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To illustrate and discuss current and proposed new concepts of effect size (ES) quantification and significance, with a focus on statistical and clinical/subjective interpretation and supported by empirical examples. Different methods for determining minimal clinically important differences (MCIDs) are reviewed, applied to practical examples (pain score differences in knee osteoarthritis), and further developed. Their characteristics, advantages, and disadvantages are illustrated and discussed. Empirical score differences between verum and placebo become statistically significant if sample sizes are sufficiently large. MCIDs, by contrast, are defined by patients' perceptions. MCIDs obtained by the most common “mean change method” can be expressed as absolute or relative scores, as different ES parameters, and as the optimal cutoff point on the receiver operating characteristic curve. They can further be modeled by linear and logistic regression, adjusting for potential confounders. Absolute and relative MCIDs are easy to interpret and apply to data of investigative studies. MCIDs expressed as effect sizes reduce bias, which mainly results from dependency on the baseline score. Multivariate linear and logistic regression modeling further reduces bias. Anchor-based methods use clinical/subjective perception to define MCIDs and should be clearly differentiated from distribution-based methods that provide statistical significance only.

Estimation of between-study heterogeneity is problematic in small meta-analyses. Bayesian meta-analysis is beneficial because it allows incorporation of external evidence on heterogeneity. To facilitate this, we provide empirical evidence on the likely heterogeneity between studies in meta-analyses relating to specific research settings. Our analyses included 6,492 continuous-outcome meta-analyses within the Cochrane Database of Systematic Reviews. We investigated the influence of meta-analysis settings on heterogeneity by modeling study data from all meta-analyses on the standardized mean difference scale. Meta-analysis setting was described according to outcome type, intervention comparison type, and medical area. Predictive distributions for between-study variance expected in future meta-analyses were obtained, which can be used directly as informative priors. Among outcome types, heterogeneity was found to be lowest in meta-analyses of obstetric outcomes. Among intervention comparison types, heterogeneity was lowest in meta-analyses comparing two pharmacologic interventions. Predictive distributions are reported for different settings. In two example meta-analyses, incorporating external evidence led to a more precise heterogeneity estimate. Heterogeneity was influenced by meta-analysis characteristics. Informative priors for between-study variance were derived for each specific setting. Our analyses thus assist the incorporation of realistic prior information into meta-analyses including few studies.

Presenting continuous outcomes in Summary of Findings tables presents particular challenges to interpretation. When each study uses the same outcome measure, and the units of that measure are intuitively interpretable (e.g., duration of hospitalization, duration of symptoms), presenting differences in means is usually desirable. When the natural units of the outcome measure are not easily interpretable, choosing a threshold to create a binary outcome and presenting relative and absolute effects become a more attractive alternative. When studies use different measures of the same construct, calculating summary measures requires converting to the same units of measurement for each study. The longest standing and most widely used approach is to divide the difference in means in each study by its standard deviation and present pooled results in standard deviation units (standardized mean difference). Disadvantages of this approach include vulnerability to varying degrees of heterogeneity in the underlying populations and difficulties in interpretation. Alternatives include presenting results in the units of the most popular or interpretable measure, converting to dichotomous measures and presenting relative and absolute effects, presenting the ratio of the means of intervention and control groups, and presenting the results in minimally important difference units. We outline the merits and limitations of each alternative and provide guidance for meta-analysts and guideline developers.

