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# unit 5 new - Statistics V3100018.001 UNIT 5 Bivariate...

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Statistics – V3100018.001 UNIT 5 – Bivariate statistics: tables, graphs, analytical measures Giuseppe Arbia , Catholic University of the Sacred Hearth, Roma, Italy 1

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Bivariate statistics (two variables at a time) We distinguish: - When both are scale (quantitative continuous) - When at least one of the two is not scale(ordinal or nominal) 2
We proceed in the same fashion as with univariate, by considering 1. Tables 2. Graphs 3. Analytical tools 3

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1. Tables We can build up bivariate frequency distributions by counting the number of individuals displaying simultaneously two variables E.g. sex and marital status 4
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There are 3 types of percentage: Row percentages Columns percentages Total percentages 6
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Example: Happiness and region Two qualitative variables 8
Example: Happiness and region (row relative frequency) Two qualitative variables 9

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Example: Happiness and region (column relative frequency) Two qualitative variables 10
Example: Happiness and region (total relative frequency) Two qualitative variables 11

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A crosstabulation can be obtained for all kinds of variables But when the variable is scale or has too many modalities a grouping into classes is needed 12
Example: income vs. number of brothers and sisters 13

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15 Some formalisms y 1 y 2 ... y h x 1 N 11 N 12 ... N 1 h N 1 ° x 2 N 21 N 22 ... N 2 h N 2 ° ... x k N k 1 N k 2 ... N kh N k ° TOTAL N ° 1 N ° 2 N ° h N °°

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16 Some formalisms y 1 y 2 ... y h x 1 N 11 N 12 ... N 1 h N 1 ° x 2 N 21 N 22 ... N 2 h N 2 ° ... x k N k 1 N k 2 ... N kh N k ° TOTAL N ° 1 N ° 2 N ° h N °° N i ° = N ij j = 1 h ! Row summation N ° j = N ij i = 1 k ! Column summation N °° = N ij j = 1 h ! i = 1 k ! Double summation
2. Graphical tools We can produce a graphical representation of the bivariate frequency distributions 17

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