This is the first introductory statistics text to use an estimation approach from the start to help readers understand effect sizes, confidence intervals (CIs), and meta-analysis (‘the new statistics’). The free ESCI (Exploratory Software for Confidence Intervals) software. The new statistics refers to recommended practices, including estimation based on Understand, discuss, and help other researchers appreciate the challenges of Cpdf. Cumming, G. (). Inference by eye: Pictures of confidence. EFFECT SIZES, CONFIDENCE. INTERVALS, AND META-ANALYSIS http://www. medical-site.info
|Language:||English, Spanish, Japanese|
|Genre:||Children & Youth|
|Distribution:||Free* [*Register to download]|
of 3/12/ This paper is available on the internet in pdf and HTML at questions are closely related and that both are essential for scientific understanding. Cumming's new statistics attempt to set exploratory research methods as the. International Statistical Review Understanding The New Statistics: Effect Sizes, Confidence Intervals, and Meta‐Analysis by Geoff Cumming. This is the first book to introduce the new statistics - effect sizes, confidence intervals, and meta-analysis - in an accessible way. It is chock full of practical.
You can download our homework help app on iOS or Android to access solutions manuals on your mobile device. Asking a study question in a snap - just take a pic. Textbook Solutions. Get access now with. Get Started. Select your edition Below by. Geoff Cumming. Can I get help with questions outside of textbook solution manuals? For example, many of the individual beta-blocker studies in the meta-analysis of Fig.
Bayes factors for the individual beta-blocker studies can be computed exactly using extensions of formulas described on pages and of Kruschke, b.
What should be the publication status of indecisive studies? Should they remain in the file drawer, unpublished? Moreover, Bayes factors should use meaningfully informed priors instead of defaults, and the magnitude and even direction of a Bayes factor can vary substantially with the prior, and different studies might be analyzed with different alternative hypotheses.
Instead of filtering publication according to whether or not a null hypothesis was rejected or accepted, publication might be based on whether or not a reasonable precision was achieved relative to the practical constraints of the study. The posterior precision is relatively invariant for vague priors. Basing publication on adequate precision will help solve the file-drawer problem because all suitably representative studies will get published, not just those studies that happen to sample enough data to reject or accept a null hypothesis relative to some particular alternative hypothesis.
Different procedures have different trade-offs, and the advantages or disadvantages of different procedures will continue to be discussed and clarified in coming years. What is clear is that the scheme in the lower part of Fig. In particular, the general scheme represents the hypothesis as a Bayesian posterior distribution over parameter values instead of only as a point value, allows simulating any sampling procedure instead of only fixed N , and encourages considering multiple goals for research such as Bayesian hypothesis testing and Bayesian precision HDI width instead of only p values.
Bayesian power and planning for precision is discussed in the video at http: Details of the general procedure are explained at length in Chapter 13 of Kruschke In other words, the editors banned the methods in the top-left cell of Fig. But Trafimow and Marks also expressed doubt about frequentist confidence intervals and Bayesian approaches involving Bayes factors. In other words, they expressed doubt about the lower-left and upper-right cells of Fig. The remaining cell, at the convergence of Bayesian methods applied to estimation, uncertainty, and meta-analysis, was not mentioned by Trafimow and Marks We believe that this convergence alleviates many of the problems that the editors were trying to avoid.
Cumming encouraged analysts to keep in mind that their particular set of data is merely one random sample, and another independent random sample might show very different trends. In Bayesian analysis there is also a dance across different random samples. Indeed, the posterior distribution revealed by a Bayesian analysis is always explicitly conditional on the data, by definition: If the data change, then the posterior distribution changes.
There is a dance of HDIs. We think that the Bayesian framework is amenable to remembering the dance of random samples. This claim might seem implausible insofar as the Bayesian framework de-emphasizes thoughts of random samples by never using a hypothetical sampling distribution for computing p values as in Fig. On the other hand, a Bayesian framework does emphasize that the results are conditional on the particular random data obtained, and that the inference is merely the best we can do given the data we happen to have.
Bayesian power analysis Fig. Perhaps most relevantly, the Bayesian framework is helpful for remembering the dance because it facilitates meta-analysis. The core premise of meta-analysis is acknowledging the variation of results across different samples. We agree with many of the claims made by Cumming and others about the advantages of estimation and meta-analysis over null hypothesis tests, but we hope to have shown that when hypothesis testing is theoretically meaningful then it is more coherently done in a Bayesian framework than in a frequentist framework.
