The scenario discusses the issue of online-shopping preference among males females. We hypothesize that more women practice online-shopping than men, who, in turn, prefer conventional way of shopping. Therefore, we hypothesize that there is an association between gender as the variable, measured on a nominal scale and the preference for kind of shopping as a categorical variable. Since we distinguish between male and female gender that corresponds to either online-shopping or to conventional way of shopping, we can observe the presence or absence of direct association. Collecting data from a random sample of 200 males and 200 females, we conduct the chi-squire test of independence. The data in the contingency table show that the descriptive analysis (70% of females practice online-shopping, whereas only 30% of males reported the same outcome) is consistent with the expected results. Therefore, the scenario indicates strong association between the named above variables.
In spite of the possibility to assume causation in this statistically significant relationship, we cannot infer it, because we do not know whether x was caused by y or vice versa and whether some third variable could explain the causality more precisely. In order to demonstrate a casual relationship such variables as, for instance, the amount of time, the kind of occupation, the place of residence, age, etc. should be applied. They alone or in the aggregate can help to specify a casual relationship and provide concrete evidence of the causality.
Analyzing the data in the example, we identify the chi-square test of association to be more suitable for the determined purpose. This choice can be explained by the nature of the variables that require the examination of whether they co-occurred rather than co-varied. Availability of additional data or evidence, different from gender alone, could make the application of correlation coefficient more suitable, showing also the strength of the relationship.
References
Corder, G.W., Foreman, D.I. (2009). Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach. Wiley, New York.
Greenwood, P.E., Nikulin, M.S. (1996) A guide to chi-squared testing. Wiley, New York.
Rodgers, J.L. and Nicewander, W.A. (1988). HYPERLINK "http://www.jstor.org/stable/2685263" Thirteen ways to look at the correlation coefficient . The American Statistician, …