When to use the Bonferroni correction

PURPOSE: The Bonferroni correction adjusts probability (p) values because of the increased risk of a type I error when making multiple statistical tests. The routine use of this test has been criticised as deleterious to sound statistical judgment, testing the wrong hypothesis, and reducing the chance of a type I error but at the expense of a type II error; yet it remains popular in ophthalmic research. The purpose of this article was to survey the use of the Bonferroni correction in research articles published in three optometric journals, viz. Ophthalmic & Physiological Optics, Optometry & Vision Science, and Clinical & Experimental Optometry, and to provide advice to authors contemplating multiple testing. RECENT FINDINGS: Some authors ignored the problem of multiple testing while others used the method uncritically with no rationale or discussion. A variety of methods of correcting p values were employed, the Bonferroni method being the single most popular. Bonferroni was used in a variety of circumstances, most commonly to correct the experiment-wise error rate when using multiple 't' tests or as a post-hoc procedure to correct the family-wise error rate following analysis of variance (anova). Some studies quoted adjusted p values incorrectly or gave an erroneous rationale. SUMMARY: Whether or not to use the Bonferroni correction depends on the circumstances of the study. It should not be used routinely and should be considered if: (1) a single test of the 'universal null hypothesis' (Ho ) that all tests are not significant is required, (2) it is imperative to avoid a type I error, and (3) a large number of tests are carried out without preplanned hypotheses.

What's in a broken promissory obligation? Developing and testing a multiple component form measure of psychological contract breach

While the literature has suggested the possibility of breach being composed of multiple facets, no previous study has investigated this possibility empirically. This study examined the factor structure of typical component forms in order to develop a multiple component form measure of breach. Two studies were conducted. In study 1 (N = 420) multi-item measures based on causal indicators representing promissory obligations were developed for the five potential component forms (delay, magnitude, type/form, inequity and reciprocal imbalance). Exploratory factor analysis showed that the five components loaded onto one higher order factor, namely psychological contract breach suggesting that breach is composed of different aspects rather than types of breach. Confirmatory factor analysis provided further evidence for the proposed model. In addition, the model achieved high construct reliability and showed good construct, convergent, discriminant and predictive validity. Study 2 data (N = 189), used to validate study 1 results, compared the multiple-component measure with an established multiple item measure of breach (rather than a single item as in study 1) and also tested for discriminant validity with an established multiple item measure of violation. Findings replicated those in study 1. The findings have important implications for considering alternative, more comprehensive and elaborate ways of assessing breach.

Probing three-way interactions in moderated multiple regression:Development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research. Copyright 2006 by the American Psychological Association.

Self-testing for cancer:a community survey

Background: Cancer-related self-tests are currently available to buy in pharmacies or over the internet, including tests for faecal occult blood, PSA and haematuria. Self-tests have potential benefits (e.g. convenience) but there are also potential harms (e.g. delays in seeking treatment). The extent of cancer-related self-test use in the UK is not known. This study aimed to determine the prevalence of cancer-related self-test use. Methods: Adults (n = 5,545) in the West Midlands were sent a questionnaire that collected socio-demographic information and data regarding previous and potential future use of 18 different self-tests. Prevalence rates were directly standardised to the England population. The postcode based Index of Multiple Deprivation 2004 was used as aproxy measure of deprivation. Results: 2,925 (54%) usable questionnaires were returned. 1.2% (95% CI 0.83% to 1.66%) of responders reported having used a cancer related self test kit and a further 36% reported that they would consider using one in the future. Logistic regression analyses suggest that increasing age, deprivation category and employment status were associated with cancer-related self-test kit use. Conclusion: We conclude that one in 100 of the adult population have used a cancer-related self-test kit and over a third would consider using one in the future. Self-test kit use could alter perceptions of risk, cause psychological morbidity and impact on the demand for healthcare.

An online study combining the constructs from the theory of planned behaviour and protection motivation theory in predicting intention to test for chlamydia in two testing contexts

