Lecture+3+SU10+_central+tendency+and+variability_-1

Lecture+3+SU10+_central+tendency+and+variability_-1 -...

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Sociology 210 Lecture 3: Measures of Central Tendency and Variability 10/08/11 Soc 210 Summer 2010 1
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Contingency Tables Shows the Relationship between two Categorical Variables In example on next slide, Independent Variable is on the left and Dependent Variable is on the top Can include row or column percentages to aid in interpretation 10/08/11 Soc 210 Summer 2010 2
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Contingency Table Examples Statistics is Fun Sex False True Total Female 16 12 28 Male 11 6 17 Total 27 18 45 Statistics is Fun Sex False True Total Female 16 (57%) 12 (43%) 28 (100%) Male 11 (65%) 6 (35%) 17 (100%) Total 27 (60%) 18 (40%) 45 (100%) Statistics is Fun Sex False True Total Female 16 (59%) 12 (67%) 28 (62%) Male 11 (41%) 6 (33%) 17 (38%) Total 27 (100%) 18 (100%) 45 (100%) 10/08/11 Soc 210 Summer 2010 3 With Row Percentages With Column Percentages
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Contingency Table Exercise Fill in the missing number that goes here Statistics is Fun Year False True Total First Year/ Soph 13 Junior 7 17 Senior 10 Total 18 45 10/08/11 Soc 210 Summer 2010 4 Hint: What information can you fill in first?
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Measures of Central Tendency Statistical measures that define the center of a distribution – the goal is to find a single score that is most typical or representative of the entire group Not always obvious which measure does the best job of characterizing the center Measures 1. Mean 2. Median 3. Mode 10/08/11 Soc 210 Summer 2010 5
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Notation: The Summation Sign (Σ) Greek capital letter sigma (Σ) is used in mathematics to indicate summation of multiple values. Here’s an example: i X 1 8 2 3 3 2 4 4 5 5 22 5 4 2 3 8 5 1 5 4 3 2 1 5 1 = + + + + = + + + + = = = i i i i X X X X X X X 10/08/11 Soc 210 Summer 2010 6 i i i X X of values all over sum = i “indexes” values of X
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The Mean Arithmetic Mean : Sum of scores divided by the number of scores Population mean = sum of data / N μ = (X 1 + X 2 + X 3 +…+ X N ) / N – Notation: each measurement of a population referred to as X i (e.g., X 1 , X 2 , X 3 ,… X N ) Sample Mean (X-bar): same formula, different notation = = n i i X n X 1 1 10/08/11 Soc 210 Summer 2010 7 = = N i i X N 1 1 μ
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Means are mainly used for interval/ratio variables It is also possible to take the mean of nominal variables that are binary (e.g., male/female, yes/no) If the binary variable is coded as “0” and “1” (e.g., 0=male, 1=female), then the mean represents the proportion of observations coded as “1” e.g., For the male/female variable, μ =.65 would mean that 65% of the population is female Many researchers do not believe in using the mean to describe central tendency of ordinal data, since the distances between ranks are not equal. However, it does happen (e.g., Likert scales: Strongly Agree, Agree,
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