Class_4

# Class_4 - Two statistical tasks Description Central...

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Measures of Variation

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Two s tatistical tasks Description Central Tendency Variability Association Inference
Measures of Variability Discrete Variables Index of Qualitative Variation Continuous Variables Range Interquartile Range Variance Standard Deviation

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For D iscrete variables, the Index of Qualitative Variation (IQV)
Religious Preference Percent Protestant 65.6 Catholic 24.2 Jewish 2.3 Other 1.2 None 6.1 No Answer 0.5

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K K p IQV K i i / ) 1 ( 1 1 2 - - = = where p = proportion of cases and K = number of categories
Religious Preference Percent Proportion Protestant 65.6 0.656 Catholic 24.2 0.242 Jewish 2.3 0.023 Other 1.2 0.012 None 6.1 0.061 No Answer 0.5 0.005

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Religious Preference Percent Proportion Proportion 2 Protestant 65.6 0.656 0.430 Catholic 24.2 0.242 0.059 Jewish 2.3 0.023 0.001 Other 1.2 0.012 0.000 None 6.1 0.061 0.004 No Answer 0.5 0.005 0.000
Religious Preference Percent Proportion Proportion 2 Protestant 65.6 0.656 0.430 Catholic 24.2 0.242 0.059 Jewish 2.3 0.023 0.001 Other 1.2 0.012 0.000 None 6.1 0.061 0.004 No Answer 0.5 0.005 0.000 i K = = 1 0 494 .

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K K p IQV K i i / ) 1 ( 1 1 2 - - = =
IQV = (1 - 0.494 ) / [(6 - 1) / 6] =   (0.506) / (5 / 6) =   (0.506) / (0.833) = 0.61

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What does this mean? When there is perfect dispersion, IQV = 1.00 When there is no dispersion, IQV = 0.00
Use the following rule of thumb: 0.00 to 0.24 " No dispersion " 0.25 to 0.49 " Weak dispersion " 0.50 to 0.74 " Moderate dispersion " 0.75 to 1.00 " Strong dispersion " IQV = 0.610 ". . . represents moderate dispersion among respondents in their expressed religious preference."

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Religious Preference Percent Proportion Proportion 2 Protestant 16.67 0.1667 0.0279 Catholic 16.67 0.1667 0.0279 Jewish 16.67 0.1667 0.0279 Other 16.67 0.1667 0.0279 None 16.67 0.1667 0.0279 No Answer 16.67 0.1667 0.0279 IQV = (1 - 0.1674) / [(6 - 1) / 6] = (0.833) / (5 / 6) = (0.833) / (0.833) = 1.00 1674 . 0 1 = = K i
Religious Preference Percent Proportion Proportion 2 Protestant 100.00 1.00 1.00 Catholic 0.00 0.00 0.00 Jewish 0.00 0.00 0.00 Other 0.00 0.00 0.00 None 0.00 0.00 0.00 No Answer 0.00 0.00 0.00          IQV = (1 - 1.000) / [(6 - 1) / 6] =   (0.000) / (5 / 6) =   (0.000) / (0.833) = 0.00 000 . 1 1 = = K i

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For C ontinuous variables, Range Interquartile range Standard deviation Variance
The Range The distance across 100% of scores Range = H – L + 1

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For example, take the following 12 values (N = 12): 5, 2, 27, 32, 3, 5, 35, 7, 31, 42, 37, 39
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## This note was uploaded on 02/04/2008 for the course PPD 404 taught by Professor Velez during the Fall '07 term at USC.

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Class_4 - Two statistical tasks Description Central...

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