We have attempted to show that Bayesian estimation, Bayesian meta-analysis, and Bayesian planning achieve the goals of the New Statistics more intuitively, directly, coherently, accurately, and flexibly than frequentist approaches. The full url is http: The full URL is http: The full url is https: Lee, Joachim Vandekerckhove, and an anonymous reviewer.
Correspondence can be addressed to John K. More information can be found at http: Skip to main content Skip to sections. Advertisement Hide. Download PDF. The Bayesian New Statistics: Hypothesis testing, estimation, meta-analysis, and power analysis from a Bayesian perspective. Brief Report First Online: Two conceptual distinctions in data analysis We frame our exposition in the context of the two conceptual distinctions in data analysis that we mentioned earlier, and which are illustrated in Fig.
The rows of Fig. The columns of Fig. We will review the two distinctions in the next sections, but we must first explain what all the distinctions refer to, namely, formal models of data. Open image in new window. Figure 2 illustrates the idea of a p value. We consider repeatedly randomly sampling from the null hypothesis, every time generating a sample in the same way that the actual data were sampled, and for every simulated sample we compute a summary statistic like the one we computed for our actual sample.
The resulting distribution of randomly generated summary values is illustrated as the cloud in Fig. The center of the cloud is where most simulated samples fall, and the periphery of the cloud represents extreme values that occur more rarely by chance.
Intuitively, if the actual outcome falls in the fringe of the cloud, then the actual outcome is not very likely to have occurred by the hypothesis, and we reject the hypothesis.
The proportion of the cloud that is as extreme as or more extreme than the actual outcome is the p value, shown at the right of Fig. Formally, a p value can be defined as follows. For a set of actual data, let T D a c t u a l be a descriptive summary value of the data, such as a t statistic.
Suppose that the actual data were sampled according to certain stopping and testing intentions denoted I. As a concrete example of NHST, we consider the simplest sort of data: For example, we might be interested in knowing the probability that people agree with a particular policy statement.
Suppose that of 18 randomly selected people, 14 agree with the statement. Please note that z refers to the number of people who agree, not to any sort of standardized score. Confidence intervals have no distributional information Notice that a confidence interval has no distributional information. Summary of frequentist approach In summary, frequentist approaches rely on sampling distributions, illustrated by the cloud of imaginary possibilities in Fig.
Then we take into account the data, namely the number of agreements z out of the number of respondents N. The modal value of the posterior distribution shows the most credible value of the parameter, given the data.
If the prior distribution is broad and diffuse, it has little influence on the posterior distribution when there are realistic i. Figure 5 shows that the choice of prior distribution has virtually no effect on the posterior distribution when the prior is relatively flat across the parameter values. Panels A and B of Fig. In panel A, an essentially uniform prior is used.
The resulting posterior distributions in Panels A and B are virtually indistinguishable. Assessing null values using intervals From the posterior distribution on the parameter, we can assess the extent to which particular values of interest, such as null values, are among the most credible values. Highest density interval vs. Figure 6 illustrates the parameter space for Bayesian null hypothesis testing.
Panel A of Fig. The null and alternative priors are indexed at the top of Panel A by the model index parameter M. The degree to which the model index shifts, from prior to posterior, is called the Bayes factor.
With respect to Fig. In panel A of Fig. In panel B of Fig. The Bayes factor of null versus alternative is denoted B F n u l l and can be defined as the ratio of the posterior odds to the prior odds: The top panel of Fig.
The values are supposed to be in the vicinity of typical intelligence quotient IQ scores, which are normed for the general population to have a mean of and a standard deviation of We are interested in the mean because we would like to know how different the central tendency of the smart-drug group is from the general population.
We are interested in the standard deviation because we would like to know how different the variability of the smart-drug group is from the general population on the scale of the data.
Stressors such as performance drugs can increase the variance of a group because not everyone responds the same way to the stressor e. Finally, we are interested in the effect size because it indicates the magnitude of the change in central tendency standardized relative to the variability in the group. Sampling and testing intentions influence p values and confidence intervals Recall the notion of a p value illustrated back in Fig.
Frequentist NHST asks the wrong question When we collect data about some phenomenon of interest and we describe the data with a mathematical model, usually our first question is about what parameter values are credible given the actual data. For example, given a set of IQ scores, we would like to know what values of the mean parameter are credible.
