stats8 - Monday, October 4...

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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 Non-Random 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 2 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 1-2 Sum of the deviations from the mean is ALWAYS = 0 Deviations 2 (Y Y) 2- 4 2 2 2 2 3 2 1 2-2 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 1-2- 4 2 2 2 2 3 2 1 2-2 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) = 2. Expected value of Y = Sampling Error difference between Y & 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 = 75 = 8 = 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 = 75 = 8 = 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 = (75 in this case) -1 Y -2 Y-3 Y +1 Y +2 Y +3 Y Sampling Distribution = Population mean Y = standard deviation of sampling distribution (standard error of the mean) pg 231 E(Y) = Samples and Populations -1 Y-2 Y-3 Y +1 Y +2 Y +3 Y Sampling distribution of means is normally distributed Estimating the standard error of the mean...
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stats8 - Monday, October 4...

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