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It is common to summarize statistical comparisons by declarations of statistical significance or non-significance. Here we discuss one problem with such declarations, namely that changes in statistical significance are often not themselves statistically significant. By this, we are not merely making the commonplace observation that any particular threshold is arbitrary-for example, only a small change is required to move an estimate from a 5.1% significance level to 4.9%, thus moving it into statistical significance. Rather, we are pointing out that even large changes in significance levels can correspond to small, non-significant changes in the underlying variables.The error we describe is conceptually different from other oft-cited problems-that statistical significance is not the same as practical importance, that dichotomization into significant and non-significant results encourages the dismissal of observed differences in favor of the usually less interesting null hypothesis of no difference, and that any particular threshold for declaring significance is arbitrary. We are troubled by all of these concerns and do not intend to minimize their importance. Rather, our goal is to bring attention to what we have found is an important but much less discussed point. We illustrate with a theoretical example and two applied examples.

Objective There is limited information on the public health impact of wildfires. The relationship of cardiorespiratory hospital admissions (n = 40 856) to wildfire-related particulate matter (PM2.5) during catastrophic wildfires in southern California in October 2003 was evaluated. Methods Zip code level PM2.5 concentrations were estimated using spatial interpolations from measured PM2.5, light extinction, meteorological conditions, and smoke information from MODIS satellite images at 250 m resolution. Generalised estimating equations for Poisson data were used to assess the relationship between daily admissions and PM2.5, adjusted for weather, fungal spores (associated with asthma), weekend, zip code-level population and sociodemographics. Results Associations of 2-day average PM2.5 with respiratory admissions were stronger during than before or after the fires. Average increases of 70 μg/m3 PM2.5 during heavy smoke conditions compared with PM2.5 in the pre-wildfire period were associated with 34% increases in asthma admissions. The strongest wildfire-related PM2.5 associations were for people ages 65– 99 years (10.1% increase per 10 μg/m3 PM2.5, 95% CI 3.0% to 17.8%) and ages 0–4 years (8.3%, 95% CI 2.2% to 14.9%) followed by ages 20–64 years (4.1%, 95% CI 20.5% to 9.0%). There were no PM2.5–asthma associations in children ages 5–18 years, although their admission rates significantly increased after the fires. Per 10 μg/m3 wildfire-related PM2.5, acute bronchitis admissions across all ages increased by 9.6% (95% CI 1.8% to 17.9%), chronic obstructive pulmonary disease admissions for ages 20–64 years by 6.9% (95% CI 0.9% to 13.1%), and pneumonia admissions for ages 5–18 years by 6.4% (95% CI 21.0% to 14.2%). Acute bronchitis and pneumonia admissions also increased after the fires. There was limited evidence of a small impact of wildfire-related PM2.5 on cardiovascular admissions. Conclusions Wildfire-related PM2.5 led to increased respiratory hospital admissions, especially asthma, suggesting that better preventive measures are required to reduce morbidity among vulnerable populations.

This article provides a comprehensive review of multiple imputation (MI), a technique for analyzing data sets with missing values. Formally, MI is the process of replacing each missing data point with a set of m > 1 plausible values to generate m complete data sets. These complete data sets are then analyzed by standard statistical software, and the results combined, to give parameter estimates and standard errors that take into account the uncertainty due to the missing data values. This article introduces the idea behind MI, discusses the advantages of MI over existing techniques for addressing missing data, describes how to do MI for real problems, reviews the software available to implement MI, and discusses the results of a simulation study aimed at finding out how assumptions regarding the imputation model affect the parameter estimates provided by MI.

Understanding the mechanics of adaptive evolution requires not only knowing the quantitative genetic bases of the traits of interest but also obtaining accurate measures of the strengths and modes of selection acting on these traits. Most recent empirical studies of multivariate selection have employed multiple linear regression to obtain estimates of the strength of selection. We reconsider the motivation for this approach, paying special attention to the effects of nonnormal traits and fitness measures. We apply an alternative statistical method, logistic regression, to estimate the strength of selection on multiple phenotypic traits. First, we argue that the logistic regression model is more suitable than linear regression for analyzing data from selection studies with dichotomous fitness outcomes. Subsequently, we show that estimates of selection obtained from the logistic regression analyses can be transformed easily to values that directly plug into equations describing adaptive microevolutionary change. Finally, we apply this methodology to two published datasets to demonstrate its utility. Because most statistical packages now provide options to conduct logistic regression analyses, we suggest that this approach should be widely adopted as an analytical tool for empirical studies of multivariate selection.