IPS6eCh02_5and2_6bb

IPS6eCh02_5and2_6bb - Looking at Data Relationships Data...

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    Looking at Data - Relationships Data analysis for two-way tables IPS Chapter 2.5
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Objectives (IPS Chapter 2.5) Data analysis for two-way tables Two-way tables Joint distributions Marginal distributions Relationships between categorical variables Conditional distributions Simpson’s paradox
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An experiment has a two-way, or block, design if two categorical factors are studied with several levels of each factor. Two-way tables organize data about two categorical variables obtained from a two-way, or block, design. (There are now two ways to group the data). Two-way tables    First factor: age Group by age Second factor: education Record education
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Two-way tables We call education the row variable and age group the column variable . Each combination of values for these two variables is called a cell . For each cell, we can compute a proportion by dividing the cell entry by the total sample size. The collection of these proportions would be the joint distribution of the two variables.
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Marginal distributions We can look at each categorical variable separately in a two-way table by studying the row totals and the column totals. They represent the marginal distributions , expressed in counts or percentages (They are written as if in a margin.) 2000 U.S. census
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The marginal distributions can then be displayed on separate bar graphs, typically expressed as percents instead of raw counts. Each graph represents only one of the two variables, completely ignoring the second one. Percent of each group, not total, so does not add to 100% Percent of total with each education level, so adds to 100% 4,459/37,786 = .118 = 11.8% Conditional distribution, not “marginal”
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Relationships between categorical  variables The marginal distributions summarize each categorical variable independently. But the two-way table actually describes the
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IPS6eCh02_5and2_6bb - Looking at Data Relationships Data...

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