# **5.2 Test-score scaling**

Next, we explore sensitivities to score scales, comparing our results based on scores rescaled via a linear transformation of 300 points to the original HLO score scale. This enables us to use a scale that starts at zero, which has useful statistical properties. In Appendix Figure B2, we corroborate this _de facto_ floor with data from EGRA, which shows that an HLO score of 300 corresponds roughly to zero percent reading comprehension.

Appendix Figure B3 compares the _L_<sup>_h_</sup> _i_<sup>valueusingthetwoscorescales.Whilethescalethat</sup> we use largely does not affect relative ranks, it does affect the degree of the absolute learning adjustment. Using the original scale (y-axis), the distance between Mexico and Ghana is 0.2; by contrast, under the re-scaled version (x-axis), the distance is closer to 0.5. Appendix Figure B4 compares results using the two score scales. In Panel A, we see that the main effect of the rescaling is to reduce the micro-LAYS values that are based on participation impacts—for example, conditional cash transfers in Malawi. This is because under the original scale, the maximum learning adjustment discounted a year of school by about half, since the _de facto_ floor of the HLO scale was 300, which produced a learning-adjustment factor, _L_<sup>_h_</sup> _i_<sup>,of0.48relativetothehigh-performancebenchmark</sup> of 625. Under the rescaling, the minimum learning factor converges to zero, and the learning adjustments drop substantially, reducing participation-based LAYS estimates. As an example, the learning adjustment in Kenya shifts from an original _L_<sup>_h_</sup> _i_<sup>of0.73to0.48,whilecountrieson</sup> the lowest tail of distribution, such as Malawi, shift from a learning-adjustment of 0.57 to 0.18. The re-scaling does not affect the computation of learning-based micro-LAYS, since those values are derived relative to an artificial high-performance benchmark of 0.8 _σ_ . However, as an added sensitivity test, we can use the old scale to derive a new corresponding high-performance benchmark of 1.8 _σ_ . Panel B plots LAYS using this new benchmark.

These sensitivity tests show that the unscaled scores yield higher values for micro-LAYS based on participation estimates. Also, although unscaled scores largely preserve rank, they understate the degree of learning adjustment, especially for countries on the lower tail of the distribution. For these reasons, in the main results presented in this paper we use micro-LAYS based on re-scaled scores. Since the lowest-performing countries are already far behind, re-scaling of scores is unlikely to yield major new insights and will not change ranks; however, we think re-scaling is important for capturing the full degree of the learning gap.

# **5.3 Standard deviations across tests and samples**

We also test sensitivity of our results to differences in standard deviations across tests and samples. This is relevant because, for the interventions included in our comparisons, we use effect sizes expressed in standard deviations of each intervention’s test and sample as inputs into LAYS. Note that this issue is not inherent to LAYS, which are just a unit of measurement that can be applied to any assessment results. In an ideal world (ideal from a comparability perspective), all interventions and national-level assessments would use the exact same test to measure learning 26