stats7 - Monday, September 27 POLS4150 RESEARCH METHODS IN...

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Monday, September 27 http://emwilk.myweb.uga.edu/POLS4150.html Course Webpage: POLS4150 – RESEARCH METHODS IN POLITICAL SCIENCE (90595) Descriptive Statistics
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Summarizing Variables Measures of Central Tendency – “typical” value in a distribution Mode – most Median – middle Mean – average Mean – sum of all values for a variable divided by N y Y N = Where: y = sum of all values of Y N = number of observations or, Mean = (y 1 + y 2 + y 3 + . .. + y N ) / N Pg 362:
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Measures of Central Tendency Example: Average turnout across 5 states: N = 5 51, 63, 54, 49, 54 Y = 49 + 51 + 54 + 54 + 63 5 = 54.2 49, 51, 54, 54, 63 Mode = 54 Median = 54 Mean:
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Measures of Central Tendency Mean, median, mode: which to use? Qualitative variables mode Presence of extreme observations median Normal distribution mean
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Measures of Central Tendency Mean, median, mode: which to use? Presence of extreme observations (outliers) Income of employees in a small company: X1 = $25,000 X2 = $25,000 X3 = $30,000 X4 = $30,000 X5 = $40,000 X6 = $40,000 X7 = $50,000 X8 = $200,000 Mean = $55,000 Median = $35,000 “Outlier”
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Measures of Central Tendency Normal Distribution Mo = Mdn = Y
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Measures of Central Tendency Positively Skewed Mo < Mdn < Y “Outlier(s)”
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Measures of Central Tendency Negatively Skewed Mo < Mdn < “Outlier(s)” Y
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Measures of Variability Set A Set B Set C 64 68 70 71 69 68 44 63 80 91 74 68 34 58 90 101 79 68 Mean: Test scores for three difference classes: 66 56 46
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Range (R) = H – L Where H = Highest value in distribution L = Lowest Value in distribution Measures of Variability
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Measures of Variability R Set A Set B Set C 64 68 70 71 69 68 7 44 63 80 91 74 68 47 34 58 90 101 79 68 67 Mean 66 56 46
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Measures of Variability Mean 64 68 70 71 69 66 Set A: Deviations: - 4 - 2 0 +1 +2 +3 Y - Y Deviation from the mean: Difference between an observation’s actual value and the mean.
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Where: σ 2 = the population variance The Variance (for populations) pg 375 Measures of Variability ( Y – Y ) 2 σ 2 N = ∑ (Y – Y ) 2 = sum of the squared deviations from the mean
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Measures of Variability Data Deviations 64 68 70 71 69 66 68 64 – 68 = Variance for Set A 68 – 68 = 70 – 68 = 71 – 68 = 69 – 68 = 66 – 68 = (Y – Y ) Y Y = - 4 0 2 3 1 -2 0 Sum of the deviations from the mean is ALWAYS = 0 Deviations 2 (Y – Y ) 2 - 4 2 0 2 2 2 3 2 1 2 -2 2 = 16 = 0 = 4 = 9 = 1 = 4 34
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Measures of Variability Data 64 68 70 71 69 66 68 64 – 68 = Variance for Set A 68 – 68 = 70 – 68 = 71 – 68 = 69 – 68 = 66 – 68 = - 4 0 2 3 1 -2 0 - 4 2 0 2 2 2 3 2 1 2 -2 2 = 16 = 0 = 4 = 9 = 1 = 4 34 / 6 = 5.67 Deviations Deviations 2 (Y – Y ) 2 (Y – Y ) Y (Y – Y ) 2 Y =
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Measures of Variability Data 44 63 80 91 74 56 68 44 – 68 = Variance for Set B 63 – 68 = 80 – 68 = 91 – 68 = 74 – 68 = 56 – 68 = - 24 - 5 12 23 6 -12 0 Sum of the deviations from the mean is ALWAYS = 0 - 24 2 -5 2 12 2 23 2 6 2 -12 2 = 576 = 25 = 144 = 529 = 36 = 144 1,454 Deviations Deviations 2 Y = (Y – Y ) Y (Y – Y ) 2
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Measures of Variability Data 44 63 80 91 74 56 68 44 – 68 = Variance for Set B 63 – 68 = 80 – 68 = 91 – 68 = 74 – 68 = 56 – 68 = - 24 - 5 12 23 6 -12 0 - 24 2 -5 2 12 2 23 2 6 2 -12 2 = 576 = 25 = 144 = 529 = 36 = 144 1,454/ 6 = 242.3 Deviations Deviations 2 Y = (Y – Y ) Y (Y – Y ) 2 (Y – Y ) 2
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Measures of Variability Data 34 58 90 101 79 46 68 34 – 68 = Variance for Set C 58 – 68 = 90 – 68 = 101 – 68 = 79 – 68 =
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stats7 - Monday, September 27 POLS4150 RESEARCH METHODS IN...

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