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***THE NORMAL CURVE (chapter 5)
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***OPENING COMMANDS
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***Clear memory
clear all

***Start saving results window
log using "C:\course\progs\Stata03.log", replace text // Windows
log using "/course/progs/Stata03.log", replace text // Macintosh

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***GRAPH COMMAND TO GENERATE NORMAL DISTRIBUTION
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***#delimit resets the character that marks the end of a command
#delimit ;

***Plot two normal distributions
***IQ scores for females and males
graph twoway (function y=normalden(x,100,10), range(40 160) lcolor(maroon) lw(medthick))
             (function y=normalden(x,100,20), range(40 160) lcolor(navy) lw(medthick)),
  title("Normal density of IQ scores for females and males", color(black))
  xtitle("IQ Units", size(medlarge)) ytitle("")
  xlabel(40(10)160)
  xscale(lw(medthick)) yscale(lw(medthick))
  legend(order(1 "Females" 2 "Males"))
  graphregion(fcolor(white));

***#delimit resets the character that marks the end of a command
#delimit cr

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***AREA UNDER THE NORMAL CURVE
***"normal" shows area below Z
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***Area below Z=0.85
display normal(0.85)
di normal(0.85)

***Area above Z=0.40
di 1-normal(0.4)

***Area below Z=-1.35
di normal(-1.35)

***Area between Z=-0.35 and Z=0.60
di normal(0.6)-normal(-0.35)

***Area between Z=0.65 and Z=1.05
di normal(1.05)-normal(0.65)

***Area above Z=1.5
di 1-normal(1.5)

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***DISTRIBUTION OF INCOME
***GENERAL SOCIAL SURVEY
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***Open 2016 GSS
use "C:\course\data\GSS2016.dta", clear // Windows
use "/course/data/GSS2016.dta", clear // Macintosh

***Histogram of income
hist conrinc, norm percent

***Boxplot of income
graph hbox conrinc

***Quantile-normal plot of income
qnorm conrinc

***Power transformation
***q<1 (reduce positive skew)
***log(y): q=0
gen lnconrinc = ln(conrinc)

***Histogram of log of income
hist lnconrinc, norm percent

***Boxplot of log of income
graph hbox lnconrinc

***Quantile-normal plot of log income
qnorm lnconrinc

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***CLOSING COMMANDS
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***Save log
log close