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***SOCI 600: INTRODUCTION TO SOCIOLOGICAL DATA ANALYSIS
***NORMAL CURVE
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***CLEAR MEMORY
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clear all

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***CREATE SHORTCUTS AND LOG FILE
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***Shortcut for folders
global codes  = "H:\course\codes"
global data   = "H:\course\data"
global output = "H:\course\output"

***Start saving results window
log using "$codes\Stata04a.log", replace text

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***OPENING COMMANDS
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***Tell Stata to not pause for "more" messages
set more off

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***GRAPH COMMAND TO GENERATE NORMAL DISTRIBUTION
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***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))

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***AREA UNDER THE NORMAL CURVE
***"normal" shows area below Z
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***Survey in a community collected information about age of individuals
***Average age = 35.5
***Standard deviation of age = 10

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***What's the probability of finding someone
***who is younger than 44 years of age?

***Estimate Z = (x - mean) / standard deviation
display (44-35.5)/10
di (44-35.5)/10

***Area below Z=0.85
di normal(0.85)

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***What's the probability of finding someone
***who is older than 40 years of age?

***Estimate Z = (x - mean) / standard deviation
di (40-35.5)/10

***Area above Z=0.45
di 1-normal(0.45)

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***What's the probability of finding someone
***who is younger than 22 years of age?

***Estimate Z = (x - mean) / standard deviation
di (22-35.5)/10

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

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***What's the probability of finding someone
***who is between 32 and 42 years of age?

***Estimate Z = (x - mean) / standard deviation
di (32-35.5)/10
di (42-35.5)/10

***Area between Z=-0.35 and Z=0.65
di normal(0.65)-normal(-0.35)

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***What's the probability of finding someone
***who is between 42 and 46 years of age?

***Estimate Z = (x - mean) / standard deviation
di (42-35.5)/10
di (46-35.5)/10

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

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***What's the probability of finding someone
***who is above 50 years of age?

***Estimate Z = (x - mean) / standard deviation
di (50-35.5)/10

***Area above Z=1.45
di 1-normal(1.45)

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***DISTRIBUTION OF INCOME
***AMERICAN COMMUNITY SURVEY
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***Open 2019 ACS
use "$data\ACS2019.dta", clear

***Complex survey design
svyset cluster [pweight=perwt], strata(strata) singleunit(scaled)

***Wage and salary income
gen income=.
  replace income=incwage if incwage!=0 & incwage!=999999
  
***Histogram of income
hist income, norm percent

***Boxplot of income
graph hbox income

***Quantile-normal plot of income
qnorm income

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

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

***Boxplot of log of income
graph hbox lnincome

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

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***What's the probability of finding someone
***who makes more than $50,000 per year?

***Original income variable (income)
***This variable does not have a normal distribution
sum income

***Log of income (lnincome)
***This variable has a distribution closer to normal
svy: mean lnincome
estat sd

***Mean = 10.27
***Standard deviation = 1.23

***$50,000 in log scale
di ln(50000)

***Estimate Z = (x - mean) / standard deviation
di (10.82-10.27)/1.23

***Area above Z=0.45
di 1-normal(0.45)

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***CLOSING COMMANDS
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***Save data
save "$data\Stata04a.dta", replace

***Save log
log close