Soil salinity often hinders plant productivity in both natural and agricultural settings. Arbuscular mycorrhizal fungal (AMF) symbionts can mediate plant stress responses by enhancing salinity tolerance, but less attention has been devoted to measuring these effects across plant-AMF studies. We performed a meta-analysis of published studies to determine how AMF symbionts influence plant responses under non-stressed vs. salt-stressed conditions. Compared to non-AMF plants, AMF plants had significantly higher shoot and root biomass ( p < 0.0001) both under non-stressed conditions and in the presence of varying levels of NaCl salinity in soil, and the differences became more prominent as the salinity stress increased. Categorical analyses revealed that the accumulation of plant shoot and root biomass was influenced by various factors, such as the host life cycle and lifestyle, the fungal group, and the duration of the AMF and salinity treatments. More specifically, the effect of Funneliformis on plant shoot biomass was more prominent as the salinity level increased. Additionally, under stress, AMF increased shoot biomass more on plants that are dicots, plants that have nodulation capacity and plants that use the C3 plant photosynthetic pathway. When plants experienced short-term stress (<2 weeks), the effect of AMF was not apparent, but under longer-term stress (>4 weeks), AMF had a distinct effect on the plant response. For the first time, we observed significant phylogenetic signals in plants and mycorrhizal species in terms of their shoot biomass response to moderate levels of salinity stress, i.e., closely related plants had more similar responses, and closely related mycorrhizal species had similar effects than distantly related species. In contrast, the root biomass accumulation trait was related to fungal phylogeny only under non-stressed conditions and not under stressed conditions. Additionally, the influence of AMF on plant biomass was found to be unrelated to plant phylogeny. In line with the greater biomass accumulation in AMF plants, AMF improved the water status, photosynthetic efficiency and uptake of Ca and K in plants irrespective of salinity stress. The uptake of N and P was higher in AMF plants, and as the salinity increased, the trend showed a decline but had a clear upturn as the salinity stress increased to a high level. The activities of malondialdehyde (MDA), peroxidase (POD), and superoxide dismutase (SOD) as well as the proline content changed due to AMF treatment under salinity stress. The accumulation of proline and catalase (CAT) was observed only when plants experienced moderate salinity stress, but peroxidase (POD) and superoxide dismutase (SOD) were significantly increased in AMF plants irrespective of salinity stress. Taken together, arbuscular mycorrhizal fungi influenced plant growth and physiology, and their effects were more notable when their host plants experienced salinity stress and were influenced by plant and fungal traits.

The standardized mean difference (SMD) can be calculated from different mean differences (MDs) and standard deviations (SDs). This study aims to investigate how clinical trials calculated, reported and interpreted the SMD, and to examine the variation between different SMDs. We searched the PubMed for randomized controlled trials of general medicine and psychiatry that estimated SMDs. We explored how the SMD was computed and interpreted. We calculated SMDs based on different MDs and SDs, and the variation in these SMD estimates for each study. We included 161 articles. Various MDs and SDs were used to calculate SMDs, yet 69.0% studies failed to provide sufficient details. Variations in SMD estimates using different MDs and SDs in one study could be substantial (median of the absolute differences was 0.3, interquartile range IQR 0.17 to 0.53). However, 68.3% studies interpreted the SMD based on the same reference, Cohen's rule of thumb. The largest variations were observed in studies with small sample sizes and large reported effects. SMDs using different MDs and SDs could vary considerably, but the report was often insufficient and the interpretation was oversimplified. To avoid selective reporting bias and misinterpretation, prespecifying and reporting the method and interpreting the result from multiple perspectives are desirable.

The Classic Random Effects Model (CREM) has some limitations when using the standardized mean difference (SMD) as effect size index. Suero et al. (2025) have reformulated CREM as a Mixture Model (MM) and have developed unbiased estimators of the main parameters µδ and τ2. They compared their performance with two classic methods widely used: Restricted Maximum Likelihood (REML; Viechtbauer, 2005) and DerSimonian & Laird estimator (DL; 1986), finding small but systematic underestimations yielded by the classic procedures. The aim of this study is to check if Suero et al.’s (2025) results can be found beyond simulation contexts. For this purpose, we created three databases with real metaanalyses (MA) from clinical, experimental and educations fields of psychology. The results found are consistent with those found by Suero et al. (2025) being the mean estimates of MM higher than those of REML and DL. We also discuss about outliers found in real MAs such as bizarre effect sizes, disproportionated sample sizes or MAs with small numbers of primary studies.

