Statistics

Non-parametric test for differences between variables

This example illustrates on how to run non-parametric test to test for differences between variables. The example uses simulated series.

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## Non-parametric difference tests
##################
set seed 1234 	# only to ensure replicability
nulldata 100 	# cross-sectional dataset

# Create some random variables
series y = normal(0, 2)  # expected value 0
series x = normal(10, 2)  # expected value 2
list L = y x			# define a list of series which can be handy

# Stats and plot
summary L --simple
boxplot L --output=display
freq y --normal --plot=display

# Non-parametric difference tests
help difftest			# see the help for information

difftest y x --sign   # Sign test -- less powerful
printf "\nP-value of the Sign-test = %.2f (test-stat = %g)\n", $pvalue, $test

difftest y x --rank-sum   # Wilcoxon rank-sum test (aka Mann-Whitney U test)
printf "\nP-value of the Wilcoxon rank-sum test = %.2f (test-stat = %g)\n", $pvalue, $test

difftest y x --signed-rank   # Wilcoxon rank test

Parametric regression-based test for differences between categories

This example loads the cross-sectional and well-known MROZ dataset. By means of an OLS regression employing a level dummy, we want to test whether men earn higher wages in large cities compared to small cities.

open mroz87.gdt

boxplot HW CIT --factorized --output=display \
  { set title "Wages of men in small and large cities" font ',15'; }

# Regression for explaining Husband's wage by CIT (0: lives in small city, 1: lives in large city)
ols HW const CIT --robust   # robust standard errors wrt eventual heteroskedasticity
printf "\nThe null hypothesis that wages in large cities are equal  \n\
  to wages in small cities can be rejected at the %.2f pct. \n\
  significance level\n", $pvalue

# Run a restriction by hand
help restrict

# Test the null that hourly wages are on average 3$ higher in large cities
restrict --bootstrap
    b[CIT] = 3
end restrict