B
Filomena Pereira-Maxwell in Medical Statistics, 2018
A significance test that is an extension of the F-test and is carried out to compare the variances of more than two populations with respect to a given measurement (as estimated from the different groups in the study sample). The test is sensitive to non-normality, so Levene’s test may be a better alternative whenever the measurement in question does not display a Normal distribution in the populations being compared. Both tests may be carried out to evaluate the assumption of homoscedasticity, or equality of variances, that is a requirement of parametric tests such as analysis of variance. Care should be taken when interpreting the test’s results, as a small P-value could be indicative of nonnormality rather than unequal variances.
TIME-SPACE CLUSTERING OF DISEASE
Richard G. Cornell in Statistical Methods for Cancer Studies, 2020
Their test is developed in analogy with the analysis of variance F test. Suppose there are n points in a plane, between any two of which we can measure a distance, getting the total of squared distances between the n(n-1)/2 possible pairs. If the n points can be divided into subgroups, similar sums of squares can be obtained within each subgroup. By subtraction, a residual for “between subgroups” is determined and a test is based on the between-to-within subgroups ratio. The test is applied to the disease incidence data by dividing the study period into subintervals each subinterval identifying a subgroup for this test, and analyzing the distribution of the points in space. Specific objective rules for identifying the subintervals are given. A statistical weakness of the David-Barton test is related to its multi-degree of freedom character.
The Sample Correlation Coefficient
Thomas S. Ferguson in A Course in Large Sample Theory, 2017
Find the asymptotic distribution of the estimate of the regression coefficient, , when sampling from a bivariate distribution. What is its asymptotic variance when sampling from a bivariate normal distribution?Find an asymptotically robustized version of the confidence intervals for σXY.Find variance-stabilizing transformations for X̅n when sampling from (a) the Poisson distribution, (λ), (b) the Bernoulli distribution, (1, p).The usual F test for the equality of variances of two independent normal populations is based on the ratio of the two sample variances, . Show that this test is not asymptotically distribution-free within the class of distributions with finite fourth moments, by finding the asymptotic distribution of within this class. Suppose both samples are of size n.
On detecting the effect of exposure mixture
Published in Journal of Applied Statistics, 2023
Instead of using covariate-adjusted outcome, one can add p covariates into model (1) for adjustment that j, by a F test, or t test, with straightforward modifications on the previously described test statistics. Under the null hypothesis, the F test statistic follows t test follows
Comparison of non‐invasive tear film stability measurement techniques
Published in Clinical and Experimental Optometry, 2018
Michael Tm Wang, Paul J Murphy, Kenneth J Blades, Jennifer P Craig
Statistical analyses were performed using Graph Pad Prism version 6.02 (http://www.graphpad.com) and IBM SPSS Statistics for Windows version 19.0 (IBM, Armonk, New York, USA). The distributions of tear film stability measurements were assessed using the D'Agostino‐Pearson omnibus normality test. Consistent with previous reports, tear film stability measurements were non‐normally distributed and thus the geometric mean is presented.1997 The non‐normally distributed measurements were then logarithmically transformed before further analysis. Comparisons of means were performed using repeated measures analysis of variance (ANOVA). Post‐hoc analyses for pairwise comparisons were conducted using multiplicity‐adjusted Tukey tests. Comparisons for variances were undertaken using the F‐test. For each pairwise comparison, the intraclass correlation coefficient (ICC) was calculated and Bland–Altman analysis performed.1986 Potential level of measurement effects of intra‐subject instrumental variability was assessed using Pearson product‐moment correlation coefficients of the mean and difference of measurements obtained from individual subjects for each pairwise comparison.1986 All tests were two‐tailed and p < 0.05 was considered significant.
Diel variation in cortisol, glucose, lactic acid and antioxidant system of black sea bass Centropristis striata under natural photoperiod
Published in Chronobiology International, 2020
Xing Ren, Jingya Zhang, Li Wang, Zhi Wang, Yan Wang
If ANOVA revealed significant differences in the physiological parameters relating to stress response and antioxidant system between the sampling times, rhythm analysis was performed using GraphPad Prism 7.00 (GraphPad Software, Inc, La Jolla, CA, USA) based on the methods for cosinor-rhythmometry (Cornelissen 2014; Refinetti et al. 2007). Briefly, a nonlinear regression curve was fitted to the data using the model: f (t) = M + A × Cos(πt/12 + φ), where f (t) was the level of the target indicator at a given time point; M (mesor) is the mean value; A (amplitude) is the difference between the peak and mean value of the wave; t is time in hours; φ is the acrophase (a measure of the timing of the peak value recurring in each cycle). The best fit values for A, M and φ are calculated by the least square method. This software-based mathematical calculation also provides determination coefficient (R2), called percent of rhythm that represents the proportion of the total variance accounted for by the fitted model. The significance of the model is tested by F-test, and the degrees of freedom are 2 and 21, respectively. The null hypothesis that there is no rhythm (the amplitude is zero, A = 0) is rejected when F > F1-α (2, 21), where α is the chosen fiducial interval for testing H0. The parameters are considered to display a circadian rhythm when P < 0.05 in ANOVA and the H0 is rejected by F-test in cosinor analysis.
Related Knowledge Centers
- Analysis of Variance
- Null Hypothesis
- Statistical Hypothesis Testing
- Type I & Type II Errors
- Test Statistic
- Standard Deviation
- Analysis of Variance
- Lack-of-Fit Sum of Squares
- Type I & Type II Errors
- Expected Value
- Multiple Comparisons Problem
- Average