# 3.3. Additional Methodological Parameters

Over-time comparability. ISATs and RSATs have been designed to be comparable since the late 1990s and early 2000s. Thus, the use of these modern assessments enables comparability over time.

Time Intervals. While this is one of the largest and most comprehensive comparable learning outcomes database produced to date, it is still sparse given limited test frequency. In past databases we smoothed time intervals over 5-year periods. This produced continuously spaced intervals, was designed to reduce noise by averaging results within these intervals and was comparable to the Barro-Lee approach for years of schooling. In this update, we have moved away from this approach. We now provide the year of the Reference Test X as documented in official reports. Since the doubloon index is a fixed conversion rate over a given interval, we produce a score for Anchor Test Y in the same year as Reference Test X. This enables greater granularity and precision of the data and enables the users of the database to make trade-offs at their discretion.

Schooling Levels. We construct a score for each grade and pool across grades within each schooling level to produce primary and secondary school scores. We include the default grade for TIMSS as the anchor grades across levels: grade 4 for primary and grade 8 for secondary. If we have data for additional grades, we include the closest grade with a preference for older grades since learning trajectories are steepest in the early years of learning introducing more scope for grade bias at earlier grades. If we have multiple test scores, we include the closest grade, and exclude the rest, rather than averaging. For example, we include PASEC grade 5 scores and exclude grade 2 scores. We include SACMEQ grade 6 scores along with PIRLS grade 4 scores at primary. If the test is designed for an age group (for example, PISA) we code it at the schooling level (for example, secondary for PISA).

Conceptually, the broader categories of primary and secondary scores enable us to categorize learning at critical schooling levels across assessments which span multiple grades and age groups. At the same time, we specify an approach to including specific grade levels to ensure we have a tight grade interval to minimize scope for grade-specific differences. While the interval is relatively small, it still leaves room for grade-fixed effects rather than test-fixed effects when linking tests. For example, linking PIRLS 2001 grade 4 with SACMEQ 2000 grade 6 might capture a grade difference in PIRLS (which is likely to increase performance) in addition to difficulty. However, to enable greater coverage, we put up with the need to expand beyond single grade level intervals. Moreover, these differences are often small and since the linking functions are applied across the entire set of countries being linked, any bias will be applied equally such that cross-country bias is eliminated for each pair-wise link and regional ranks will be preserved.

We distinguish primary from secondary schooling since enrollment rates drop off quickly between levels in many developing countries. This introduces a potential selection term in secondary school scores, with the highest performing students progressing in the system, biasing scores up due to selection rather than actual learning. We give this methodological 14