Null hypotheses are often false a priori One argument against using null hypotheses is that in many applications they are straw men that can be rejected with enough data. Null hypothesis tests ignore magnitude and uncertainty A more important general problem of point-value hypothesis testing is that the result of a hypothesis test reveals nothing about the magnitude of the effect or the uncertainty of its estimate, which we should usually want to know.
Null hypothesis testing hinders cumulative science and meta-analysis One of the main casualties inflicted by the black-and-white thinking of hypothesis testing is cumulative science. Better done Bayesian To discuss meta-analysis, we first discuss hierarchical models, because models for meta-analysis are a case of hierarchical models. HDI is seamless for complex hierarchical models, unlike the CI Bayesian methods are especially convenient for complex hierarchical models for two reasons.
Anything we want to know about the parameter estimates can be directly read off the full posterior distribution, and without any need for additional assumptions to create sampling distributions for p values and confidence intervals.
Figure 8 shows a forest plot of the results. The top of Fig. Brophy et al. The left panel of Fig.
The right panel of Fig. This result provides clinicians with important information to decide if the number of lives saved is worth the cost and possible side effects of the treatment. As an example of a RCT with a split-plot structure, consider the fictitious data summarized in Fig. The structure of the scenario is analogous to the one presented by Cumming , p.
We consider two treatments for anxiety, viz. Every subject had their anxiety measured at four times: There were 15 subjects in the control condition, 12 in medication, and 13 in counseling. Figure 10 shows the overall trends, where it can be seen that all three groups had similar pre-treatment anxiety levels. After treatment, anxiety levels in the medication and counseling treatments appear to be lower than in the control condition, but anxiety levels seem to rise during follow-up after medication.
Please note that these are completely fictitious data, merely for illustration of analysis methods. All of these comparison are computed merely by looking at the corresponding difference of cell means in the joint posterior distribution. The procedure for traditional power analysis is diagrammed in the upper part of Fig. The analyst hypothesizes a specific point value for a parameter such as effect size.
Then random samples of simulated data are generated from the hypothesis. Every sample of simulated data is created according to the intended stopping rule that will be used for the real data. For example, the stopping rule could be a fixed sample size, N. Because of random variability in the sample, only some of the simulated samples will have data extreme enough to reject the null hypothesis.
If the power is not big enough, then a larger N is considered. Bayesian estimation can help us remember the dance Cumming encouraged analysts to keep in mind that their particular set of data is merely one random sample, and another independent random sample might show very different trends. Bayesian estimation does everything the New Statistics desires, better We agree with many of the claims made by Cumming and others about the advantages of estimation and meta-analysis over null hypothesis tests, but we hope to have shown that when hypothesis testing is theoretically meaningful then it is more coherently done in a Bayesian framework than in a frequentist framework.
Allenby, G. The hierarchical Bayesian revolution: How Bayesian methods have changed the face of marketing research. Marketing Research , 16 , 20— Google Scholar. Anderson, D. Null hypothesis testing: Problems, prevalence, and an alternative. The Journal of Wildlife Management , 64 4 , — CrossRef Google Scholar.
Beaumont, M. The Bayesian revolution in genetics. Nature Reviews Genetics. Berry, S. Bayesian adaptive methods for clinical trials. Boca Raton, FL: CRC Press. Brooks, S. Bayesian computation: A statistical revolution.
Philosophical Transactions of the Royal Society of London. Series A , , — Brophy, J. A Bayesian meta-analysis. Annals of Internal Medicine , , — Carlin, B. Bayesian methods for data analysis , 3rd edn.
Cohen, B. Explaining psychological statistics , 3rd edn. Hoboken, New Jersey: Cohen, J. Statistical power analysis for the behavioral sciences , 2nd edn. Hillsdale, NJ: Cox, D. Principles of statistical inference. Cambridge, UK: Cambridge University Press. Cumming, G.
Inference by eye: Pictures of confidence intervals and thinking about levels of confidence. Teaching Statistics , 29 3 , 89— The new statistics why and how. Psychological Science , 25 1 , 7— Confidence intervals: Better answers to better questions. A primer on the understanding, use and calculation of confidence intervals based on central and noncentral distributions.
Educational and Psychological Measurement , 61 , — Dienes, Z. Using Bayes to get the most out of non-significant results. Frontiers in Psychology , 5 , How Bayes factors change scientific practice. Journal of Mathematical Psychology , 72 , 78— Doyle, A. The sign of four.
