurs when each of the ,ariablesis a perfect monotone function of the other.


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wo sets of ,ariables are taken and ranks are assigned

according to their positions in the ascending order of the,alues.

0ifferences between the ranks of each obser,ation on the two,ariables are calculated( and 1 is gi,en by!


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23ample !


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he standard error of the coefficient *+ was determinedby Pearson in 456 and )osset in 475. 't is


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$esults'f the ,alue is -( there is a perfect negati,e correlation

'f the ,alue falls between - and -5.8( there is a strong negati,e correlation

'f the ,alue falls between -5.8 and 5( there is a weak negati,e correlation

'f the ,alue is 5( there is no correlation'f the ,alue falls between 5 and 5.8( there is a weak positi,e correlation

'f the ,alue falls between 5.8 and ( there is a strong positi,e correlation

'f the ,alue is ( there is a perfect positi,e correlation between the 7 sets of data.

'f the ,alue is 5( state that null hypothesis is accepted. 9therwise( say it is re:ected.


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Kendalls Rank Correlation

he Kendalls rank correlation ( commonly referred toas Kendall's tau ( ( is a statistic method used to measure

the association between two measured ;uantities.

A tau testis a non parametric hypothesis test forstatistical dependence based on the tau coefficient.

"pecifically( it is a measure of rank correlation( i.e.( thesimilarity of the orderings of the data when ranked byeach of the ;uantities. 't is named after Maurice &endall(who de,eloped it in 4


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he &endall > coefficient is defined as!

%oncordant pairs 0iscordant pairs

%oncordant pairs 0iscordant pairs

$ange!- -.5 to .5


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@ypothesis test

he &endall#s rank correlation is often used in a statisticalhypothesis test to establish whether two ,ariables may beregarded as statistically dependent. his test is non-parametric( as it does not rely on any assumptions on thedistributions ofXor Yor the distribution of *X(Y+.


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!d"anta#es of Non-parametric Methods

Nonparametric methods re;uire no or ,ery limitedassumptions to be made about the format of the data( andthey may therefore be preferable when the assumptionsre;uired for parametric methods are not ,alid.

Nonparametric methods can be useful for dealing withune3pected( outlying obser,ations that might beproblematic with a parametric approach.


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Nonparametric methods are intuiti,e and are simple to

carry out by hand( for small samples at least.Nonparametric methods are often useful in the analysis of

ordered categorical data in which assignation of scores toindi,idual categories may be inappropriate.

or e3ample( non-parametric methods canbe used to analyse soft drink consumption directly using thecategories ne,er( a few times per year( monthly( weekly( afew times per week( daily and a few times per day. 'n

contrast( parametric methods re;uire scores *i.e. 6+ to beassigned to each category.


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$isad"anta#es of Non-parametric MethodsNonparametric methods may lack power as compared with

more traditional approaches . his is a particular concern ifthe sample size is small or if the assumptions for thecorresponding parametric method.

Nonparametric methods are geared toward hypothesistesting rather than estimation of effects. 't is often possibleto obtain nonparametric estimates and associated confidenceinter,als( but this is not generally straightforward.


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ied ,alues can be problematic when these are common(

and ad:ustments to the test statistic may be necessary.

Appropriate computer software for nonparametricmethods can be limited( although the situation isimpro,ing. 'n addition( how a software package deals withtied ,alues or how it obtains appropriateP ,alues may notalways be ob,ious.


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%onclusionhe use of non-parametric methods may be necessary when data ha,e a ranking

but no clear numerical interpretation( such as when assessing preferences.

Non-parametric methods make fewer assumptions(

heir applicability is much wider than the corresponding parametric methods. 'nparticular( they may be applied in situations where less is known about theapplication in ;uestion.

Also( due to the reliance on fewer assumptions( non-parametric methods aremore robust.

he use of non-parametric methods is simple and easy.

But the wider applicability and increased robustnessof non-parametric tests comesat a cost! in cases where a parametric test would be appropriate( non-parametrictests ha,e less power(or e3ample. larger sample size.


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YearBrinjal Prices

(Rs/1kg)Onion Prices

(Rs/1kg)

1988 66.60 69.10

1989 69.50 66.10

1990 74.60 55.50

1991 72.70 52.20

1992 71.0 59.50

199 72.60 64.40

1994 66.70 65.60

1995 61.80 78.20

1996 58.70 82.80

1997 6.10 90.0

1998 59.60 72.0

1999 6.40 74.50

2000 68.60 79.40

Find the correlation between the price ofbrinjals and onions.


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YearBrinjal Prices

(Rs/1kg)Onion Prices

(Rs/1kg)Rank!Brinjal

Rank!Onion " "2

1988 66.60 69.10 6 7 #1 1

1989 69.50 66.10 9 6 9

1990 74.60 55.50 1 2 11 1211991 72.70 52.20 12 1 11 121

1992 71.0 59.50 10 7 49

199 72.60 64.40 11 4 7 49

1994 66.70 65.60 7 5 2 4

1995 61.80 78.20 10 #7 49

1996 58.70 82.80 1 12 #11 121

1997 6.10 90.0 4 1 #9 81

1998 59.60 72.0 2 8 #6 6

1999 6.40 74.50 5 9 #4 16

2000 68.60 79.40 8 11 # 9

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What Are Non Parametric Methods!

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