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One-Factor Models
Published in Julian J. Faraway, Linear Models with Python, 2021
There are many ways to make the adjustment, but Tukey’s honest significant difference (HSD) is the easiest to understand. It depends on the studentized range distribution which arises as follows. Let X1,…,Xn be i.i.d. N(μ,σ2) and let R=maxiXi−miniXi be the range. Then R/σ^ has the studentized range distribution qn,ν where ν is the number of degrees of freedom used in estimating σ.
Introductory Statistical Experimental Designs
Published in Jiro Nagatomi, Eno Essien Ebong, Mechanobiology Handbook, 2018
Julia L. Sharp, Patrick D. Gerard
The critical value C from Tukey-Kramer's procedure comes from a Studentized range distribution: C=q∝(t,N−t)2 where q∝(t, N − t) is the 1 − α percentile from a Studentized range distribution. Using Tukey–Kramer's method, we will reject Ho if |y¯i−y¯j|≥q∝(t,N−t)2sW2(1ni+1nj)=Wij*.
Statistical Methods for Data Analytics
Published in Adedeji B. Badiru, Data Analytics, 2020
where qn−k,k;α is the value of the studentized range distribution with n − k degrees of freedom and k samples such that the cumulative probability equals 1−α.
Exploring User Micro-Behaviors Towards Five Wearable Device Types in Everyday Learning-Oriented Scenarios
Published in International Journal of Human–Computer Interaction, 2021
Neha Rani, Sharon Lynn Chu, Qing Li
The post-questionnaire included two measures which are presented in this paper.The first assessed the perceived usability of the wearable device used. This was measured using an adapted version of the IBM PSSUQ (Post-Study System Usability Questionnaire) on 5-point Likert scales, shown in Appendix B. The questionnaire constituted of 19 items with 3 sub-scales namely System Quality, Information Quality, and Interface Quality. The second measure assessed the usability of the mobile app. The mobile app usability scale also used an adapted version of the IBM PSSUQ 19 items. All the questionnaire data were collected into a spreadsheet. Scores were reverse-coded where required. Then all the quantitative data were uploaded into a statistical analysis software package (SPSS). We ran the Tukey HSD test to calculate pairwise comparisons for each measure. The Tukey HSD test intrinsically controls for possible Type I errors that can arise from conducting multiple pairwise comparisons, since it is based on a variation of the t distribution that takes into account the number of means being compared (the studentized range distribution) (Lane, 2020) (Lane, 2020). The Tukey HSD test can be used without an omnibus test like the one-way ANOVA (see (Wilkinson, 1999)).
Effect of gauge length on loop strength of sewing threads
Published in The Journal of The Textile Institute, 2019
Vinay Kumar Midha, Ashish Kumar Gupta, A. Mukhopadhyay
The twist per unit length is measured using a direct counting method according to ASTM standard D1423. Tensile testing of the threads is performed at a gauge length of 250 mm on a Tinius Oleson universal testing machine as per ASTM standard D2256. Thirty tests are carried out and the error at the 95% confidence level is less than 4%. Thread strength and loop strength tests are carried out at different gauge lengths (50, 100, 150, 200, 250, and 2.5 mm) using a test speed, corresponding to 20s breaking time for all the threads. About 50 tests of each sample are done and the mean value is calculated. Statistical significant testing is carried out at 95% confidence level to investigate whether the mean values of thread strength and loop strength at successive gauge lengths are statistically significant with respect to the mean values in the lower gauge length. Tukey’s test is used to find the statistical significance. The Tukey’s test (or Tukey procedure), also called Tukey’s honest significant difference test, is a post hoc test based on the studentized range distribution. Tukey’s HSD compares all possible pairs of means to find out which specific groups means (compared with each other) are statistically different. For pair wise comparisons amongst the means, Tukey’s HSD for each pair of means is calculated using Equation (1):
Stochastic Petri-net models to predict the degradation of ceramic claddings
Published in Building Research & Information, 2019
C. Ferreira, L. Canhoto Neves, A. Silva, J. de Brito
When the null hypothesis is rejected, it is concluded that at least the mean of one group tested is statistically different from the others. However, the ANOVA test does not indicate which groups are statistically different from each other. To determine that, a Tukey multiple comparison test (Hochberg & Tamhane, 1987) must be performed. This test is based on the studentized range distribution and it is optimal for procedures with equal sample sizes. The Tukey test compares all pairwise possible between groups and it can be stated that the groups compared are statistically different and the null hypothesis is rejected if the following relationship is verified:where and are the mean of the groups and respectively; is the within-groups mean squares obtained from the one-way ANOVA test; and are the number of observations in groups and respectively; and is the upper th percentile of the studentized range distribution with parameter and degrees of freedom and a significance level of .