handout 4 - Handout 4.Descriptive study of bivariate data...

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1 1 Handout 4.Descriptive study of bivariate data Categorical data (Chapter 3, section 2). Numerical data (Chapter 3, sections 4, 5, 6). Bivariate data - For each unit in the sample, measure two values. Example : Data were collected to measure the effect of the body weight on the blood pressure in individuals aged between 15 and 30. Sample unit: individual aged between 15 and 30. Variables measured in each sample unit: body weight and blood pressure. 2 Both discrete Both numerical Bivariate data Discrete and numerical Do not consider 1. Described by a contingency table 2. Summaries via frequencies 1. Described by a scatter plot 2. Summaries via correlation coefficient, regression line 3 Example 4.1 • The manager of a company wants to investigate the association between type of defects found on furniture and the production shift. • A sample of 309 furniture defects produced the following contingency table Type of defect 20 5 13 D 49 17 33 3 34 31 26 2 45 21 15 1 C B A Shift 15 defects A produced in shift 1 4 Example 4.1 cont’d • To analyze the distribution of frequency between the two categorical variables, it is best to complete the table by the row and column totals, from which one can compute the row/column conditional frequency distributions or the joint frequency distribution. 309 38 128 69 74 (mar ginal) Total 119 96 94 (marginal) Total Type of defect 20 5 13 D 49 17 33 3 34 31 26 2 45 21 15 1 C B A Shift 74 defects A produced in all shifts 96 shifts of type 2
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2 5 Relative frequencies • Divide each cell frequency by the total frequency, to get the relative frequencies. 1.00 0.12 0.42 0.22 0.24 Total 0.39 0.30 0.31 Tot al Type of defect 0.07 0.01 0.04 D 0.16 0.05 0.11 3 0.11 0.10 0.08 2 0.15 0.07 0.05 1 C B A Shift Which is the most common type of defect? Which is the most common combination of shift/type of defect? Which is the most common type of defect in the first shift? 6 Row relative frequencies • Divide each cell frequency by the row total, to get the relative frequencies per row. These numbers are now comparable across rows.
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This note was uploaded on 04/17/2008 for the course HONORS 191 taught by Professor Palmero during the Spring '08 term at UMass (Amherst).

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handout 4 - Handout 4.Descriptive study of bivariate data...

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