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In education, multisite trials involve randomization of pupils into intervention and comparison groups within schools. Most analytical models in multisite educational trials ignore that the impact of an intervention may be school dependent. This study investigates the impact of statistical models on the uncertainty associated with an effect size using comparable outcomes and covariates from ten multisite educational trials funded by the UK's Education Endowment Foundation. Ordinary least squares (OLS) models often assume that the pupil's outcomes within schools are independent, which is not always true. Multilevel models address this limitation by incorporating heterogeneity between schools to account for intra-school dependency. This inflates the confidence interval of an effect size obtained from the multilevel models than from an OLS model. For a multisite trial, the heterogeneity between schools also includes the differences in the expected impact of intervention between schools. Ignoring this additional school-by-intervention variation in a multisite trial could affect both its interpretation and conclusions. A robust approach to estimate the confidence intervals for effect size from multisite trials is by treating effect size as a parameter with its distribution. This paper is important for evaluating evidence from multisite trials by accounting for all sources of variability.

Educational stakeholders are keen to know the magnitude and importance of different interventions. However, the way evidence is communicated to support understanding of the effectiveness of an intervention is controversial. Typically studies in education have used the standardised mean difference as a measure of the impact of interventions. This measure, commonly known as the effect size, is problematic, in terms of how it is interpreted and understood. In this study, we propose a "gain index" as an alternative metric for quantifying and communicating the effectiveness of an intervention. This is estimated as the difference in the percentage of children who make positive gains between the intervention and control groups. Analysis of four randomized controlled trials in education supports the expectation that most children make progress due to normal school activities, which is independent of the intervention. This study elaborates a method to illustrate how trials with a positive gain index and with a higher percentage of pupils with positive gain in the intervention group can be used to communicate which trials are effective in improving educational outcomes.

Meta-analysis is the synthesis of findings from research projects, which enables an estimate of the average or pooled effect across various studies. This study presents findings from the intention to treat analysis for a series of educational evaluations in England using a two-stage meta-analysis with standardised outcome data and individual participant data meta-analyses. The research estimates the overall impact of educational trials on pupils eligible for Free School Meals (FSM) and the attainment gap in literacy and mathematics performance between FSM and non-FSM pupils based on analysis of 88 trials and data from over half a million pupils. For the meta-analyses, frequentist and Bayesian multilevel models were used to estimate the individual and pooled effect size across categories of explanatory variables such as age groups (key stages in England) and aspects of the type of interventions (one-to-one, small group, whole class). Results indicated that the overall impact of interventions on the literacy outcomes of FSM pupils was positive, with a pooled effect size of 0.06 (0.03, 0.08). However, for mathematics, no overall effect on FSM pupils was observed. Analysis of the attainment gap indicated that literacy outcomes for FSM pupils were improved by interventions marginally more than for non-FSM pupils (pooled attainment gap 0.01 (-0.01, 0.04)). The risk of bias assessment showed that estimates were consistent across different methodological approaches. Overall, evidence from this study can be used to identify, test and scale educational interventions in schools to improve educational outcomes for disadvantaged pupils.

Educational researchers advocate the use of an effect size and its confidence interval to assess the effectiveness of interventions instead of relying on a p-value, which has been blamed for lack of reproducibility of research findings and the misuse of statistics. The aim of this study is to provide a framework, which can provide direct evidence of whether an intervention works for the study participants in an educational trial as the first step before generalizing evidence to the wider population. A hierarchical Bayesian model was applied to ten cluster and multisite educational trials funded by the Education Endowment Foundation in England, to estimate the effect size and associated credible intervals. The use of posterior probability is proposed as an alternative to p-values as a simple and easily interpretable metric of whether an intervention worked or not. The probability of at least one month's progression or any other appropriate threshold is proposed to use in education outcomes instead of using a threshold of zero to determine a positive impact. The results show that the probability of at least one month's progress ranges from 0.09 for one trial, GraphoGame Rime, to 0.94 for another, the Improving Numeracy and Literacy trial.