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Unformatted text preview: Monday, October 4 http://emwilk.myweb.uga.edu/POLS4150.html Course Webpage: POLS4150 – RESEARCH METHODS IN POLITICAL SCIENCE (90595) Drawing inferences from samples Samples and Populations Chapter 7: Generalizing from samples to populations Sample 1,000 U.S. Population: 300,000,000 Generalize NonRandom Samples: • Unscientific, cannot generalize Random Samples: • Every member of the population has an equal chance of being selected • Population must be properly defined Samples and Populations Sample statistics Population parameters mean variance standard deviation S 2 S µ σ 2 σ Y Sample statistic – an estimator of the population parameter based on the drawn sample. Population Parameter – exact value of a variable in the population. The standard deviation (for samples) – pg 376 Measures of Variability ∑ ( Y – Y) 2 S N – 1 = √ Measures of Variability Data Deviations 64 68 70 71 69 66 68 64 – 68 = Variance for Set A – assuming a sample 68 – 68 = 70 – 68 = 71 – 68 = 69 – 68 = 66 – 68 = (Y – Y) Y Y = 4 2 3 12 Sum of the deviations from the mean is ALWAYS = 0 Deviations 2 (Y – Y) 2 4 2 2 2 2 3 2 1 22 2 = 16 = 0 = 4 = 9 = 1 = 4 34 Measures of Variability Data 64 68 70 71 69 66 68 64 – 68 = Variance for Set A – assuming a sample 68 – 68 = 70 – 68 = 71 – 68 = 69 – 68 = 66 – 68 = Y 4 2 3 12 4 2 2 2 2 3 2 1 22 2 = 16 = 0 = 4 = 9 = 1 = 4 34 / 5 = 6.8 ∑ (Y – Y) 2 Y = S = 2.61 Deviations (Y – Y) Deviations 2 (Y – Y) 2 Frequency Distribution Score f . Below 65 4 65 – 69 7 70 – 74 13 75 – 79 20 80 – 84 22 85 – 89 16 90 – 94 12 95  100 6 . N = 100 Frequency distribution – pg 355 # of observations for each value of a variable Example: distribution of test scores Samples and Populations Sampling Distribution – probability distribution of sample means 1. Normally distributed E(Y) = µ 2. Expected value of Y = µ Sampling Error – difference between Y & µ Generalizing from samples to populations Sample 1,000 U.S. Population: 300,000,000 Generalize Sampling Distribution Ex: population of 1million nationally administered standardized test scores µ = 75 σ = 8 µ = 75 83 67 59 91 99 51 Area under the curve includes ALL 1 million population scores Sampling Distribution Ex: population of 1million nationally administered standardized test scores µ = 75 σ = 8 µ = 75 83 67 59 91 99 51 Area under the curve includes ALL 1 million population scores Take a sample of n = 1,000 Y = 73 s = 4 Take another sample of n = 1,000 Y = 76 s = 5 Sampling Distribution Score f . 72 6 73 8 74 22 75 29 76 19 77 12 78 4 . N = 100 Say we take 100 samples of N = 1,000 Frequency distribution of sample means: Average of these sample means = 74.99 If an infinite amount of samples are taken, the average of the sample means = µ (75 in this case) µ1 σ Y µ µ µ µ µ µ2 σ Y3 σ Y +1 σ Y +2 σ Y +3 σ Y Sampling Distribution µ = Population mean σ Y = standard deviation of sampling distribution (standard error of the mean) – pg 231 E(Y) = µ Samples and Populations µ1 σ Y2 σ Y3 σ Y +1 σ Y +2 σ Y +3 σ Y Sampling distribution of means is normally distributed Estimating the standard error of the mean...
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 Fall '10
 wilk
 Political Science, Normal Distribution, Standard Deviation, Fiorina P

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