# _4.5. Detailed decompositions at percentiles using a “hybrid” approach_

Table A4a and A4b in the appendix contain the (transformed) RIF regression coefficients at selected quantiles (10<sup>th,</sup> 50<sup>th</sup> and 90<sup>th</sup> ). Students in the right age for 8<sup>th</sup> grade are associated with a higher score, while the effect of being an overage student reduces scores and more so at higher point in the score distribution. Speaking the test language at home seems beneficial to high scoring students, but the opposite is the case below the median. The effect of books at home is complex; high scoring student with the most books at home are associated with a higher score in science; however, the pattern for mathematics is different, with students below the median associated with a higher score in 2003, but a lower score in 2007. The effect of having a parent with tertiary education is small for poorly performing students, but increases substantially at higher points in the distribution, especially in science. Having both parents born in Ghana has a strong positive association with scores in 2003 and less so in 2007. Two of the most powerful regressors have to do with paid work and time spent on homework. At the median, a child in combining paid work with study results in a decline in mathematics (science) score by 10 points (18 points); likewise, spending no time on homework decreases scores by 13 (17) points.

Larger 8th grade enrolment is associated with higher scores.<sup>6</sup> The association between community size and performance is strong but heterogeneous. For example, in science there a strong positive association between high performing students in large cities (>500,000) and performance in 2003; for students below the median the positive association is strongest for medium-size communities (15,000-500,000). However, small communities (<3,000) are consistently associated with lower performance in both mathematics and science. In 2003, students in schools with low proportion of disadvantaged students performed better; however, this association seems to have disappeared or reversed in 2007. There is some evidence that ability grouping by schools is negatively associated with performance, especially I science. Students in schools with a severe absenteeism problem performed worse, while high performing students in schools with high index of good attendance performed better.

Teacher age is negatively associated with student performance, while the opposite is the case for teacher years of experience. Having a teacher with university education (ISCED 5A) results in a significant increase in student scores (but mostly in science), and this effect increased in 2007 compared to 2003. Finally, the practice of pay incentives to teachers has a moderate by consistently positive association with performance, and more so at higher points in the distribution.

Decompositions results (given in tables 5a and 5b, with detailed results in tables A5a and A5b in the appendix) are derived from the 2-step procedure outlined in the methodology section. In the first step, the changes in score and its two constituent components are derived using reweighting, without imposing specific functional forms or parametric distributions when deriving estimates of the total gap. In deriving the re-weighting functions, the probability that a person belongs in the “year 2003” group conditional on (propensity score) is estimated from a logit regression. In the second step, estimates of the effects of each individual variable on the test score gap are generated. The estimation of unconditional quantile regression involves deriving

> 6 The Ministry of Education (2004) of Ghana in its summary of its key findings on TIMSS 2003 found a positive correlation between class size and student performance.

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