Interpretation Of Confidence Intervals Research Articles

Concept and Interpretation of Confidence Interval: How to Overcome Limitations of P-value

Knowing the estimate (mean or proportion) for the whole population is not feasible due to a lack of resources. Therefore, we rely on a sample estimate to draw conclusions about the population. The range of values in which the true population estimate lies is called a confidence interval (CI) which is more reliable than single estimate. For descriptive studies, CIs should be reported along with the point estimate (mean or proportion). For effect sizes in inferential statistics (mean difference, odds ratio, risk ratio, etc.), the p-value should be supplemented with a CI for strength and direction of the association.

Why proper understanding of confidence intervals and statistical significance is important.

Why proper understanding of confidence intervals and statistical significance is important.

A Tale of Confusion From Overlapping Confidence Intervals.

In clinical research presentations, study results are commonly reported in the form of P values and confidence intervals as an estimate of association and treatment effect. The interpretation of confidence intervals that overlap can be confusing and difficult for the reader to draw clinically meaningful conclusions. In this brief report, we describe the basics of confidence intervals and present an example from a recently published randomized control trial to illustrate a common confusion that overlapping confidence intervals between the means of two independent groups may not necessarily reject the true significant difference of effect. It is recommended that investigators use the direct difference of means between groups for confidence interval estimation to reduce type II errors. Clinicians should interpret overlapping confidence intervals with caution and avoid the assumption that overlapping confidence intervals always implies a lack of difference of treatment effect to decide application of treatment.

The Interpretation of Scholars' Interpretations of Confidence Intervals: Criticism, Replication, and Extension of Hoekstra et al. (2014).

Hoekstra et al. (Psychonomic Bulletin & Review, 2014, 21:1157–1164) surveyed the interpretation of confidence intervals (CIs) by first-year students, master students, and researchers with six items expressing misinterpretations of CIs. They asked respondents to answer all items, computed the number of items endorsed, and concluded that misinterpretation of CIs is robust across groups. Their design may have produced this outcome artifactually for reasons that we describe. This paper discusses first the two interpretations of CIs and, hence, why misinterpretation cannot be inferred from endorsement of some of the items. Next, a re-analysis of Hoekstra et al.'s data reveals some puzzling differences between first-year and master students that demand further investigation. For that purpose, we designed a replication study with an extended questionnaire including two additional items that express correct interpretations of CIs (to compare endorsement of correct vs. nominally incorrect interpretations) and we asked master students to indicate which items they would have omitted had they had the option (to distinguish deliberate from uninformed endorsement caused by the forced-response format). Results showed that incognizant first-year students endorsed correct and nominally incorrect items identically, revealing that the two item types are not differentially attractive superficially; in contrast, master students were distinctively more prone to endorsing correct items when their uninformed responses were removed, although they admitted to nescience more often that might have been expected. Implications for teaching practices are discussed.

Understanding Confidence Intervals With Visual Representations [English

Bu calismada dogru kullanim ve yorumlama ile guven araliklarinin arastirmalarda sunulmasinin onemi uzerinde durulmustur. American Psychological Association (APA) (2010) yayim kilavuzu, guven araliklari degerlerine cok onem vermekte ve calismalarda rapor edilmesi gerektigini belirtmektedir. Arastirmacilar tarafindan eksik ve yanlis da yorumlanabilen guven araliklari bu calismada ayrintili olarak ele alinmis, kitaplardan da ornekler verilerek dogru ve yanlis tanimlar degerlendirilmis ve gorsel sunum ile orneklendirilerek okuyucularin guven araliklari konusunu daha kolay anlamalari amaclanmistir

Interval Estimation of Treatment Effects In Randomized Trials: When do Confidence Intervals Have Nominal Coverage?

SummaryIn the classical theory of randomized trials (RTs), the treatment effect is defined as a mean difference of potential outcomes. To achieve nominal coverage probability for confidence intervals (CIs) on treatment effects in RTs, certain assumptions are necessary. Specifically, one must either make assumptions about the joint distribution of potential outcomes or enroll subjects in the trial by random sampling of the target population on which the treatment effect is defined. In practice, no such sampling usually takes place and assumptions about the joint distribution of potential outcomes cannot be verified based on observed data. Furthermore, the most common of these assumptions, such as treatment‐unit additivity (TUA) or independence are biologically implausible in most RTs involving human subjects. Hence, it is not usually possible to construct CIs on treatment effects with nominal coverage probability. However, for any joint distribution of potential outcomes, the standard estimator of the variance of the difference of two independent sample means produces CIs with asymptotic coverage at least at the nominal level. This interpretation of CIs as conservative bounds may not always hold in conventional regression models applied to RT data.

