Chapter 3: Descriptive Study of Bivariate Data

Univariate Data: data involving a single variable. Multivariate Data: data involving more than one variable. Bivariate Data: data involving two variables.

Bivariate Data There are two types of Bivariate Data: Bivariate Categorical Data and Bivariate Measurement Data.

Univariate vs. Bivariate Univariate Categorical : Bivariate Categorical:

Univariate vs. Bivariate Univariate Measurement: Bivariate Measurement:

SUMMARIZATION OF BIVARIATE CATEGORICAL DATA

Calculation of Relative Frequencies and make a contingency table

Data:

The total frequency for any row is given in the right-hand margin and those for any column given at the bottom margin. Both are called marginal totals.

Depending on the specific context of a cross-tabulation, one may also wish to examine the cell frequencies relative to a marginal total.

Data in this summary form are commonly called cross-classified or cross-tabulated data. In statistical terminology, they are also called contingency tables.

SIMPSON’S PARADOX

Consider the data:

The proportion of males admitted: 233/ 557=.418. Proportion of females admitted, 88/ 282 =.312.

Does there appear to be a gender bias?

In mechanical engineering, the proportion of males admitted, 151 / 186 =.812, is smaller the proportion of females admitted, 16/18 =.889. In history department, the proportion of males admitted, 82/371 =.221, is smaller than the proportion of females admitted, 72/264 =.273.

When the data are studied department by department, the reverse but correct conclusion holds; females have a higher admission rate in both cases! “Department” is an unrecorded or lurking variable.

Group Work 10: Find two examples of Simpson’s Paradox. Due: Wednesday, Sept 10 th.