Learning in Bridge, Public and Private Schools in Lagos
Table 11 Comparison of Bridge with private schools Literacy Coefficient on Bridge Dummy
R squared
Regression with no controls (Table 10, Col 1)
0.351
0.045
Regression with controls (Table 10, Col 2)
0.233
0.128
Effect size if selection on unobserved variables = selection on observed variable (Beta, β if σ = 1)
0.161
Selection
1
Required relative selection on unobservables (Delta, σ) for true effect size to be equal to zero (β = 0) R Max (Assumed maximum possible R squared is equal 1.3 times the R-squared achieved in the regression with controls (Table 10, Col 2)
2.232
0.166
This estimate of σ is based on an assumption that the maximum possible R-Squared is 1.3 times the Rsquared reached in the fully controlled model. This value is proposed by Oster (2016) based on an analysis of 65 randomized studies from top five economics journals. 90 percent of the randomized studies are robust to a R Max of 1.3 times the r-squared reached in the fully controlled model. We demonstrate the sensitivity of the main estimate to varying the maximum possible r-squared in the figure below. For the true coefficient to be zero, the maximum possible R-squared would need to be 1.7 times the R-squared achieved in the fully controlled model. Figure 35 Sensitivity of coefficient estimate to varying maximum possible r-squared
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