Standard errors and confidence intervals in within-subjects designs: Generalizing Loftus and Masson (1994) and avoiding the biases of alternative accounts

Repeated measures designs are common in experimental psychology. Because of the correlational structure in these designs, the calculation and interpretation of confidence intervals is nontrivial. One solution was provided by Loftus and Masson (Psychonomic Bulletin & Review 1:476–490, 1994). This solution, although widely adopted, has the limitation of implying same-size confidence intervals for all factor levels, and therefore does not allow for the assessment of variance homogeneity assumptions (i.e., the circularity assumption, which is crucial for the repeated measures ANOVA). This limitation and the method’s perceived complexity have sometimes led scientists to use a simplified variant, based on a per-subject normalization of the data (Bakeman & McArthur, Behavior Research Methods, Instruments, & Computers 28:584–589, 1996; Cousineau, Tutorials in Quantitative Methods for Psychology 1:42–45, 2005; Morey, Tutorials in Quantitative Methods for Psychology 4:61–64, 2008; Morrison & Weaver, Behavior Research Methods, Instruments, & Computers 27:52–56, 1995). We show that this normalization method leads to biased results and is uninformative with regard to circularity. Instead, we provide a simple, intuitive generalization of the Loftus and Masson method that allows for assessment of the circularity assumption.

Confidence interval based parameter estimation--a new SOCR applet and activity.

Many scientific investigations depend on obtaining data-driven, accurate, robust and computationally-tractable parameter estimates. In the face of unavoidable intrinsic variability, there are different algorithmic approaches, prior assumptions and fundamental principles for computing point and interval estimates. Efficient and reliable parameter estimation is critical in making inference about observable experiments, summarizing process characteristics and prediction of experimental behaviors. In this manuscript, we demonstrate simulation, construction, validation and interpretation of confidence intervals, under various assumptions, using the interactive web-based tools provided by the Statistics Online Computational Resource (http://www.SOCR.ucla.edu). Specifically, we present confidence interval examples for population means, with known or unknown population standard deviation; population variance; population proportion (exact and approximate), as well as confidence intervals based on bootstrapping or the asymptotic properties of the maximum likelihood estimates. Like all SOCR resources, these confidence interval resources may be openly accessed via an Internet-connected Java-enabled browser. The SOCR confidence interval applet enables the user to empirically explore and investigate the effects of the confidence-level, the sample-size and parameter of interest on the corresponding confidence interval. Two applications of the new interval estimation computational library are presented. The first one is a simulation of confidence interval estimating the US unemployment rate and the second application demonstrates the computations of point and interval estimates of hippocampal surface complexity for Alzheimers disease patients, mild cognitive impairment subjects and asymptomatic controls.

Statistics at the bench: A step‐by‐step handbook for biologists

Statistics at the bench: A step‐by‐step handbook for biologists

Putting Research in Context: Understanding Confidence Intervals from One or More Studies

To support wider use and higher quality interpretation of confidence intervals (CIs) in psychology. We discuss the meaning and interpretation of CIs in single studies, and illustrate the value of CIs when reviewing and integrating research findings across studies. We demonstrate how to find CIs from summary statistics and published data in some simple situations. We provide the ESCI graphical software, which runs under Microsoft Excel, to assist with calculating and plotting CIs. (www.latrobe.edu.au/psy/esci) The wider use of CIs in psychology should support quality research communication and integrated interpretation of findings in context.

Parameter identification and model verification in systems of partial differential equations applied to transdermal drug delivery

The purpose of this paper is to present some numerical tools which facilitate the interpretation of simulation or data fitting results and which allow computation of optimal experimental designs. They help to validate mathematical models describing the dynamical behavior of a biological, chemical, or pharmaceutical system, without requiring a priori knowledge about the physical or chemical background. Although the ideas are quite general, we will concentrate our attention to systems of one-dimensional partial differential equations and coupled ordinary differential equations. A special application model serves as a case study and is outlined in detail. We consider the diffusion of a substrate through cutaneous tissue, where metabolic reactions are included in form of Michaelis–Menten kinetics. The goal is to simulate transdermal drug delivery, where it is supposed that experimental data are available for substrate and metabolic fluxes. Numerical results are included based on laboratory data to show typical steps of a model validation procedure, i.e., the interpretation of confidence intervals, the compliance with physical laws, the identification and elimination of redundant model parameters, the computation of optimum experimental designs and the identifiability of parameters by determining weight distributions.