Spencer Blackett. Edwards, W. Bayesian statistical inference for psychological research. Psychological Review , 70 , — Freedman, L. Stopping rules for clinical trials incorporating clinical opinion. Biometrics , 40 , — Gallistel, C. The importance of proving the null. Psychological Review , 2 , — Gelman, A.
Gigerenzer, G. Surrogate science: The idol of a universal method for scientific inference. Journal of Management , 41 2 , — Greenland, S. Statistical tests, p values, confidence intervals, and power: A guide to misinterpretations.
The American Statistician. Gregory, P. Hartung, J. Hobbs, B. Practical Bayesian design and analysis for drug and device clinical trials. Journal of Biopharmaceutical Statistics , 18 1 , 54— Howell, D.
Statistical methods for psychology 8th edition , 8th edn. Belmont, CA. Howson, C.
Scientific reasoning: The Bayesian approach , 3rd edn. Open Court: Jeffreys, H. Theory of probability Oxford. Oxford University Press. Johnson, D. Statistical sirens: The allure of nonparametrics. Ecology , 76 , — The insignificance of statistical significance testing. Journal of Wildlife Management , 63 , — Kass, R.
Bayes factors. Journal of the American Statistical Association , 90 , — Kelley, K. Effect size and sample size planning. In Little, T. Oxford Handbook of Quantitative Methods Vols. Volume 1, Foundations, pp.
New York: Kline, R. Beyond significance testing: Reforming data analysis methods in behavioral research. Washington, DC: American Psychological Association. Kruschke, J. Bayesian assessment of null values via parameter estimation and model comparison. Perspectives on Psychological Science , 6 3 , — Doing Bayesian data analysis: Burlington, MA: Bayesian estimation supersedes the t test. Journal of Experimental Psychology: General , 2 , — Doing Bayesian data analysis, Second Edition: The time has come: Bayesian methods for data analysis in the organizational sciences.
Organizational Research Methods , 15 , — Bayesian data analysis for newcomers. Bayesian estimation in hierarchical models. In Busemeyer, J. Oxford Handbook of Computational and Mathematical Psychology: Lakens, D. Performing high-powered studies efficiently with sequential analyses. European Journal of Social Psychology , 44 7 , — Lazarus, R. Effects of failure stress upon skilled performance. Journal of Experimental Psychology , 43 2 , — Lee, M.
Bayesian cognitive modeling: Lesaffre, E. Superiority, equivalence, and non-inferiority trials. PubMed Google Scholar. Liddell, T. Ostracism and fines in a public goods game with accidental contributions: The importance of punishment type. Judgment and Decision Making , 9 6 , — Lindley, D. The future of statistics: A Bayesian 21st century. Advances in Applied Probability , 7 , — Lunn, D. The BUGS book: A practical introduction to Bayesian analysis. Boca Raton, Florida: Maxwell, S.
Designing experiments and analyzing data: A model comparison perspective , 2nd edn. Mahwah, NJ: Sample size planning for statistical power and accuracy in parameter estimation. Annual Review of Psychology , 59 , — Mayo, D. A commentary. Error statistics.
In Bandyopadhyay, P. Handbook of the Philosophy of Science. Volume 7: Philosophy of Statistics pp. McGrayne, S. The theory that would not die, Yale University Press.
Meehl, P. Theory-testing in psychology and physics: A methodological paradox. Philosophy of Science , 34 , — Theoretical risks and tabular asterisks: Sir Karl, Sir Ronald, and the slow progress of soft psychology. Journal of consulting and clinical Psychology , 46 4 , The problem is epistemology, not statistics: Replace significance tests by confidence intervals and quantify accuracy of risky numerical predictions, What if there Were no Significance Tests, —, Mahwah, NJ, Erlbaum Harlow, L.
Morey, R. BayesFactor package for R. Ntzoufras, I. Pitchforth, J. Plummer, M. JAGS version 3. Poole, C. Beyond the confidence interval. American Journal of Public Health , 77 2 , — Rogers, J. Using significance tests to evaluate equivalence between two experimental groups.
Psychological Bulletin , 3 , — Rosenthal, R. Psychological Bulletin , 86 3 , — Rothman, K. Disengaging from statistical significance.
Rouder, J. Psychonomic Bulletin and Review , 18 , — A Bayes factor meta-analysis of recent extrasensory perception experiments: Comment on Storm, Tressoldi, and Di Risio Psychological Bulletin , 1 , — Bayesian t -tests for accepting and rejecting the null hypothesis.