To explore the impact of using different data standardization and scale-specific re-expression methods (i.e., processes to convert standardized data into scale-specific units) in meta-analyses using standardized mean differences (SMDs). We used data assessed by the Short Physical Performance Battery and the Barthel Index from a meta-analysis of randomized controlled trials which synthesized evidence of physical activity effectiveness on the functional capacity of hospitalized older adults. We standardized the data using study-specific pooled standard deviations (SDs), an internal, and an external SD references. Bayesian meta-analyses were performed for each method to compare the posterior distributions of the meta-analysis parameters. Posterior estimates were re-expressed into scale-specific units applying different methods established in the Cochrane guidelines. Meta-analysis estimates depend on the used standardization method. Analyses including data standardized using the largest SD reference presented lower estimates with less uncertainty in both scales. The method applied for re-expressing SMDs into scale-specific units impacted in their posterior clinical interpretation. The most similar results across models were obtained when using the same SD reference to standardize and re-express data. Different data standardization methods yielded different meta-analysis estimates on the SMD scale. To avoid the introduction of bias, the use of a single scale-specific SD reference to standardize data is recommended and instead of study-specific pooled sample SDs. Meta-analysis software packages may therefore change their default methods to allow this method by a single scale-specific SD. To re-express the SMDs into scale-specific units, we suggest the application of the same SD reference that was used for data standardization.

The classical meta-analytical random effects model (REM) has some weaknesses when applied to the standardized mean difference, g . Essentially, the variance of the studies involved is taken as the conditional variance, given a δ value, instead of the unconditional variance. As a consequence, the estimators of the variances involve a dependency between the g values and their variances that distorts the estimates. The classical REM is expressed as a linear model and the variance of g is obtained through a framework of components of variance. Although the weaknesses of the REM are negligible in practical terms in a wide range of realistic scenarios, all together, they make up an approximate, simplified version of the meta-analytical random effects model. We present an alternative formulation, as a mixture model, and provide formulas for the expected value, variance and skewness of the marginal distribution of g . A Monte Carlo simulation supports the accuracy of the formulas. Then, unbiased estimators of both the mean and the variance of the true effects are proposed, and assessed through Monte Carlo simulations. The advantages of the mixture model formulation over the “classical” formulation are discussed.

What Works Clearinghouse (WWC, 2022 ) recommends a design-comparable effect size (D-CES; i.e., g AB ) to gauge an intervention in single-case experimental design (SCED) studies, or to synthesize findings in meta-analysis. So far, no research has examined g AB ’s performance under non-normal distributions. This study expanded Pustejovsky et al. ( 2014 ) to investigate the impact of data distributions, number of cases ( m ), number of measurements ( N ), within-case reliability or intra-class correlation (ρ), ratio of variance components (λ), and autocorrelation (ϕ) on g AB in multiple-baseline (MB) design. The performance of g AB was assessed by relative bias ( RB ), relative bias of variance ( RBV ), MSE , and coverage rate of 95% CIs ( CR ). Findings revealed that g AB was unbiased even under non-normal distributions. g AB ’s variance was generally overestimated, and its 95% CI was over-covered, especially when distributions were normal or nearly normal combined with small m and N . Large imprecision of g AB occurred when m was small and ρ was large. According to the ANOVA results, data distributions contributed to approximately 49% of variance in RB and 25% of variance in both RBV and CR . m and ρ each contributed to 34% of variance in MSE . We recommend g AB for MB studies and meta-analysis with N  ≥ 16 and when either (1) data distributions are normal or nearly normal, m  = 6, and ρ = 0.6 or 0.8, or (2) data distributions are mildly or moderately non-normal, m  ≥ 4, and ρ = 0.2, 0.4, or 0.6. The paper concludes with a discussion of g AB ’s applicability and design-comparability, and sound reporting practices of ES indices.