Does ethnic diversity erode social trust? Continued immigration and corresponding growing ethnic diversity have prompted this essential question for modern societies, but few clear answers have been reached in the sprawling literature. This article reviews the literature on the relationship between ethnic diversity and social trust through a narrative review and a meta-analysis of 1,001 estimates from 87 studies. The review clarifies the core concepts, highlights pertinent debates, and tests core claims from the literature on the relationship between ethnic diversity and social trust. Several results stand out from the meta-analysis. We find a statistically significant negative relationship between ethnic diversity and social trust across all studies. The relationship is stronger for trust in neighbors and when ethnic diversity is measured more locally. Covariate conditioning generally changes the relationship only slightly. The review concludes by discussing avenues for future research.

Mixed-effects multilevel models are often used to investigate cross-level interactions, a specific type of context effect that may be understood as an upper-level variable moderating the association between a lower-level predictor and the outcome. We argue that multilevel models involving cross-level interactions should always include random slopes on the lower-level components of those interactions. Failure to do so will usually result in severely anti-conservative statistical inference. We illustrate the problem with extensive Monte Carlo simulations and examine its practical relevance by studying 30 prototypical cross-level interactions with European Social Survey data for 28 countries. In these empirical applications, introducing a random slope term reduces the absolute t-ratio of the cross-level interaction term by 31 per cent or more in three quarters of cases, with an average reduction of 42 per cent. Many practitioners seem to be unaware of these issues. Roughly half of the crosslevel interaction estimates published in the European Sociological Review between 2011 and 2016 are based on models that omit the crucial random slope term. Detailed analysis of the associated test statistics suggests that many of the estimates would not reach conventional thresholds for statistical significance in correctly specified models that include the random slope. This raises the question how much robust evidence of cross-level interactions sociology has actually produced over the past decades.

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Mixed effects multilevel models are often used to investigate cross-level interactions, a specific type of context effect that may be understood as an upper-level variable moderating the association between a lower-level predictor and the outcome. We argue that multilevel models involving cross-level interactions should always include random slopes on the lower-level components of those interactions. Failure to do so will usually result in severely anti-conservative statistical inference. Monte Carlo simulations and illustrative empirical analyses highlight the practical relevance of the issue. Using European Social Survey data, we examine a total 30 cross-level interactions. Introducing a random slope term on the lower-level variable involved in a cross-level interaction, reduces the absolute t-ratio by 31% or more in three quarters of cases, with an average reduction of 42%. Many practitioners seem to be unaware of these issues. Roughly half of the cross-level interaction estimates published in the European Sociological Review between 2011 and 2016 are based on models that omit the crucial random slope term. Detailed analysis of the associated test statistics suggests that many of the estimates would not meet conventional standards of statistical significance if estimated using the correct specification. This raises the question how much robust evidence of cross-level interactions sociology has actually produced over the past decades.

An ever-growing number of studies investigates the relation between ethnic diversity and social cohesion, but these studies have produced mixed results. In cross-national research, some scholars have recently started to investigate more refined and informative indices of ethnic diversity than the commonly used Hirschman-Herfindahl Index. These refined indices allow to test competing theoretical explanations of why ethnic diversity is associated with declines in social cohesion. This study assesses the applicability of this approach for sub-national analyses. Generally, the results confirm a negative association between social cohesion and ethnic diversity. However, the competing indices are empirically indistinguishable and thus insufficient to test different theories against one another. Follow-up simulations suggest the general conclusion that the competing indices are meaningful operationalizations only if a sample includes: (1) contextual units with small and contextual units with large minority shares, as well as (2) contextual units with diverse and contextual units with polarized ethnic compositions. The results are thus instructive to all researchers who wish to apply different diversity indices and thereby test competing theories.

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Quantitative comparative social scientists have long worried about the performance of multilevel models when the number of upper-level units is small. Adding to these concerns, an influential Monte Carlo study by Stegmueller (2013) suggests that standard maximum-likelihood (ML) methods yield biased point estimates and severely anti-conservative inference with few upper-level units. In this article, the authors seek to rectify this negative assessment. First, they show that ML estimators of coefficients are unbiased in linear multilevel models. The apparent bias in coefficient estimates found by Stegmueller can be attributed to Monte Carlo Error and a flaw in the design of his simulation study. Secondly, they demonstrate how inferential problems can be overcome by using restricted ML estimators for variance parameters and a t-distribution with appropriate degrees of freedom for statistical inference. Thus, accurate multilevel analysis is possible within the framework that most practitioners are familiar with, even if there are only a few upper-level units.

This study explores how researchers’ analytical choices affect the reliability of scientific findings. Most discussions of reliability problems in science focus on systematic biases. We broaden the lens to emphasize the idiosyncrasy of conscious and unconscious decisions that researchers make during data analysis. We coordinated 161 researchers in 73 research teams and observed their research decisions as they used the same data to independently test the same prominent social science hypothesis: that greater immigration reduces support for social policies among the public. In this typical case of social science research, research teams reported both widely diverging numerical findings and substantive conclusions despite identical start conditions. Researchers’ expertise, prior beliefs, and expectations barely predict the wide variation in research outcomes. More than 95% of the total variance in numerical results remains unexplained even after qualitative coding of all identifiable decisions in each team’s workflow. This reveals a universe of uncertainty that remains hidden when considering a single study in isolation. The idiosyncratic nature of how researchers’ results and conclusions varied is a previously underappreciated explanation for why many scientific hypotheses remain contested. These results call for greater epistemic humility and clarity in reporting scientific findings.