Using Linear Probability to Verify Random Assignment

A number of variables are omitted from the model and it is safe to do so as long as they are not correlated with regressors. This would be evidence of assignments to the control group that
are systematic. This can be checked using a regression. Since small is an indicator, we use a linear probability regression.

The independent variables include a constant, boy white_asian, tchexper and freelunch.

The result is

OLS, using observations 1-3743
Dependent variable: small

Heteroskedasticity-robust standard errors, variant HC3

Coefficient Std. Error

t-ratio

p-value

const

0.4665

0.0253

18.46

7.33e-073

boy

0.0014

0.0163

0.09

0.931

white_asian

0.0044

0.0197

0.22

0.823

tchexper

-0.0006

0.0014

-0.42

0.676

freelunch

-0.0009

0.0183

-0.05

0.961

Sum squared resid 930.9297

S. E. of

regression

0.499044

R[52]

0.000063

Adjusted R2

-0.001007

F(4, 3738)

0.059396

P-value(F)

0.993476

The overall-F statistic is not significant at 10%. None of the individual t-ratios are significant. Finally, a test of the hypothesis that the constant is ві = 0.5 cannot be rejected. A value of 0.5 would be consistent with assigning children to a small or large class by a fair coin flip. I think it is safe to omit these regressors from the model.

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