cd "C:\Users\Aki\Documents\stata"
log using march7.log, replace

**************MARCH 7. INFERENTIAL STATISTICS*************
**doing statistical tests
**STATISTICS OF TWO CATEGORICAL VARIABLES
sysuse auto, clear
tab rep78 foreign
tab rep78 foreign, chi2 
//this test is used to check the relationship between two categorical variables, var x (rep78) and var y (foreign)
//H0: there is no relationship. If P-value is small, then you reject the H0. There is some relationship between these two variables.

**testing means. 
**e.g. do men earn more than women? (statistically)
**are foreign cars more expensive than domestic? (is there any statistical difference?)
**is the difference in means of prices (the average prices) between foreign vs domestic cars is significantly different from 0?

su price 
**is the average price of cars different from 6000?
ttest price == 6000
//cannot reject the H0. The mean price of cars is not statistically different from 6000

**are foreign cars more expensive than domestic?
ttest price, by(foreign)
//H0: Mean price (domestic) = mean price (foreign)
//OR: Mean price (domestic) - mean price (foreign) = 0
//cannot reject H0: there is no statistical difference in average prices of foreign and domestic cars
su price if foreign==1
su price if foreign==0

//t-test is about two means: means are equal


***bivariate correlation and regression
**Pearson's correlation (bivariate correlation)
correlate price mpg weight
//correlations between mpg and price, between mpg and weight are negative
//correlation between weight and price is positive
//the strongest correlation is between weight and mpg

pwcorr price mpg weight, sig
//we have also an information about the statistical significance of correlations.
//all correlations here are statistically significant

***tests for variances
use nlsw, clear
sum wage if country==1
sum wage if country==2
sum wage if country==3

oneway wage country, tab
//ANOVA is shown at the second, bottom part of the table. For between groups comparison, high F and small P means that statistically, the difference in variance between different groups of countries is high 
//Bartlett's test: Ho is that the variances are equal. With small P-value, reject ths H0 and conclude that the variances are not equal

anova wage country
//checks for equal variances to see if there is a difference between different groups. test if mean of a dependent var is the same for two unrelated groups
//analysis of variance

//dependent variable should be continous, independent var should be categorical / dummy
//dependent var should be approximately normally distributed 

histogram wage

anova wage country##south


pwmean wage, over(country) effects
//pairwise comparisons of means with equal variables (!) to determine which groups differed from each other
log close