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Concluding Remarks
Published in Song S. Qian, Mark R. DuFour, Ibrahim Alameddine, Bayesian Applications in Environmental and Ecological Studies with R and Stan, 2023
Song S. Qian, Mark R. DuFour, Ibrahim Alameddine
We use a one sample t-test problem to illustrate the severe testing concept. In a t-test contrasting the null hypothesis of against the alternative hypothesis , we decide which one is supported by the data by first assuming that H0 is true. Under H0, the t-test assumption is that the observed data follows a normal distribution with mean μ0 (i.e., ), which implies that the test statistic , where is the sample average and s is the sample standard deviation. The t-distribution has a range of . Although any value of the test statistic is possible under the null hypothesis, the likelihood of observing a value of the t-statistic decreases under H0 and increases under Ha as the observed value increases. Statistical hypothesis testing is, then, a means to weigh the evidence for and against H0. The evidence is in the form of the p-value.
Selected Statistical Topics of Regulatory Importance
Published in Demissie Alemayehu, Birol Emir, Michael Gaffney, Interface between Regulation and Statistics in Drug Development, 2020
Demissie Alemayehu, Birol Emir, Michael Gaffney
Statistical hypothesis testing in a regulatory setting involves the calculation under the null hypothesis of the probability that the observed treatment effect on a specific variable is due to chance alone. In a randomized study, if this probability (p-value) is low, the null hypothesis (usually that the treatment effect is 0) is rejected and a treatment effect is established. If only one primary variable is used to establish a treatment effect, then the requirement that p < α controls the probability of incorrectly concluding a treatment effect at α. The issue of multiplicity of endpoints refers to the clinical trial setting where more than one variable is used to establish a treatment effect. The chances of obtaining at least one p-value below α increase with the number of endpoints. For example, the probability under the null hypothesis that at least one p-value is less than 0.05 for three independent hypotheses is 1 – (0.95)3 = 0.14. Thus, regulators cannot accept a level α test for each variable if the goal is to rule out incorrectly concluding a treatment effect (Type I error) at an overall probability of α.
A Framework for Testing Biomarker Subgroups in Confirmatory Trials
Published in Nusrat Rabbee, Biomarker Analysis in Clinical Trials with R, 2020
We assume that you can estimate the correlation between the test statistics, which makes the Dunnett procedure more powerful than a Bonferroni correction. The statistical framework is set up by Glimm et al. [3] and mentioned above. The underlying basis is that the test statistics are normally distributed. In oncology, for example, where the log rank test statistic or the regression coefficient from the Cox proportional hazards model are normally distributed. Therefore, this assumption is useful in many settings. The framework they introduce is based on contrast estimation and statistical hypothesis testing in ANOVA models. The general null hypothesis is which is a level α test where . The cumulative distribution function of under the null and any alternative hypothesis is a multivariate normal or central t distribution. This makes the procedure more powerful than Bonferroni. In this procedure, we have to derive critical values and P values from this multivariate distribution to test our hypotheses of interest. Glimm et al. explain that setting the critical values results in the ordinary Dunnett’s procedure; and setting differential weights leads us to a weighted Dunnett’s test procedure. The weighted Dunnett procedure and the corresponding R code are presented by Glimm [5].
Identifying a motivational process surrounding adherence to exercise and diet among adults with type 2 diabetes
Published in The Physician and Sportsmedicine, 2020
Manon Laroche, Peggy Roussel, Francois Cury
Once the reliability of the measurements was verified the descriptive statistics (mean, standard deviation, distribution) and correlations of the key variables were examined. Then, a path model for evaluating the combined contribution (direct and indirect effects) of each variable – SOC strategy, promotion focus, prevention focus – on exercise, general diet, fruit and vegetable consumption, high-fat food consumption, and spacing of carbohydrates was run. In this model, age, gender, number of comorbidities and educational level were included as control variables. This path analysis was conducted by using Lisrel 9.1. The .05 level of significance was used for all statistical hypothesis testing. Beta represents the standardized regression coefficient. As for previous analyzes, the recommendations of Meyers et al. [27] were applied to assess the adequacy of the model (CFI and GFI ≥ .90; RMSEA ≤ .08). Finally, using SPSS software 18.0, a bootstrapping method [29] resample set at 5000 samples with bias-corrected 95% confidence intervals was employed to test the significance of the indirect effects. Point estimates of indirect effects are considered significant when zero is not contained in 95% confidence intervals [29].
Antioxidant and Anti-Diabetic Functions of a Polyphenol-Rich Sugarcane Extract
Published in Journal of the American College of Nutrition, 2019
Jin Ji, Xin Yang, Matthew Flavel, Zenaida P.-I. Shields, Barry Kitchen
A statistical analysis was performed for all the study results. First, a correlation analysis was carried out to determine whether there is a relationship between the two variable (x, y) pairs of the study results. Then, a statistical hypothesis testing was performed. Because of the small sample sizes, the Kruskal–Wallis test, a nonparametric test, was used. The Kruskal–Wallis test is the nonparametric alternative to a one-way analysis of variance and does not require normal distributions. The null hypothesis of this test is that all the medians are equal. The alternative hypothesis is that the medians are different. If the Kruskal–Wallis test is significant, it indicates that at least two concentrations have significantly different medians. The statistical analysis was performed using the SAS® software, version 9 (SAS Institute, Inc.).
Basic statistical considerations for physiology: The journal Temperature toolbox
Published in Temperature, 2019
Aaron R. Caldwell, Samuel N. Cheuvront
“Describe statistical methods with enough detail to enable a knowledgeable reader with access to the original data to verify the reported results. When possible, quantify findings and present them with appropriate indicators of measurement error or uncertainty (such as confidence intervals). Avoid sole reliance on statistical hypothesis testing, such as the use of P values, which fails to convey important quantitative information. … Give numbers of observations. … References for study design and statistical methods should be to standard works (with pages stated) when possible rather than to papers where designs or methods were originally reported. Specify any general-use computer programs used.” – International Committee of Medical Journal Editors [148].