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Average Power in Non-Normal Settings
Published in Andrew P. Grieve, Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials, 2022
A mid-point rule (Section 2.2.3) could be used to determine the unconditional POS. Alternatively, the predictive distribution of the t-statistic for n1 future observations per arm isin which the distribution was also developed by Lecoutre (1984, 1999). The expression is the value of the t-statistic based on the prior data/distribution (4.7). The unconditional power is then given by
Reliability, Validity, and the Measurement of Change in Serial Assessments of Athletes
Published in Mark R. Lovell, Ruben J. Echemendia, Jeffrey T. Barth, Michael W. Collins, Traumatic Brain Injury in Sports, 2020
Michael D. Franzen, Robert J. Frerichs, Grant L. Iverson
Crawford and Howell (1998) introduced a new, and more technically accurate, regression method for comparing predicted and obtained scores. This newer method addresses the error that arises from the use of sample coefficients to estimate population regression coefficients. In McSweeney et al.’s (1993) approach, the regression equation is specific to the sample and therefore represents an optimal fit of the sample data. It is assumed that the sample is representative of the population and that the derived equation may be used to accurately predict posttest scores for individuals who were not in the original sample. A failure to adjust the regression equation to reflect the estimation of population regression coefficients might increase the likelihood that discrepant scores would be identified as significantly changed. This error would be magnified for pretest scores that are further from the mean pretest score. The new method accounts for this potential error by multiplying a correction factor to the SEE for each individual case. It should be noted that the authors recommended the use of the t-statistic, rather than the z-statistic, when working with samples rather than populations. A tα/2 (df = N – 2) is therefore used to replace the zα/2 value (e.g., 1.96 or 1.64) used in other methods to demarcate the bounds of reliable change.
Methods of Analysis
Published in Andrei I. Holodny, Functional Neuroimaging, 2019
The most straightforward method of limiting the number of type I errors associated with multiple comparisons is the Bonferroni correction. This method decreases the critical p value in proportion to the number of comparisons being made. For an overall test at the a significance level, one could select individual voxels among N total voxels as active if p ≤ a/N. For example, if there are 10,000 voxels in the brain and one wants to have α significance level of 0.01, the p value of the test should be set at 0.01/10,000 = 10 −6. However, such a stringent value could remove some true positive pixels. For example, if the degree of freedom is 90, this corresponds to a t-statistic threshold of 5.1. If the noise standard deviation is about 2% of the baseline signal, this means that imaging would detect BOLD signal changes of about 1.1% . 1.5 T is the most common field strength which is used in the clinical setting, and the BOLD signal change of 1.1% is a reasonable value to set for the primary and secondary motor regions during, for example, finger-tapping tasks. However, it may not be a reasonable value when detecting other regions, for example, cognitive related regions, where percent signal changes of lower than 1% are usual. In other words, such voxel-wise detection methods are good at detecting large BOLD signal changes. A drawback of the methods is that there is a potential to remove a large region of activation in which each voxel has only a small signal change.
Bayesian t-tests for correlations and partial correlations
Published in Journal of Applied Statistics, 2020
Min Wang, Fang Chen, Tao Lu, Jianping Dong
We are interested in testing X and Y drawn from a bivariate normal population. Let n paired measurements. The t-statistic is given by t distribution with v = n−2 degrees of freedom under α level of significance, if either p-value
The t-test: An Influential Inferential Tool in Chaplaincy and Other Healthcare Research
Published in Journal of Health Care Chaplaincy, 2018
Katherine R. B. Jankowski, Kevin J. Flannelly, Laura T. Flannelly
Interpretation of the t-test result is guided by the probability (p value) of the outcome (t statistic). If the probability is very small, a researcher can conclude that the difference between sample means is unusual. The t-test does not prove anything. It indicates the probability of obtaining the observed difference between the means. When the result is significant, the t-test indicates that the outcome happens 5.0%, 2.5%, or 1.0% of the time, or even less often. It is up to the researcher to infer from all of the information regarding the samples if there is truly an important difference between two samples and what that difference means. The t-test result is just the beginning to understanding the story of what is being studied.
Dual agonist–antagonist effect of ulipristal acetate in human endometrium and myometrium
Published in Expert Review of Molecular Diagnostics, 2021
Ana Salas, Paula Vázquez, Aixa R. Bello, Delia Báez, Teresa A. Almeida
Differential gene expression analysis were performed using nSolver, which calculates the ratio of difference in the means of the log-transformed normalized data to the square root of the sum of the variances of samples in the two groups (Control and UPA) to assist in determining whether the fold change calculated is statistically significant. nSolver performs a two-tailed t-test on the log-transformed normalized data that assumes unequal variance. The distribution of the t-statistic was calculated using the Welch–Satterthwaite equation for the degrees of freedom in the estimation of the 95% confidence limits for observed differential expression between the two groups. The significance threshold was set at P ≤ 0.05.