A good female friend of mine (lets call her K) recently made the following post on facebook: "Men in DC, Disaster..."

I think that there is a selection bias here that has contaminated the results of this experiment. Let us examine the average treatment effect as follows:

If we let: D equal the treatment indicator, where treatment is defined as romantic exposure of a DC guy to K; Y equal the outcome variable, which is K's happiness, then we can define the average treatment effect ATE as:

ATE = E[Y1-Y0] =

( αE[Y1|D=1] + (1-α)E[Y0|D=0] ) + ( (1-α)E[Y1|D=0]−(α)E[Y0|D=1] )

where the first term is the observed outcome:

αE[Y1|D=1] + (1-α)E[Y0|D=0]

and the second term is the selection bias:

(1-α)E[Y1|D=0]−(α)E[Y0|D=1].

So that:

(observed outcome) = ATE - selection bias

The first term in the selection bias is the expected happiness of K had she dated DC men that she did not date, and the second term is the expected happiness of K had she not dated DC men that she did date. α is the proportion of DC men that K did in fact date.

Within the selection bias term, I argue that the former term is likely much higher than the latter term, making the overall selection bias highly positive, thus leading to the very negative observed outcome despite the true average treatment effect (romantic exposure to DC men) being actually highly positive.

Why does the selection bias lead to such poor observed outcomes? Because the DC men that get romantic exposure to K are on average worst of all DC men (perhaps she tends to scare the good ones off?)

To eliminate the selection bias, K needs to do some RANDOMIZATION - i.e. she should date a random selection of men and then measure her happiness after each date. The results may very well redeem DC men in general.

Note that this research project is actually self funding (even the jerks will pay for dinner/coffee), which would help in a pitch to the MIT poverty action lab to run the experiment. Good luck to her!

If we let: D equal the treatment indicator, where treatment is defined as romantic exposure of a DC guy to K; Y equal the outcome variable, which is K's happiness, then we can define the average treatment effect ATE as:

ATE = E[Y1-Y0] =

( αE[Y1|D=1] + (1-α)E[Y0|D=0] ) + ( (1-α)E[Y1|D=0]−(α)E[Y0|D=1

where the first term is the observed outcome:

αE[Y1|D=1] + (1-α)E[Y0|D=0]

and the second term is the selection bias:

(1-α)E[Y1|D=0]−(α)E[Y0|D=1

So that:

(observed outcome) = ATE - selection bias

The first term in the selection bias is the expected happiness of K had she dated DC men that she did not date, and the second term is the expected happiness of K had she not dated DC men that she did date. α is the proportion of DC men that K did in fact date.

Within the selection bias term, I argue that the former term is likely much higher than the latter term, making the overall selection bias highly positive, thus leading to the very negative observed outcome despite the true average treatment effect (romantic exposure to DC men) being actually highly positive.

Why does the selection bias lead to such poor observed outcomes? Because the DC men that get romantic exposure to K are on average worst of all DC men (perhaps she tends to scare the good ones off?)

To eliminate the selection bias, K needs to do some RANDOMIZATION - i.e. she should date a random selection of men and then measure her happiness after each date. The results may very well redeem DC men in general.

Note that this research project is actually self funding (even the jerks will pay for dinner/coffee), which would help in a pitch to the MIT poverty action lab to run the experiment. Good luck to her!

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