Meta-analysis to integrate effect sizes within a paper: Possible misuse and Type-1 error inflation

In recent years an increasing number of papers have employed meta-analysis to integrate effect sizes of researchers’ own series of studies within a single paper (“internal meta-analysis”). Although this approach has the obvious advantage of obtaining narrower confidence intervals, we show that it could inadvertently inflate false-positive rates if researchers are motivated to use internal meta-analysis in order to obtain a significant overall effect. Specifically, if one decides whether to stop or continue a further replication experiment depending on the significance of the results in an internal meta-analysis, false-positive rates would increase beyond the nominal level. We conducted a set of Monte-Carlo simulations to demonstrate our argument, and provided a literature review to gauge awareness and prevalence of this issue. Furthermore, we made several recommendations when using internal meta-analysis to make a judgment on statistical significance.

The impact of European legislative and technology measures to reduce air pollutants on air quality, human health and climate

European air quality legislation has reduced emissions of air pollutants across Europe since the 1970s, affecting air quality, human health and regional climate. We used a coupled composition-climate model to simulate the impacts of European air quality legislation and technology measures implemented between 1970 and 2010. We contrast simulations using two emission scenarios; one with actual emissions in 2010 and the other with emissions that would have occurred in 2010 in the absence of technological improvements and end-of-pipe treatment measures in the energy, industrial and road transport sectors. European emissions of sulphur dioxide, black carbon (BC) and organic carbon in 2010 are 53%, 59% and 32% lower respectively compared to emissions that would have occurred in 2010 in the absence of legislative and technology measures. These emission reductions decreased simulated European annual mean concentrations of fine particulate matter(PM2.5) by 35%, sulphate by 44%, BC by 56% and particulate organic matter by 23%. The reduction in PM2.5 concentrations is calculated to have prevented 80 000 (37 000–116 000, at 95% confidence intervals) premature deaths annually across the European Union, resulting in a perceived financial benefit to society of US$232 billion annually (1.4% of 2010 EU GDP). The reduction in aerosol concentrations due to legislative and technology measures caused a positive change in the aerosol radiative effect at the top of atmosphere, reduced atmospheric absorption and also increased the amount of solar radiation incident at the surface over Europe. We used an energy budget approximation to estimate that these changes in the radiative balance have increased European annual mean surface temperatures and precipitation by 0.45 ± 0.11 °C and by 13 ± 0.8 mm yr−1 respectively. Our results show that the implementation of European legislation and technological improvements to reduce the emission of air pollutants has improved air quality and human health over Europe, as well as having an unintended impact on the regional radiative balance and climate.

High-precision measurements of the co-polar correlation coefficient: non-Gaussian errors and retrieval of the dispersion parameter µ in rainfall

The co-polar correlation coefficient (ρhv) has many applications, including hydrometeor classification, ground clutter and melting layer identification, interpretation of ice microphysics and the retrieval of rain drop size distributions (DSDs). However, we currently lack the quantitative error estimates that are necessary if these applications are to be fully exploited. Previous error estimates of ρhv rely on knowledge of the unknown "true" ρhv and implicitly assume a Gaussian probability distribution function of ρhv samples. We show that frequency distributions of ρhv estimates are in fact highly negatively skewed. A new variable: L = -log10(1 - ρhv) is defined, which does have Gaussian error statistics, and a standard deviation depending only on the number of independent radar pulses. This is verified using observations of spherical drizzle drops, allowing, for the first time, the construction of rigorous confidence intervals in estimates of ρhv. In addition, we demonstrate how the imperfect co-location of the horizontal and vertical polarisation sample volumes may be accounted for. The possibility of using L to estimate the dispersion parameter (µ) in the gamma drop size distribution is investigated. We find that including drop oscillations is essential for this application, otherwise there could be biases in retrieved µ of up to ~8. Preliminary results in rainfall are presented. In a convective rain case study, our estimates show µ to be substantially larger than 0 (an exponential DSD). In this particular rain event, rain rate would be overestimated by up to 50% if a simple exponential DSD is assumed.

Bootstrapping prediction intervals for autoregressive models

Methods of improving the coverage of Box–Jenkins prediction intervals for linear autoregressive models are explored. These methods use bootstrap techniques to allow for parameter estimation uncertainty and to reduce the small-sample bias in the estimator of the models’ parameters. In addition, we also consider a method of bias-correcting the non-linear functions of the parameter estimates that are used to generate conditional multi-step predictions.