Lecture 10

# Lecture 10 - POL2156B FOUNDATIONS OF RESEARCH INVESTIGATING...

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POL2156B FOUNDATIONS OF RESEARCH INVESTIGATING RELATIONSHIPS

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LECTURE PLAN Measures of Association Correlation
MEASURES OF ASSOCIATION: GAUGING THE STRENGTH OF RELATIONSHIPS Table percentages are easy to illustrate, are easily understood by others, and give a concrete indication of patterns and relationships between two variables. But there are also single statistics, measures of association , that summarize the overall pattern in a table and the strength of the relationship between two variables.

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MEASURES OF ASSOCIATION There are a variety of different measures, but we’ll focus on three: Lambda : used for tables with nominal variables Gamma and Tau B : used for tables with two ordinal variables
MEASURES OF ASSOCIATION FOR NOMINAL VARIABLES 1) Proportional-reduction-in-error (PRE) measures: these essentially measure the difference between what is actually observed in a table and what we would expect to find in a table if there was no relationship. These measures range from 0 to 1. 1 is a perfect relationship: e.g. the more of x, the more of y). The closer the measure is to zero, the weaker the relationship.

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MEASURES OF ASSOCIATION: LAMBDA Catholic Protestant Other None Total Vote Party A 132 74 61 65 332 Vote Party B 57 203 19 86 365 Vote Party C 20 34 60 105 219 Total 209 311 140 256 916 If we had no other information about why people voted, our safest guess would be that they voted for the Party B, because that is the modal value. But we could be wrong as many as 551 times (332+219) Once we know people’s religions, we can then use the modal values for each religion to guess. We would guess that Catholics vote for party A, Protestants for Party B, and so on. We would possibly make errors as many as 415 times (77+108+79+151) Simply by knowing people’s religion, we could reduce our guessing error by a proportion of: (551-415)/551 = .25
MEASURES OF ASSOCIATION FOR ORDINAL VARIABLES 2) Gamma, Somer’s D, Tau B, and Tau C essentially measure the difference between the number of pairs of cases that are ranked the same on both variables (example: person 1 scores “low” and “low” on both variables, and person 2 scores “high” and “high”) and the number of pairs of cases that are ranked differently (example: person 1 scores “low” on the x variable, but “high” on the y variable, and person 2 scores “high” on the x variable, but “moderate” on the y variable).

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## This note was uploaded on 01/31/2012 for the course POL 2107 taught by Professor Bourgault during the Spring '08 term at University of Ottawa.

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Lecture 10 - POL2156B FOUNDATIONS OF RESEARCH INVESTIGATING...

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