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## Intro Stats and Data Analysis

by: Dr. Leon Koss

68

0

5

# Intro Stats and Data Analysis ECON 2370

Marketplace > University of Houston > Economcs > ECON 2370 > Intro Stats and Data Analysis
Dr. Leon Koss
UH
GPA 3.89

Staff

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COURSE
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Staff
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Class Notes
PAGES
5
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KARMA
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## Popular in Economcs

This 5 page Class Notes was uploaded by Dr. Leon Koss on Saturday September 19, 2015. The Class Notes belongs to ECON 2370 at University of Houston taught by Staff in Fall. Since its upload, it has received 68 views. For similar materials see /class/208206/econ-2370-university-of-houston in Economcs at University of Houston.

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Date Created: 09/19/15
Notes Econ 2370 Statistics and Probability 1 Moment Statistics Advantages Mathematically interrelated and related to other moments All have the same assumptions They provide the only i neasures of skewness and kurtosis They provide suf cient information to reconstruct a frequency distribution function Assumption Interval or ratio data univariate system General Moment Equation 1 N Wk i1 1 any variable having its origin at some point x x real or arbitrary origin operationally defined m the k moment about x Moments about the origin x O X raw score First Moment Ml Mean 2 X N 1 1 M 7E 2972 X l A i1 1 JV i1ltfnq Second Moment Mg Mi Xi quotagt1ltX2 2 N i1 7 N i1ff Third Moment fl13 A 7 1 i 3 1 U 3 i1 Fourth Moment flI4 N 7 1 d 4 1 U 4 in Xi A7fung i1 Spring 2000 1 Notes Econ 2370 Statistics and Probability Moments about the mean r X x1 Xi X raw score First Moment m1 1 N m1 0 Second Moment mz Variance 1 2 2 m2 1T M2 Ml Standard Deviation s Third Moment m3 1 y m3 IT 7 x3 M3 311111112 BilIf For a symmetrical distribution M3 0 This functionm is related to skewness but it is in uenced by the size of the unit of measure Fourth Moment m4 1 r 7m 1T 7 x3 M 411111113 611151112 3M m4 is directly related to kurtosis but it in uenced by the size of the metric unit Spring 2000 2 Notes Econ 2370 Statistics and Probability Standardized Moments r X 21 standardized score First Moment m 1 r111jzil Second Moment 12 1 121jzf1 Third Moment 13 Skewness N y 1 17W 31W x 2AMquot a3 N Z 7 7 3 1 2 1 7 m3 r 3 i1 MA12 Mf 8 3 Fourth Moment a4 Kurtosis a4 30 1 Z4 7 AMA 411111113 6Ali217l12 317W 7 77M i Mg M 122 Variach l4i7 i1 Interpretation of Moment Statistics Mean M 1 15 moment about the origin central tendency measure Variance mz 2nd moment about the mean dispersion measure Skewness r13 3rd standardize moment skewness measure 13 0 gt symmetrical 13 gt 0 gt positively skewed r13 lt 0 gt negatively skewed for 13 between 2 02 the distribution can be assumed to be normal with respect to skewness Kurtosis 14 30 45 standardized moment kurtosis measure 14 3 0 gt same peakedness normal curve 14 3 gt 0 gt more peakedness than normal curve Spring 2000 3 Notes Econ 2370 Statistics and Probability a4 3 lt 0 gt flattter than normal curve for 14 3 between 1 05 the curve can be considered normal with respect to kurtosis Example of years attending University of Houston Years Studmts X F FgtltX FgtltX2 FgtltX3 FgtltX4 1 5 5 5 5 5 2 4 8 16 32 64 3 3 9 27 81 243 4 7 28 112 448 1792 5 1 5 25 125 6 1 6 36 216 1296 N21 2X 61 Ml 290476 m1 000000 1 000000 2X2 221 Mg 10152381 mz 208617 2 100000 2X3 907 Mg 4319048 Mg 050167 13 016649 2X4 4025 1114 1916666 7m 902988 14 207483 Mean M 1 290476 9 Variance m2 208617 Standard Deviation 1m2 14443572 Skewness r13 016649 gt assumed normal Kurtosis a4 4192517 gt flatter than a normal distribution curve Spring 2000 4 Notes Econ 2370 Statistics and Probability 2 Single Sample Tests 21 Single sample test of the mean Where a is known Make Assumption Level of measurement interval Model random sampling population nornally distributed a some known value HO p some number Obtain a Sampling Distribution Z distribution M some number a Choose a Signi cance Level and Critical Region x 005 001 or 0001 One or two tail test H1 p 7 some number Compute a Test Statistics Make a decision Formula for computing the con dence interval Zgax 3 p 3 X Z0X 1 x Spring 2000 5

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