chap6 - Descriptive statistics Chapter 6 1 Statistics...

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Descriptive statistics Chapter 6 1
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Statistics • Descriptive statistics organizing, summarizing and displaying data • Inferential statistics using sample data to draw conclusions about a population • Probability vs statistics : Probability: population sample (deductive) Statistics: sample population (inductive) 2
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Reduction of blood cholesterol level Fifteen adult males between the ages of 35 and 50 participated in a study to evaluate the effect of diet and exercise on blood cholesterol levels. The blood cholesterol levels were measured for each subject initially, and then 3 months after participating in an aerobic exercise program and switching to a low fat diet 3
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Participant Before After Participant Before After 1 265 229 9 260 247 2 240 231 10 279 239 3 258 227 11 283 246 4 295 240 12 240 218 5 251 238 13 238 219 6 245 241 14 225 226 7 287 234 15 247 233 8 314 256 milligrams per deciliter 4
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Does the program reduce blood cholesterol level? Descriptive Compute summary statistics Visualize the data Inferential Test hypotheses etc. Draw conclusions: is there strong evidence that the program is effective? 5
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Summarizing data 6
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Location of data Sample mean (location of data): for a sample of n observations Sample mean of cholesterol level before: 261.80, after: 234.93 = = + + = n i i n x n n x x x 1 1 1 " 7
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Compute sample mean in R Entering data > LevelBefore < c(265, 240, 258, 295, 251, 245, 287, 314, 260, 279, 283, 240, 238, 225, 247) > LevelAfter < c(229, 231, 227, 240, 238, 241, 234, 256, 247, 239, 246, 218, 219, 226, 233) Computing sample mean > mean(LevelAfter) [1] 234.9333 8
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Reading data from a file Save data in a text file, e.g., cholesterol.txt , in your working directory (set this from R file menu) > Level < read.table( " cholesterol.txt " , header=T) 9
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> mean(Level) LevelBefore LevelAfter 261.8000 234.9333 Assume this method in the following Reference: Introductory Statistics with R by Dalgaard, 2nd Edition, free e-book from library 10
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• Level$LevelBefore calls the LevelBefore column in cholesterol.txt > LevelBefore (haven’t defined this in R) Error: object 'LevelBefore' not found > Level$LevelBefore [1] 265 240 258 295 251 245 287 314 260 279 283 240 238 225 247 11
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The rich distorts the average income 12
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Sample median • Sample median : divide data into 2 equal parts, same # of observations below and above A sample of 5 scores: 92, 82, 76, 88, 62, arrange them in ascending order median = x (3) = 82 x (1) x (2) x (3) x (4) x (5) 62 76 82 88 92 13
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A sample of 6 scores: 92, 82, 76, 88, 62, 50 median = ( x (3) +x (4) )/2 = 79 A sample of n
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This note was uploaded on 03/16/2010 for the course GE 331 taught by Professor Negarkayavash during the Spring '09 term at University of Illinois at Urbana–Champaign.

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chap6 - Descriptive statistics Chapter 6 1 Statistics...

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