Comments and recommendations regarding the hypothesis testing controversy

AbstractHypothesis tests are routinely misinterpreted in scientific research. Specifically, the failure to reject a null hypothesis is often interpreted as support for the null hypothesis while the rejection of a null hypothesis is often interpreted as evidence of an important finding. Many of the most frequently used hypothesis tests are “non‐informative” because the null hypothesis is known to be false prior to hypothesis testing. We discuss the limitations of non‐informative hypothesis tests and explain why confidence intervals should be used in their place. Several examples illustrate the use and interpretation of confidence intervals. Copyright © 2007 John Wiley & Sons, Ltd.

Editors Can Lead Researchers to Confidence Intervals, but Can't Make Them Think

Since the mid-1980s, confidence intervals (CIs) have been standard in medical journals. We sought lessons for psychology from medicine's experience with statistical reform by investigating two attempts by Kenneth Rothman to change statistical practices. We examined 594 American Journal of Public Health (AJPH) articles published between 1982 and 2000 and 110 Epidemiology articles published in 1990 and 2000. Rothman's editorial instruction to report CIs and not p values was largely effective: In AJPH, sole reliance on p values dropped from 63% to 5%, and CI reporting rose from 10% to 54%; Epidemiology showed even stronger compliance. However, compliance was superficial: Very few authors referred to CIs when discussing results. The results of our survey support what other research has indicated: Editorial policy alone is not a sufficient mechanism for statistical reform. Achieving substantial, desirable change will require further guidance regarding use and interpretation of CIs and appropriate effect size measures. Necessary steps will include studying researchers' understanding of CIs, improving education, and developing empirically justified recommendations for improved statistical practice.

Bayesian Modeling and Real‐world Problems

Academic Emergency MedicineVolume 10, Issue 7 p. 780-782 Free Access Bayesian Modeling and Real-world Problems Roger J. Lewis MD, PhD, Roger J. Lewis MD, PhD (roger@emedharbor.edu), Department of Emergency Medicine, Harbor–UCLA Medical Center, Torrance, CASearch for more papers by this author Roger J. Lewis MD, PhD, Roger J. Lewis MD, PhD (roger@emedharbor.edu), Department of Emergency Medicine, Harbor–UCLA Medical Center, Torrance, CASearch for more papers by this author First published: 28 June 2008 https://doi.org/10.1197/aemj.10.7.780Citations: 2AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. References 1 Williams K. G., Schootman M., Quayle K. S., Struthers J., Jaffe D. M.. Geographic variation of pediatric burn injuries in a metropolitan area. Acad Emerg Med. 2003; 10: 743– 52. 2 Bernardinelli L., Clayton D., Montomoli C.. Bayesian estimates of disease maps: how important are priors? Stat Med. 1995; 14: 2411– 31. 3 Berry D. A.. A case for Bayesianism in clinical trials. Stat Med. 1993; 12: 1377– 93; discussion 1395–404. 4 Berry D. A.. Interim analyses in clinical trials: classical vs. Bayesian approaches. Stat Med. 1985; 4: 521– 6. 5 D. A. Berry, D. K. Stangl, (eds). Bayesian Biostatistics. New York : Marcel Dekker, Inc., 1996. 6 Freedman L. S., Spiegelhalter D. J.. Comparison of Bayesian with group sequential methods for monitoring clinical trials. Controlled Clin Trials. 1989; 10: 357– 67. 7 Gelman A., Carlin J. B., Stern H. S., Rubin D. B.. Bayesian Data Analysis, Texts in Statistical Science. London : Chapman & Hall, 1995. 8 Lewis R. J., Wears R. L.. An introduction to the Bayesian analysis of clinical trials. Ann Emerg Med. 1993; 22: 1328– 36. 9 Mollie A.. Bayesian mapping of disease. In: W. R. Gilks, S. Richardson, D. J. Spiegelhalter (eds). Markov Chain Monte Carlo in Practice. Boca Raton ; FL : Chapman & Hall, 1996, pp 359– 79. 10 Press S. J.. Bayesian Statistics: Principles, Models, and Applications. New York : John Wiley & Sons, Inc., 1989. 11 Smith T. C., Spiegelhalter D. J., Thomas A.. Bayesian approaches to random-effects meta-analysis: a comparative study. Stat Med. 1995; 14: 2685– 99. 12 Spiegelhalter D. J.. Bayesian methods for cluster randomized trials with continuous responses. Stat Med. 2001; 20: 435– 52. 13 Young K. D., Lewis R. J.. What is confidence? Part I: the use and interpretation of confidence intervals. Ann Emerg Med. 1997; 30: 307– 10. 14 Young K. D., Lewis R. J.. What is confidence? Part II: detailed definition and determination of confidence intervals. Ann Emerg Med. 1997; 30: 311– 8. Citing Literature Volume10, Issue7July 2003Pages 780-782 ReferencesRelatedInformation

Teaching Confidence Intervals with Java Applets

SummaryConfidence intervals are pedagogically important but often misinterpreted. This article describes Java applets designed to help students understand two interpretations of confidence intervals.