Altman, Machin, situation. As we mentioned above, method for calculating such intervals. Bird discussed CIs for a these effects are negligible. The pattern of the e, f, and g means and CIs suggests that we have Interpretation of CIs no evidence of any substantial differences among those three effects.
Effect h is at most small. If a comparison of f and h The Manual states unequivocally p. Consider Fig. Usually, that will be the main ESs, and neglecting much of that information. We briefly consider three possible objections to this Reference values could be chosen that are clinically impor- approach to interpretation. First, it is too subjective. Yes, tant, predicted by different theories under test Velicer et al.
Any interpre- ous other aspects of planning, conducting, and reporting tation must depend on the research context, but the figure research.
It is probably of little interest whether conclusions. Yes, but if the extent of are approximately equal, and tell us mainly that the next fuzziness of wording approximately matches uncertainty as experiment needs increased precision.
Conversely, the c and indicated by CI width, our words are accurately representing the findings. Any greater specificity of wording would be misleading. A third possible objection is that such wording is, or should be, consistent with what p-values indicate and is thus merely NHST by stealth, and it would be better to have it out in Large the open. However, con- sidering the CIs as ranges of plausible true values gives a clear Medium interval-based rationale for interpreting non-overlap of inde- pendent CIs as evidence of a difference; it keeps the focus on ESs and suggests how large the difference is likely to be.
We are under no illusion that our few wording suggestions Small above give sufficient guidance for interpreting ESs and CIs. We encourage psychologists to explore how best to think about and discuss point and interval estimates, towards the goal of a more quantitative discipline.
Reference effect sizes are marked by dotted lines. NHST because awareness of power—often depressingly Meta-analysis low—can prompt steps to increase power. Taking in the Manual especially pp. Cooper described the sion, measured by MOE, which has the advantage that no process of conducting a large meta-analysis, and Borenstein, null hypothesis and no population ES need be specified.
The approach holds great promise, but better guid- research literature. We Tables and figures encourage the use of a forest plot whenever it helps.
Software based on the forest plot can make it easy to explain the basic The Manual states p. There are four sample tables that The Manual confirms meta-analysis as part of the main- include CIs pp. CIs can be included in tables by stream. A future step may be a requirement similar to The using either the [. The Manual notes p. Also, it reformers, will prompt a general swing to estimation and is CIs that medicine has recommended since the s.
The Manual recognises the problem by stating p. The sample figure with error bars p. If your The Manual suggests p. Study 2 8 10 18 Positive d favours the experimental condi- tion Exp ; negative favours the comparison Study 3 28 30 56 Comp.
Relative weights are the percent- ages contributed by the three studies to the overall meta-analysis. In addition, CIs on com- framework. Use knowl- tion of RCTs, which pose a challenge because they usually edgeable judgment to interpret in the research context.
The current include them. Kelley and Maxwell discussed CIs and the use actually impede scientific progress. The focus of research of precision for planning in the context of multiple regres- should be on. We thank Fatima Saleem for this information.
The APA does not give permission for any direct quota- ful and wide-ranging commentaries. They they can be easily located. In this article, we have mainly considered simple estima- Altman, D. Statistics with confidence: Confidence intervals and statistical guidelines tion based on populations assumed normally distributed.
London: BMJ Books. The discussions of Gregson and Grayson et al. Publication manual of the emphasise that many statistical techniques can contribute APA 6th ed. Washington, DC: Author. Publication manual of the American Psychological Association. Compari- broaden the range of applicability of an estimation approach. Journal of Personality Assessment, 67, — Analysis of variance via confidence intervals. London: estimation does not sidestep the issue of possibly capitalising Sage.
We believe, however, that the shift from Introduction to meta-analysis. Chichester: Wiley. Cohen, J. Statistical power analysis for the behavioral sciences dichotomous hypothesis testing to estimation is a funda- 2nd ed. Hillsdale, NJ: Erlbaum. Research synthesis and meta-analysis: A step- and theorising, whatever statistical techniques are used. Thousand Oaks, CA: Sage. Frontiers in Quantitative Psychology and Measurement, 1 26 , 1—9. Meta-analysis: Pictures that explain how quantitative models Rodgers, The recommendations experimental findings can be integrated.
Salvador, Brazil. Chance Eds. Evidence, inference, Proceedings. Signs of obsolescence in psycholo- Cumming, G. Inference by eye: Pictures of confidence inter- gical statistics: Significance versus contemporary theory.