% hw1_1.m 
% Economics 696F, Spring 2007
% suggested solution to HW1, Question 1

% Data for this question:

T=[zeros(10,1)
   ones(10,1)];
Y=[-1.1
-2.1
-0.7
-0.7
0.4 
0.8 
-0.1
1.8 
0.1 
1.1 
-2.3
1.1 
0.1 
1.0 
-0.6
-1.7
2.3 
2.4 
2.6 
4.6];

% First calculate sample means
yhat1 = mean(Y(T==1))
yhat0 = mean(Y(T==0))
tauhat = yhat1 - yhat0
% this yielded: tauhat=1

% Find p-value for hypothesis of no treatment effect 
J=500000; % number of simulations
exceed = 0; % number of times a simulation exceeds observed tauhat

for j=1:J,
    % first, create a hypothetical random treatment assignment
    R = randn(20,1);
    medR = median(R);
    T_j = R>medR;
    yhat1_j = mean(Y(T_j==1));
    yhat0_j = mean(Y(T_j==0));
    tauhat_j = yhat1_j - yhat0_j;
    if abs(tauhat_j)>abs(tauhat),
        exceed=exceed+1;
    end; 
end;    

pvalue_sim=exceed/J
% this led to a p-value of 0.20366

% finally, calculate t-statistic 
s1squared = sum( (Y(T==1)-yhat1).^2)/9
s0squared = sum( (Y(T==0)-yhat0).^2)/9
t_stat = (yhat1-yhat0)/sqrt(s1squared/10+s0squared/10)

% t-stat is 1.3087
% p-value (using normal approximation) is approximately .2

% end hw1_1.m