Problems with Using the Normal Distribution – and Ways to Improve Quality and Efficiency of Data Analysis

Background: The Gaussian or normal distribution is the most established model to characterize quantitative variation of original data. Accordingly, data are summarized using the arithmetic mean and the standard deviation, by x 6 SD, or with the standard error of the mean, x 6 SEM. This, together with corresponding bars in graphical displays has become the standard to characterize variation. Methodology/Principal Findings: Here we question the adequacy of this characterization, and of the model. The published literature provides numerous examples for which such descriptions appear inappropriate because, based on the ‘‘95 % range check’’, their distributions are obviously skewed. In these cases, the symmetric characterization is a poor description and may trigger wrong conclusions. To solve the problem, it is enlightening to regard causes of variation. Multiplicative causes are by far more important than additive ones, in general, and benefit from a multiplicative (or log-) normal approach. Fortunately, quite similar to the normal, the log-normal distribution can now be handled easily and characterized at the level of the original data with the help of both, a new sign, x /, times-divide, and notation. Analogous to x 6 SD, it connects the multiplicative (or geometric) mean x * and the multiplicative standard deviation s * in the form x * x /s*, that is advantageous and recommended. Conclusions/Significance: The corresponding shift from the symmetric to the asymmetric view will substantially increas

Risk Factors for SARS Transmission from Patients Requiring Intubation: A Multicentre Investigation in Toronto, Canada

In the 2003 Toronto SARS outbreak, SARS-CoV was transmitted in hospitals despite adherence to infection control procedures. Considerable controversy resulted regarding which procedures and behaviours were associated with the greatest risk of SARS-CoV transmission.A retrospective cohort study was conducted to identify risk factors for transmission of SARS-CoV during intubation from laboratory confirmed SARS patients to HCWs involved in their care. All SARS patients requiring intubation during the Toronto outbreak were identified. All HCWs who provided care to intubated SARS patients during treatment or transportation and who entered a patient room or had direct patient contact from 24 hours before to 4 hours after intubation were eligible for this study. Data was collected on patients by chart review and on HCWs by interviewer-administered questionnaire. Generalized estimating equation (GEE) logistic regression models and classification and regression trees (CART) were used to identify risk factors for SARS transmission. ratio ≤59 (OR = 8.65, p = .001) were associated with increased risk of transmission of SARS-CoV. In CART analyses, the four covariates which explained the greatest amount of variation in SARS-CoV transmission were covariates representing individual patients.Close contact with the airway of severely ill patients and failure of infection control practices to prevent exposure to respiratory secretions were associated with transmission of SARS-CoV. Rates of transmission of SARS-CoV varied widely among patients