Testing Sequential Connections in Contingency Tables using Coefficient of Contingency in Pharmaceutical Statistics
G. Mokesh Rayalu, J. Ravi Sankar*, A. Felix
Department of Mathematics, School of Advanced Sciences, VIT University, Tamil Nadu, India – 632014.
*Corresponding Author Email: ravisankar.j@vit.ac.in
ABSTRACT:
In the case of two attributes, ChiSquare test may be used in testing the significant association between them by considering a twoway contingency table .When three or more attributes to be considered at a time, used chisquare test for independence of two attributes may not be applicable. In this case, one may observe sequential contingencies across different groups of manifold contingency tables. In this article, sequential connections across different groups manifold contingency tables have been tested by using Log Odds Ratio and coefficients of contingency.
KEYWORDS: Manifold Contingency table, Angular Transformation, Legit transformation, pharmaceutical statistics.
1. INTRODUCTION:
In recent years a great deal of research has been directed to the modeling and measurement of pharmaceutical biological relationships [2, 4]. Biometrics is the art and science of using statistical methods for the measurement of biological relationships [4]. The scope of Biometry has been broadened since its origin, as is apparent from the emergence example. Also, the number of researchers working in pharmaceutical statistics has increased economously and the store of available biometric theories and practical methods has been extended systematically [3, 4, 5, 7].
In most of the Medical research problems, one may come across sequential contingencies or connectedness across different groups in the form of manifold contingency table [1, 2]. In such situations the usual chisquare test may not be directly applicable. The Analysis of Variance (ANOVA) technique can be applied after taking angular transformation on cell frequencies of the contingency table. In the present study, an attempt has been made by developing an advanced test for sequential contingencies across the groups.
2. TEST FOR COMPARING SEQUENTIAL CONTINGENCIES ACROSS K GROUPS IN A THREE WAY (2X2XK) MANIFOLD CONTINGENCY TABLE USING LOG ODDS RATIO:
Consider a 2x2xk manifold contingency table for three attributes A,B,C with two, two and k levels respectively.

C_{1} _{ } 
C_{2} 
……. 
C_{k} 


B_{1} 
B_{2} 
B_{1} 
B_{2} 
……. 
B_{1} 
B_{2} 
A_{1}
A_{2} 
O_{111}
O_{211} 
O_{121}
O_{221} 
O_{112}
O_{212} 
O_{122}
O_{222} 
……. ……. 
O_{11k}
O_{21k} 
O_{12k}
O_{22k} 
One may wish to test the significance of the differences in sequential connections or contingencies across k groups. A fundamental distinction may be made between the measures of association in contingency tables which are either sensitive or insensitive to the marginal(row) totals. Logit transformation provides a measure to the marginal total. The Logit is defined by [7]
4. CONCLUSIONS:
Pharmaceutical statistics is a grouping field of statistical science. One may observe frequently the applications of chisquare test in dealing with contingency tables for attributes in pharmaceutical statistics. In the present study, some new tests for comparing sequential contingencies (connections) across different groups in a three way manifold contingency table have been developed for pharmaceutical statistics. Generally, application of the proposed test is simple, when that compared with the application of ANOVA technique for manifold contingency table.
5. REFERENCES:
1. Agresti, A. (1990). “Categorical Data Analysis”, John Wiley, New York .
2. Armitage, P. (1955). “Tests for linear trends in proportions and frequencies”, Biometrics 11, 375386.
3. Fienberg, S.E (2000). “Contingency tables and loglinear models: Basic theory and new developments”, Journal of the American Statistical Association 95, 643647.
4. Fleiss, J.L. (1981), “Statistical Method in Biological Proportions”, 2^{nd} Ed. Wiley, New York.
5. Johnson, R.A and Wichern, D.W (2009), “Applied Multivariate statistical Analysis” Fifth edition PHI learning private Ltd., New Delhi.
6. Kanji, G.K (1999), “100 Statistical Tests” second edition, sage publications, London.
7. McCullagh, P. and Nelder, J.A (1989). “Generalized Linear Models”, 2^{nd} Ed. Chapman and Hall, London.
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Received on 13.07.2016 Modified on 22.07.2016
Accepted on 21.08.2016 © RJPT All right reserved
Research J. Pharm. and Tech 2016; 9(11): 19021904.
DOI: 10.5958/0974360X.2016.00389.9
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