What Are Non Parametric Methods! (1)

8/12/2019 What Are Non Parametric Methods! (1)

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What are non parametric methods? A commonly used method in statistics where

small sample sizes are used to analyze nominal data. Non-parametric method is used when the researcher does notknow anything about the parameters of the sample chosen

from the population. Non-parametric statistics (in the sense of a statistic over data,

which is defined to be a function on a sample that has nodependency on a parameter), whose interpretation does notdepend on the population fitting any parameterised

distributions. Order statistics, which are based on the ranks of observations,

are one example of such statistics and these play a central rolein many non-parametric approaches.


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Non-parametric methods are widely used forstudying populations that take on a rankedorder (such as movie reviews receiving one to

four stars). The use of non-parametric methodsmay be necessary when data have a rankingbutno clear numerical interpretation, such aswhen assessing preferences. In terms of levels

of measurement, non-parametric methodsresult in "ordinal" data.
http://en.wikipedia.org/wiki/Rankinghttp://en.wikipedia.org/wiki/Rankinghttp://en.wikipedia.org/wiki/Numericalhttp://en.wikipedia.org/wiki/Preferenceshttp://en.wikipedia.org/wiki/Preferenceshttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Preferenceshttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Level_of_measurementhttp://en.wikipedia.org/wiki/Preferenceshttp://en.wikipedia.org/wiki/Numericalhttp://en.wikipedia.org/wiki/Ranking


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Types of Non-parametric MethodsThe two commonly used non-parametric correlations are :

Spearmans Rank Correlation

Kendall Tau


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Spearman's Rank Correlation In statistics, Spearman's rank correlation

coefficientor Spearman's rho, named after CharlesSpearman and often denoted by the Greek letter (rho) or

as , is a non-parametric measure of statisticaldependence between two variables.

It assesses how well the relationship between two variablescan be described using a monotonic function.

If there are no repeated data values, a perfect Spearmancorrelation of +1 or 1 occurs when each of the variables is aperfect monotone function of the other.


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Two sets of variables are taken and ranks are assigned

according to their positions in the ascending order of thevalues.

Differences between the ranks of each observation on thetwo variables are calculated, and is given by:


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Example :


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The standard error of the coefficient () wasdetermined by Pearson in 1907 and Gosset in 1920. It is


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Hypothesis If the value is -1, there is a perfect negative correlation If the value falls between -1 and -0.5, there is a strong negative

correlation If the value falls between -0.5 and 0, there is a weak negative

correlation If the value is 0, there is no correlation If the value falls between 0 and 0.5, there is a weak positive

correlation If the value falls between 0.5 and 1, there is a strong positive

correlation If the value is 1, there is a perfect positive correlation between

the 2 sets of data. If the value is 0, state that null hypothesis is accepted.

Otherwise, say it is rejected.


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Kendall Rank Correlation Coefficient

The Kendall rank correlation coefficient,commonly referred to as Kendall's tau ()

coefficient, is a statistic used to measurethe association between two measured quantities.A tau testis a non parametric hypothesis test forstatistical dependence based on the tau coefficient.

Specifically, it is a measure of rank correlation, i.e., thesimilarity of the orderings of the data when ranked byeach of the quantities. It is named after MauriceKendall, who developed it in 1938.


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Let (x1,y1), (x2,y2), , (xn,yn) be a set of observations

of the joint random variablesXand Yrespectively,such that all the values of (xi) and (yi) are unique.

Any pair of observations (xi,yi) and (xj,yj) are said tobe concordantif the ranks for both elements agree:

that is, if bothxi>xjandyi>yjor ifbothxi


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The Kendall coefficient is defined as:


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Hypothesis test

The Kendall rank coefficient is often used as a teststatistic in a statistical hypothesis test to establishwhether two variables may be regarded as statistically

dependent. This test is non-parametric, as it does notrely on any assumptions on the distributionsofXor Yor the distribution of (X,Y).


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Nonparametric methods are intuitive 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 whichassignation of scores to individual categories may be

inappropriate.For example, non-parametric methods

can be used to analyse soft drink consumption directlyusing the categories never, a few times per year,

monthly, weekly, a few times per week, daily and a fewtimes per day. In contrast, parametric methods requirescores (i.e. 17) to be assigned to each category.


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Disadvantages of Non-parametric Methods Nonparametric methods may lack power as compared

with more traditional approaches . This is a particularconcern if the sample size is small or if the assumptionsfor the corresponding parametric method.

Nonparametric methods are geared toward hypothesistesting rather than estimation of effects. It is oftenpossible to obtain nonparametric estimates andassociated confidence intervals, but this is not generallystraightforward.


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Tied values can be problematic when these arecommon, and adjustments to the test statistic may benecessary.

Appropriate computer software for nonparametric

methods can be limited, although the situation isimproving. In addition, how a software package dealswith tied values or how it obtains appropriate Pvaluesmay not always be obvious.


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Conclusion Non parametric methods helps statisticians to find out

the Non-Parametric along with Parametric methodshelps us in research in offices,hospitals,schools.etc.


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Year

Potatoes 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 71.30 59.50

1993 72.60 64.40

1994 66.70 65.60

1995 61.80 78.20

1996 58.70 82.80

1997 63.10 90.30

1998 59.60 72.30

1999 63.40 74.50

2000 68.60 79.40

Find the correlation between the price of

potatoes and onions.


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Year

Potatoes Prices

(Rs/1kg)

Onion Prices

(Rs/1kg)

Rank:

Potatoes

Rank:

Onions d d2

1988 66.60 69.10 6 7 -1 1

1989 69.50 66.10 9 6 3 9

1990 74.60 55.50 13 2 11 1211991 72.70 52.20 12 1 11 121

1992 71.30 59.50 10 3 7 49

1993 72.60 64.40 11 4 7 49

1994 66.70 65.60 7 5 2 4

1995 61.80 78.20 3 10 -7 49

1996 58.70 82.80 1 12 -11 121

1997 63.10 90.30 4 13 -9 81

1998 59.60 72.30 2 8 -6 36

1999 63.40 74.50 5 9 -4 16

2000 68.60 79.40 8 11 -3 9

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What Are Non Parametric Methods! (1)

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