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Chapter 3: Descriptive Study of Bivariate Data
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Univariate Data: data involving a single variable. Multivariate Data: data involving more than one variable. Bivariate Data: data involving two variables.
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Bivariate Data There are two types of Bivariate Data: Bivariate Categorical Data and Bivariate Measurement Data.
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Univariate vs. Bivariate Univariate Categorical : Bivariate Categorical:
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Univariate vs. Bivariate Univariate Measurement: Bivariate Measurement:
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SUMMARIZATION OF BIVARIATE CATEGORICAL DATA
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Calculation of Relative Frequencies and make a contingency table
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Data:
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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.
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Depending on the specific context of a cross-tabulation, one may also wish to examine the cell frequencies relative to a marginal total.
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Data in this summary form are commonly called cross-classified or cross-tabulated data. In statistical terminology, they are also called contingency tables.
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SIMPSON’S PARADOX
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Consider the data:
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The proportion of males admitted: 233/ 557=.418. Proportion of females admitted, 88/ 282 =.312.
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Does there appear to be a gender bias?
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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.
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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.
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Group Work 10: Find two examples of Simpson’s Paradox. Due: Wednesday, Sept 10 th.
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