Chlamydia is a common sexually transmitted infection that has potentially serious consequences unless detected and treated early. The health service in the UK offers clinic-based testing for chlamydia but uptake is low. Identifying the predictors of testing behaviours may inform interventions to increase uptake. Self-tests for chlamydia may facilitate testing and treatment in people who avoid clinic-based testing. Self-testing and being tested by a health care professional (HCP) involve two contrasting contexts that may influence testing behaviour. However, little is known about how predictors of behaviour differ as a function of context. In this study, theoretical models of behaviour were used to assess factors that may predict intention to test in two different contexts: self-testing and being tested by a HCP. Individuals searching for or reading about chlamydia testing online were recruited using Google Adwords. Participants completed an online questionnaire that addressed previous testing behaviour and measured constructs of the Theory of Planned Behaviour and Protection Motivation Theory, which propose a total of eight possible predictors of intention. The questionnaire was completed by 310 participants. Sufficient data for multiple regression were provided by 102 and 118 respondents for self-testing and testing by a HCP respectively. Intention to self-test was predicted by vulnerability and self-efficacy, with a trend-level effect for response efficacy. Intention to be tested by a HCP was predicted by vulnerability, attitude and subjective norm. Thus, intentions to carry out two testing behaviours with very similar goals can have different predictors depending on test context. We conclude that interventions to increase self-testing should be based on evidence specifically related to test context.

Probabilistic multiple model neural network based leak detection system:experimental study

This paper presents an effective decision making system for leak detection based on multiple generalized linear models and clustering techniques. The training data for the proposed decision system is obtained by setting up an experimental pipeline fully operational distribution system. The system is also equipped with data logging for three variables; namely, inlet pressure, outlet pressure, and outlet flow. The experimental setup is designed such that multi-operational conditions of the distribution system, including multi pressure and multi flow can be obtained. We then statistically tested and showed that pressure and flow variables can be used as signature of leak under the designed multi-operational conditions. It is then shown that the detection of leakages based on the training and testing of the proposed multi model decision system with pre data clustering, under multi operational conditions produces better recognition rates in comparison to the training based on the single model approach. This decision system is then equipped with the estimation of confidence limits and a method is proposed for using these confidence limits for obtaining more robust leakage recognition results.

Early design verification of complex assembly variability using a hybrid - model based and physical testing - methodology

Design verification in the digital domain, using model-based principles, is a key research objective to address the industrial requirement for reduced physical testing and prototyping. For complex assemblies, the verification of design and the associated production methods is currently fragmented, prolonged and sub-optimal, as it uses digital and physical verification stages that are deployed in a sequential manner using multiple systems. This paper describes a novel, hybrid design verification methodology that integrates model-based variability analysis with measurement data of assemblies, in order to reduce simulation uncertainty and allow early design verification from the perspective of satisfying key assembly criteria.

Successful development and testing of a Method for Aggregating The Reporting of Interventions in Complex Studies (MATRICS)

Objectives: To develop a tool for the accurate reporting and aggregation of findings from each of the multiple methods used in a complex evaluation in an unbiased way. Study Design and Setting: We developed a Method for Aggregating The Reporting of Interventions in Complex Studies (MATRICS) within a gastroenterology study [Evaluating New Innovations in (the delivery and organisation of) Gastrointestinal (GI) endoscopy services by the NHS Modernisation Agency (ENIGMA)]. We subsequently tested it on a different gastroenterology trial [Multi-Institutional Nurse Endoscopy Trial (MINuET)]. We created three layers to define the effects, methods, and findings from ENIGMA. We assigned numbers to each effect in layer 1 and letters to each method in layer 2. We used an alphanumeric code based on layers 1 and 2 to every finding in layer 3 to link the aims, methods, and findings. We illustrated analogous findings by assigning more than one alphanumeric code to a finding. We also showed that more than one effect or method could report the same finding. We presented contradictory findings by listing them in adjacent rows of the MATRICS. Results: MATRICS was useful for the effective synthesis and presentation of findings of the multiple methods from ENIGMA. We subsequently successfully tested it by applying it to the MINuET trial. Conclusion: MATRICS is effective for synthesizing the findings of complex, multiple-method studies.

Aviation fuel gauging sensor utilizing multiple diaphragm sensors incorporating polymer optical fiber Bragg gratings

A high-performance fuel gauging sensor is described that uses five diaphragm-based pressure sensors, which are monitored using a linear array of polymer optical fiber Bragg gratings. The sensors were initially characterized using water, revealing a sensitivity of 98 pm/cm for four of the sensors and 86 pm/cm for the fifth. The discrepancy in the sensitivity of the fifth sensor has been explained as being a result of the annealing of the other four sensors. Initial testing in JET A-1 aviation fuel revealed the unsuitability of silicone rubber diaphragms for prolonged usage in fuel. A second set of sensors manufactured with a polyurethane-based diaphragm showed no measurable deterioration over a three month period immersed in fuel. These sensors exhibited a sensitivity of 39 pm/cm, which is less than the silicone rubber devices due to the stiffer nature of the polyurethane material used.