Descriptive Study of Bivariate Data 二元資料簡介

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Bivariate Categorical Data

When two traits are observed for the individual sampling units and each trait is recorded in some qualitative categories, the resulting data can be summarized in the form of a two-way frequency table. The categories for one trait are marked along the left margin, those for the other along the upper margin, and the frequency counts recorded in the cells. Data in this summary form are commonly called cross-classified or cross-tabulated data. In statistical terminology, they are also called contingency tables.

A survey was conducted by sampling 400 persons who were questioned regarding union membership and attitude toward decreased national spending on social welfare programs. The cross-tabulated frequency counts are presented as follow. To gain further understanding of how the responses are distributed, calculate the relative frequencies of the cells

Table 1 Cross-Tabulated Frequency Counts

For this purpose, we divide each cell frequency by the sample size 400. The relative frequencies (for instance, 84/400=.21) are shown in Table 2.

Table 2 Relative Frequencies for the Data of Table 1

From the calculations in Table 3, it appears that the attitude patterns are different between the two groups - support seems to be stronger among union members than nonmembers.

Table 3 Relative Frequencies by Group