12_13_quant stat

12_13_quant stat - Review of Quantitative Statistics CS 378...

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1 Review of Quantitative Statistics CS 378 Lecture 6
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2 Two Branches • Descriptive Statistics How can we report or display data? • Inferencial Statistics What meaning can we obtain from the data?
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3 Descriptive Statistics Example Data 3, 5, 3, 4, 2, 5, 10, 2, 1, 5, 8 • Measure of Central Tendancy Mean X = 4.36 œ ¸ ± 3œ" 8 X n1 1 48 i (the center of mass or the balance point) Median X 4 ~ X n odd n even œ H ÐÑ 8" # Ð " Ñ 88 ## XX 2 + where X is ith smallest X value Ð3Ñ (the center of probability) Mode MAX(X ) 5 œ i
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4 Descriptive Statistics Example Data 3, 5, 3, 4, 2, 5, 10, 2, 1, 5, 8 • Variability Variance 6.6 œ œ ±± 3œ" 3œ" 88 ## ÐÑ 3œ" 8 # (X X (X ) nn ii X) i n Ñ ± (division by n 1 for inference) Range Max(X ) Min(X ) 9 œ 3 i Inter Quartile Range 75th %-ile 25th %-ile • Other Measures Skewness Kurtosis
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5 Descriptive Statistics Displaying Data Single Group 8.7 10.1 10.6 8.7 11.1 9.7 10.3 10.9 9.0 8.4 9.2 9.4 11.2 10.8 9.9 7.5 9.4 10.1 12.2 10.0 8.7 8.6 9.4 9.1 10.2 9.8 11.7 11.2 11.0 11.0 10.0 10.4 9.9 10.3 9.9 10.9 10.3 8.8 7.6 9.7 8.4 10.1 10.8 9.6 10.5 9.9 10.2 10.3 9.2 10.1 9.7 10.2 11.4 12.0 7.9 10.6 8.4 8.5 9.1 8.8 11.0 9.3 9.6 9.3 9.9 10.5 10.5 10.0 10.6 10.1 11.1 8.4 10.1 11.8 10.8 9.9 8.6 10.2 10.1 9.7 10.0 9.8 10.3 9.0 10.1 9.4 10.1 11.3 8.7 11.1 10.6 10.6 10.2 8.9 11.0 10.7 9.0 9.4 9.6 10.5
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6 Histograms Cumulative Frequency Plots
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7 Descriptive Statistics Displaying Data Multiple Group Observations I n d e p V a r 123456T o t a l s A v e r a g e 5 7 8 15 11 9 10 60 10.00 10 12 17 13 18 19 15 94 16.54 15 14 18 19 17 16 18 102 12.00 20 19 25 22 23 18 20 127 21.17 383 15.96 Box Plots
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8 Tier Plots
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9 Inferential Statistics Random Sample only random (not systematic or Ê induced) error is involved Random Sampling Methods Simple use a randomization technique (eg. random Ê number generator) to select sample Stratified Sampling to account for a variables representation in the population (eg income level) 1. break up population into strata (groupings) of that variable (eg <$10,000, [$10,000, $50,000), etc) 2. keep starta %-age in sample the same as in population but randomly sample within each starta Real Life Issue have to work with what you have--be Ê honest & document.
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10 Inferential Statistics - Concepts • Parametric vs Nonparametric Parametric - X has some distributional form f (i.e. i normal) but we do no know the parameters, use data to estimate the parameters. Non parametric - no distributional form is assumed Parametric is easier and more efficeint but if the distributional assumption is invalid results are meaningless
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11 Inferential Statistics - Concepts Point Estimation Basics Given an unknown parameter and sample X , . .., X ) " n what are some estimators for ? They are functions @) of the random sample i.e. (X) 3, or max(X) or , . ..... ~~ @ œ ± 3œ" 8 3 X n an estimator is a random variable woth a probability Ê distribution and an estimate is a realization of that random variable! What is a good estimator? Properties unbiassedness E[ (X)] and inimum variance ~ œ
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12 Inferential Statistics - Concepts Interval Estimation Basics (Confidence Interval) Procedure 1. find some function h( (X), ) of the estimator with ~ @) a known distribution, 2. find percentage points such P r { h ( ( X ) , ) } 1 ~ )@ ) ) α αα /2 1 /2 ŸŸ œ s o l v e f o r . ) Examples is N(0,1) X /n .
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12_13_quant stat - Review of Quantitative Statistics CS 378...

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