Rmnon Parametric Test

7/28/2019 Rmnon Parametric Test

1/8

NON PARAMETRIC TEST


2/8

NON PARAMETRIC TEST

Some of the important non-parametric test are

1)Rank Correlation

2)Sign Test

3)Wilcoxon Test

4)U Test

5)Kendals coefficient of concordance

The use of parametric statistics is based on the assumption that the population

from which the sample is drawn is normally distributed & data are collected on aninterval or ratio scale. Nonparametric statistics on the other hand make no explicit

assumption regarding the normality of distribution in the population & are used

when the data are collected on a nominal or ordinal scale.

CORRELATION

Rank correlation

a) when ranks are given

r = 1 6 D/ N3 N

b) when ranks are not given

Ranks are not repeated when ranks are assigned

Ranks are repeated when ranks are assigned


3/8

SIGN TEST

Sign test uses signs (+ & - ) to replace the data. Let us assume that two pairs of

data X & Y are given. Each element of the series is compared with the data

element of another series. If the first element of X series , for example is

greater than the first element Y series, we write + sign. Let us assume that thesecond element of X series is less than the second element of Y series , we

write sign & so on. If the difference is 0 ,it will not be counted while

considering n. Under this test we assume that the null hypothesis that + & -

signs are equally distributed i.e. p & q will have equal proportion ( )

.Approach of normal curve is used while accepting or rejecting the hypothesis P (s) > value of the normal curve = Accept

P (s) < value of the normal curve = Reject


4/8

WILCOXON TEST (SIGNED RANK TESTS)

The wilcoxon signed ranks test applies to two sample designs involving repeated

measures, matched pairs or before & after measures. Under this method ,

difference between each observation is measured & ranks are assigned either on

the ascending order or descending order. While applying the ranks , signs areignored for the time being. Depending upon whether the difference is a positive

value or negative value ,signs are assigned. Sign + is assigned for positive

difference & - sign for the negative values. For zero , no signs are assigned

.Smaller of the two sums of the signed ranks is taken & compared with the table

value to accept the hypothesis or not.

U TEST

It is one of the best known non parametric tests' test is also called the Mann-

Whitney-Wilcoxon (MWW) ,Wilcoxon rank-sum test, or WilcoxonMann-Whitney

test. This test is used for assessing whether two independent samples of

observations have come from the same distribution. If the calculated probability of U is greater than the significant value 0.05, Ho is

accepted else Ho is rejected


5/8

KENDAL S COEFFICIENT OF CONCORDANCE

Kendals coefficient of concordance (W) is a measure of association between K

rankings on N individuals i.e. .a set of N individuals are ranked on each of K

variables & these rankings are to be compared. This measure is used to test

association between three or more sets of ranking .This is applicable where N is

less than or equal to 7.The formula used to calculate w is given under

W = S/ 112 k2 (N3 N )

Accept or Reject criteria

If the value of S calculated is greater than or equal to the table value , then HO Irejected & viceversa.Ho here refers to K sets of ranking are independent.


6/8

KRUSKAL WALLIS

The kruskal wallis one way analysis of variance is the nonparametric test used

when the dependent variable is on an ordinal scale , & the independent

variable is normally scaled . MULTIVARIATE ANALYSIS FACTOR

It examines several variables & their relationships simultaneously ,in contrast to

bivariate analyses which examine relationships between two variables &

univariate analyses where one variable at a time is examined for generalization

from the sample to the population. MANOVA is similar to ANOVA with the difference that ANOVA tests the mean

differences of more than two groups on one dependent variable , whereas

MANOVA tests mean differences among groups across several dependent

variables simultaneously by using sums of squares & cross product matrices.

MANOVA circumvents bias by simultaneously testing all the dependentvariables , cancelling out the effects of any intercorrelations among them

In MANOVA tests the independent variable is measured on a nominal scale &

the dependent variables on an interval or ratio scale.


7/8

CLUSTER

Cluster analysis is used to classify objects or individuals into mutually exclusive

& collectively exhaustive groups with high homogeneity within clusters & low

homogeneity between clusters.

In other words cluster analysis helps to identify objects that are similar to one

another based on some specified criterion. For instance if our sample consists

of a mix of respondents with different brand preferences for a product , cluster

analysis will cluster individuals by their preferences for each of the different

brands

MULTIDIMENSIONAL SCALING

It groups objects in multidimensional space. Objects that are perceived by

respondents to be different are distanced , & the greater the perceptual

differences , the greater the distance between the objects in the

multidimensional space. In other words multidimensional scaling provides a

spatial portrayal of respondents perception of products, services, or other

items of interest & highlights the perceived similarities & differences


8/8

DISCRIMINANT ANALYSIS

It helps to identify the independent variables that discriminate a normally

scaled dependent variable of interest- say those who are high on a

variable from those who are low on it. The linear combination of

independent variables indicates the discriminating function showing thelarge difference that exists in the two group means. In other words the

independent variables measured on an interval or ratio scale discriminate

the groups of interest to the study

Documents

Rmnon Parametric Test