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Abstract

Analysis of means (ANOM) is a graphical alternative for the analysis of variance (ANOVA) that was primarily developed for multiple mean comparisons. The ANOM is a simple graphical display that provides a visualization of statistically significant results and it allows validating their practical significance without deep statistics knowledge. The classical ANOM has been developed to analyze fixed mean effects, and its recent developments allow testing random and mixed effects. On the other hand, analysis of covariance (ANCOVA) is an extension of ANOVA that applies to test means in the presence of uncontrollable concomitant/nuisance variables. To effectively communicate the statistical findings from ANCOVA to a general audience on some public interest issue areas such as COVID‐19, visualization of statistically significant results is a practical approach. This paper provides a graphical alternative for multiple group comparisons in ANCOVA as an extension of the ANOM. The proposed graphical alternative is validated and compared with the ANCOVA using a Monte Carlo simulation study. The simulation results indicated that the proposed method stands strong for practical ANCOVA problems. In addition, a COVID‐19 application and two additional applications related to toxicology and business are used to exhibit the value of the proposed graphical procedure in practice.

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Preface Introduction 1. One-Factor Balanced Studies 2. One-Factor Unbalanced Studies 3. Testing for Equal Variances 4. Complete Multi-Factor Studies 5. Incomplete Multi-Factor Studies 6. Axial Mixture Designs 7. Heteroscedastic Data 8. Distribution-Free Techniques Appendix A: Figures Appendix B: Tables Appendix C: SAS Examples References Index.
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Statistical hypothesis testing involving the comparison of three or more means and/or proportions is a frequent undertaking in medical statistics. For comparison of means, analysis of variance is a common choice and for comparison of proportions, χ(2) tests are common. However, both these approaches have important limitations which include the need for post hoc testing to identify the unusual group(s) without an integral graphical device to present the final results. These limitations are elegantly overcome by the analysis of means, which is widely used in industrial statistics, and illustrated here using means and proportions.
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In this paper we investigate the power function of the Studentised range test for comparing the means of normal populations in the one-way fixed effects analysis of variance model. The main results provide rigorous proofs of certain least favourable configurations of population means. These results are important in the calculation of the sample sizes required to guarantee power levels under certain restrictions on the ranges of the population means.
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To assess means and constraints of preconception care implementation. Three strategies were applied to promote preconception health: organisation of a campaign, production of guidelines, and implementation of a preconception pilot clinic. Three surveys investigated the knowledge and practices of women before and after the campaign, and one survey assessed the attitudes of gynaecologists. Posters and leaflets are more efficient than TV spots; implementation of a pilot clinic enhances all activities in the field of preconception health. With regard to constraints, we observed that (i) preconception care could not be provided when pregnancy was unplanned; (ii) the necessity of postponing pregnancy interfered with vaccinations; (iii) the compliance of women with regard to the prolonged intake of folates is poor; (iv) the application of guidelines by providers is inconsistent; (v) providers lack training regarding genetic ethical stakes; and (vi) practitioners find it difficult to integrate the concept of private eugenics and to envision the probabilistic character of the clinical manifestations of inherited diseases. We propose (i) flour fortification with folic acid; (ii) timely immunisation by preventive medicine at school, and (iii) continuous training of health care providers in the provision of preconception care.
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The objective of this study was to demonstrate through a case study how an analysis of means (ANOM) chart can be used to compare groups and to advocate the usefulness of this method in improvement work. The ANOM technique was used to compare referral rates among providers at the Dartmouth-Hitchcock Medical Center's Spine Center. The purpose was to see whether there were any differences across providers in referral rates to Behavioral Medicine services for patients who scored low on their mental health score and whether referral rates were any different among the patient characteristics. ANOM charts were also used to determine whether patient characteristics were different among the providers. Six of the 17 providers had significantly different referral rates compared to the overall referral rate of 38%. Seven patients' characteristics had a significantly different referral rate compared to the system's rate. The additional ANOM charts used to compare providers relative to specific patient characteristics demonstrated several special causes and revealed characteristic referral patterns for some of the providers analyzed. The ANOM chart may be underutilized in health care improvement work. The ANOM procedure of analyzing patient characteristics to determine differences among providers could be explored in other patient populations and settings.
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