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One and Two Restrictions on Randomization
Published in Daryl S. Paulson, Applied Statistical Designs for the Researcher, 2003
The basic Latin square model is: where Latin squares are row–column equal. Note that there is one and only one treatment j for each column k and each row i.
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Published in Filomena Pereira-Maxwell, Medical Statistics, 2018
A study design that extends the two-period crossover design to the comparison of more than two different treatments. A multiperiod crossover trial may be carried out as a complete or incomplete block design. In the former case, each block (i.e. each individual) receives all treatments under study, a different treatment in each of the trial’s periods. The ‘treatment sequence’ x ‘trial period’ array for treatment allocation forms a Latin square, in which the number of periods equals the number of blocks. As each treatment appears only once in each sequence, the number of treatments equals also the number of trial periods. Within a Latin square, individuals are randomized to unique treatment sequences so that in any given period, each of the treatments is administered to just one individual and each individual receives all treatments under study across the different trial periods. This affords the ability to control both individual variability and period effects. Every possible treatment pair sequence occurs only once. Latin squares may be replicated as needed, to accommodate the total sample size (i.e. the total number of blocks) in a trial. Randomization should be carried out independently in each square. FLEISS (1999; p. 282) shows a number of Latin squares that are suitable for the multiperiod crossover design, including the following Latin square for a study design comparing four different treatments. Details of the complete randomization procedure are also given. See POCOCK (1983) and SENN (2002) for discussion of the suitability of this study design to certain types of research, among other relevant issues. See also balanced incomplete block design.
Stiffness estimation of transversely anisotropic materials using a novel indentation tester with a rectangular hole
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Atsutaka Tamura, Mika Saiki, Jun-ichi Hongu, Takeo Matsumoto
Instead of investigating all possible combinations to analyze the influence of a specific set of design parameters, which can be tremendously time-consuming, the DOE uses a relatively small and specific combination of parameters to achieve the same goal. Thus, it reduces the time costs and increases productivity. A Graeco–Latin square design is one of the typical applications in the DOE; in this design, the experimental units are grouped in three ways, and the designs for N = 3-, 4-, and 5-level factors are often employed (Miyakawa 2000). In this study, three 3-level factors were selected, meaning that each design variable had three possible values. That is, Young’s moduli assigned for the ground matrix, i.e. 1, 3, and 5 Pa, were labeled as levels 1, 2, and 3, respectively. Similarly, the material anisotropy ratio of Young’s modulus (Epr/E), 1, 2, and 3, corresponded to levels 1, 2, and 3, respectively. Further, each indentation (δ) or elevation, i.e. 40, 60, and 80 µm, was labeled as levels 1, 2, and 3, respectively (Table 2).
Comparative pharmacokinetic evaluation of extended release itopride HCl pellets with once daily tablet formulation in healthy human subjects: a two treatment, four period crossover study in fasted and fed condition
Published in Drug Development and Industrial Pharmacy, 2019
Muhammad Iqbal Nasiri, Rabia Ismail Yousuf, Muhammad Harris Shoaib, Fahad Siddiqui, Faaiza Qazi, Kamran Ahmed, Sohail Anwer, Kamran Zaheer
Statistical analysis, i.e. two-way analysis of variance (ANOVA) test was performed using the same software for the analysis of test product (Itopride HCl 150 mg ER pellets) under fasted (A) and fed (B) conditions and the reference product (Ganaton 150 mg OD Tablet) under fasted (C) and fed (D) conditions. Latin Square option was used for analysis of conventional two treatments, two sequences, four period, randomized crossover study. As per FDA guidelines different parameters like subject effect nested, sequence effect, and period effect were determined by Latin Square ANOVA. After log-transformation, the geometric mean ratio of Cmax,Tmax, AUC0–48, and AUC0–∞ under fed and fasting conditions were analyzed for the test product (Pellets). For the reference product (Ganaton OD Tablet), two-way analysis of variance was also applied to logarithmic transformed values of Cmax, Tmax, AUC0–48, and AUC0–∞ under fed and fasted conditions, then geometric mean ratio was computed.
Ergonomics investigation for orientation of the handles of wood routers
Published in International Journal of Occupational Safety and Ergonomics, 2018
Siddharth Bhardwaj, Abid Ali Khan
A 7 × 2 full factorial design was used for the experiment. Seven combinations of handles were tested over two routing tasks, i.e., beading and dado. Hence, each participant performed 14 set of experiments. Handle type and tool bit were taken as independent variables, while vibration level at the right hand (right hand was exposed to greater vibration in the routing task compared to the left [35]), EMG of the ECRB and BB muscles and discomfort score were considered the dependent variables. To ensure the principle of randomization, each participant was made to perform the 14 trials in random order as per Latin square randomization [38]. The random order for the trials was realized through the Latin square methodology to ensure no two participants were presented the same sequence of experimental treatments.