Book Review

The present book review of Statistics With Confidence is framed in terms of both the recent report of the APA Task Force on Statistical Inference and ongoing movements in the field. The review is structured in terms of two major issues: the interpretation of confidence intervals (null hypothesis significance testing [NHST] versus non-NHST) and the ethics of statistics.

Understanding and using confidence intervals in clinical research.

Confidence intervals contain a wealth of clinically relevant information that is not available in the P value and usual significance testing. Numerous articles discuss the hazards of interpreting study results based solely on the P value, raising both practical and philosophical concerns. The general recommendation is that clinical research should not just test hypotheses, but also describe magnitudes of clinical effect. To this end, the confidence interval is a crucial tool in interpreting clinical studies. In this report, we show how one may use confidence intervals to gain further insight into clinical research. For example, by using confidence intervals, one can identify statistically significant results that are clinically imprecise, or conversely, statistically nonsignificant results that are quite precise. In addition, confidence intervals, like the P value, are influenced by sample size. We show how sample sizes that are sufficiently large to test hypotheses may be too small to generate precise estimates of the magnitude of effect. The application and interpretation of confidence intervals are demonstrated through the use of several examples.

Complex sample design effects and inference for mental health survey data

AbstractMental health researchers world‐wide are using large‐scale sample survey methods to study mental health epidemiology and services utilization in general, non‐clinical populations (Alegria et al. in press). This article reviews important statistical methods and software that apply to descriptive and multivariate analysis of data collected in sample surveys. A comparative analysis of mental health surveys in international locations is used to illustrate analysis procedures and ‘design effects’ for survey estimates of population statistics, model parameters and test statistics.This article addresses the following questions. How should a research analyst approach the analysis of sample survey data? Are there software tools available to perform this analysis? Is the use of ‘correct’ survey analysis methods important to interpretation of survey data? It addresses the question of approaches to the analysis of complex sample survey data. The latest developments in software tools for the analysis of complex sample survey data are covered, and empirical examples are presented that illustrate the impact of survey sample design features on the interpretation of confidence intervals and test statistics for univariate and multivariate analyses. Copyright © 1998 Whurr Publishers Ltd.

What Is Confidence? Part 1: The Use and Interpretation of Confidence Intervals

Hypothesis testing and the P value it generates are overemphasized in statistical analyses published in medical journals. An alternative, the confidence interval (CI), offers significantly more information to readers interpreting results. There have been many authoritative calls for the report of CIs in place of P values,1-7 such as that of the International Committee of Medical Journal Editors, whose guidelines for statistical reporting give the following instructions: “When possible, quantify findings and present them with appropriate indicators of measurement error or uncertainty (such as confidence intervals),” and “Avoid sole reliance on statistical hypothesis testing, such as the use of P values, which fails to convey important quantitative information.”8 In this article, part 1, we provide an overview of CIs for the clinician reading the medical literature. We describe the advantages of CIs and explain and illustrate their proper interpretation. In part 2, which follows this article, we provide added information important for clinical researchers, including a precise definition of CIs, a compact reference to methods for calculating CIs in common situations, and an explanation of the difference between CIs and probability intervals.9 [Young KD, Lewis RJ: What is confidence? Part 1: The use and interpretation of confidence intervals. Ann Emerg Med September 1997;30:307-310.]

What can the foundations discussion contribute to data analysis? And what may be some of the future directions in robust methods and data analysis?

The discussion of the philosophical foundations of statistics is not necessarily far remote from practical data analysis, even though, fortunately, a good data analysis does not depend very much on the philosophical framework adopted. Some clarification for data analysis can be provided about the purposes of estimation and testing, the choice between parameter estimation and prediction, the role of parametric models, the difference between epistemic and physical probabilities, the interpretation of confidence intervals and fiducial probabilities, the description of a state of partial knowledge, including the use of upper and lower probabilites, and other topics. This paper contains first some remarks on future directions in robust methods, in loose connection with foundations, but in close connection with the title of the workshop. It then gives a brief description of a new approach to the foundations of statistics, and in the main part it discusses a number of suggestions and consequences for data analysis as mentioned above, which can be derived from the study and discussion of the foundations of statistics.