Analysis of Association

It is often of interest to know if two variables are associated, and, if so, to what degree. In cases like this, the data set to be analyzed will consist of a certain number of pairs of data. 

Consider the example of age and weight in children. As a general statement, it would be fair to say that age and weight are associated. This statement alone, however, does not tell us how they are related or how closely they are related. A more informative general statement is that as age increases, weight increases. This 

Consider first the example of a positive association. In the case of children s age and weight, these variables are not perfectly associated, since there are children of the same age who differ in weight. Consider now the example of a negative association. The age of a car and its value are also not perfectly related Initially identical cars may have been maintained very differently, such that, when they are both five years old, one is worth much more than the other. The degree of closeness of an association is a separate characteristic of the relationship between two variables than is the direction of their association. There are close and less close positive associations and close and less close negative associations. 

Numerically, correlation coefficients can range from -1 to +1. A value of -1 indicates a perfect negative linear relationship as one variable increases, the other decreases in a precise linear fashion. A value of 0 indicates a complete lack of linear association between two variables. A value of +1 indicates a perfect positive linear relationship as one variable increases, the other increases in a precisely linear fashion. (The technique of correlation cannot meaningfully describe nonlinear patterns of association between two variables, such as curvilinear and exponential relationships.) 

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W. Horwitz, Official Methods of Analysis of Association of Off dal Analytical Chemists, AO AC, Washington, D.C. 

In addition to the determination of molar mass distributions and various molar mass averages there are many experiments, requiring sometimes sophisticated data evaluation, that can be carried out with an analytical ultracentrifuge. Examples are the analysis of association, the analysis of heterogeneity, the observation of chemical reactions, and protein characterization, to mention only a few. A detailed discussion is beyond the scope of this article, but there is excellent literature available [77-79,81,87-89]... 

Evaluating through factory inspections, including the collection and analysis of associated samples, the conditions and practices under which drugs and drug products are manufactured, packed, tested, and held, and... 

Comings, D. E., Gade-Andavolu, R., Gonzalez, N., et al. (2000) Multivariate analysis of associations of 42 genes in ADHD, ODD and conduct disorder. Clin. Genet. 58, 31-40. 

Abdolmaleky, H. M., Earaone, S. V., Glatt, S. J., and Tsuang, M. T. (2004) Meta-analysis of association between the T102C polymorphism of the 5HT2a receptor gene and schizophrenia. Schizophr. Res. 67, 53-62. 

Table ll.Analysis of association based on a partial set of cathode polarization data from experiments with an aqueous 0.732 mol dm"3 CuS04 1.484 mol dm"3 H2S04 solution,... 

TABLE 7.2 Meta-analysis of Association Studies on HTR2C Cys23Ser in Clozapine Response... 

Situations such as items 2 to 4 can only be understood from the analysis of associated units, and not from studies of component units. Note that... 

Williams J, McGulFin P, Nothen M, Owen MJ. Meta-analysis of association between the 5-HT2a receptor T102C polymorphism and schizophrenia. EMASS Collaborative Group. European Multicentre Association Study of Schizophrenia. Lancet 1997 349(9060) 1221. 

Li D, He L. 2007b. G72/G30 genes and schizophrenia A systematic meta-analysis of association studies. Genetics 175 917-922. 

Meta-analysis of association studies between DAOA and schizophrenia under fixed-effects model... 

Exerdse 17 Simulation of association kinetics using numerical integration, and Exerdse 18 Analysis of association kinetics)... 

Haberly LB, Bower JM. 1984. Analysis of association fiber system in piriform cortex with intracellular recording and staining techniques. J Neurophysiol 51 90-112. 

The acceptor and donor strength of many functions besides fhose of fhe amide type have been characterized by the analysis of associations between simple molecules, such as, e.g., phenols and anilines, for which fhousands of experimental data exist, mosfly measured in chloroform or in carbon tetrachloride [94, 95]. Although these data are hampered by less well-defined structures compared to supramolecular complexes, they not only give a fairly consistent basis for the prediction of hydrogen-bonded associations but also can be used, e.g., for crown efher and cryptand complexes with alkali or ammonium ligands [32]. 

Zerban, F. W., and Martin, James, Methods of Analysis of Association of... 

Sklar, L.A., Finney, D.A., Oades, Z.G., Jesaitis, A.J., Painter, R.G. and Gochrane, G.G. (1984). The dynamics of ligand-receptor interactions Real-time analysis of association, dissociation, and internalization of an N-formly peptide and its receptors on the human neutrophil./. Biol. Chem. 259, 5661-5669. 

CoCo Statistics package for analysis of associations between discrete variables... 

Morris, C. C. (2006). Generalized linear regression analysis of association of imiversal helmet laws with motorcyclist fatality rates. Accid. Anal Prev., 38, 142-147. Muller, A. (2004). Florida s Motorcycle Helmet Law Repeal and Fatality Rates. Am. J. Pub. Health, 94(4), 556-558. 

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