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Water Quality and Monitoring
Published in Yeqiao Wang, Fresh Water and Watersheds, 2020
Major water quality study designs include the plot, single watershed, above and below, two watersheds, paired watershed, multiple watershed, and trend station (Table 33.2). Plots are generally small areas (fractions of an acre) that are replicated on the landscape. All plots are treated alike except for the factor(s) under study. A major advantage of the plot design is that it has a control. A control is a plot that is monitored like all others but does not receive the treatment. The primary statistical approach used is the analysis of variance of a randomized complete block design. A single watershed has sometimes been used to evaluate the water quality changes both before and after a treatment is applied. This design should not be used because the effect due to the treatment cannot be separated from other confounding effects such as year-to-year differences in climate. Two watersheds, one with a treatment and one without, have been incorrectly used to evaluate the effects of a practice on water quality. This design should always be avoided because differences might be inherent in the two watersheds. The above-and-below watershed approach is sometimes viewed as a single watershed with monitoring above and below a practice. In actuality, there are two watersheds being monitored, one nested within the other. If the above- and-below approach is applied both before and after the practice is installed, this approach can be analyzed as a paired watershed design as described later. The above-and- below design is analyzed as a t-test of the differences between paired observations at the above and below stations.
Introductory Statistical Experimental Designs
Published in Jiro Nagatomi, Eno Essien Ebong, Mechanobiology Handbook, 2018
Julia L. Sharp, Patrick D. Gerard
In some experiments, it is apparent that there is a large amount of variation among experimental units. Typically, this translates into less precise statistical inference because variation among experimental units has an impact on the width of confidence intervals and the power of hypothesis tests, for example. One possible way to mitigate the impact of excessive variation among experimental units is through the use of blocking in the experimental design. Blocking entails creating groups of homogeneous experimental units that are similar in the design phase, while the blocks themselves ideally differ. Block effects can be included in statistical models and accounted for, hopefully reducing remaining variation upon which inference can be based. The simplest and most common type of block design is the randomized complete block design. In the randomized complete block design, blocks of experimental units are created. Experimental units are randomized to treatments of interest separately within each block. Additionally, each treatment is assigned to one and only one experimental unit in each block. Some examples of blocking follow.
The Analysis of Variance for Designed Experiments
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Stress in cows prior to slaughter. What is the level of stress (if any) that cows undergo prior to being slaughtered? To answer this question, researchers designed an experiment involving cows bred in Normandy, France. (Applied Animal Behaviour Science, June 2010.) The heart rate (beats per minute) of a cow was measured at four different pre-slaughter phases—(1) first phase of visual contact with pen mates, (2) initial isolation from pen mates for prepping, (3) restoration of visual contact with pen mates, and (4) first contact with human prior to slaughter. Data for eight cows (simulated from information provided in the article) are shown in the table on p. 771. The researchers analyzed the data using an analysis of variance for a randomized block design. Their objective was to determine whether the mean heart rate of cows differed in the four pre-slaughter phases.
Worker assignment in dual resource constrained assembly job shops with worker heterogeneity: an assessment by simulation
Published in International Journal of Production Research, 2020
Matthias Thürer, Haiwen Zhang, Mark Stevenson, Federica Costa, Lin Ma
To give a first indication of the performance impact of our experimental factors, statistical analysis of our results was conducted using an ANOVA (Analysis of Variance). ANOVA is here based on a block design, which is typically used to account for known sources of variation in an experiment. In our ANOVA, we treat the efficiency factor α as the blocking factor. This allows the main effects of this environmental factor and the main and interaction effects of our three control related factors – the Where Rule, Who Rule, and dispatching rule – to be captured. The results are presented in Table 5. All main effects, except for the dispatching rule in terms of the percentage of tardy work orders, were found to be statistically significant. Similarly, all two-way and three-way interactions were found to be statistically significant for all performance measures considered.