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Experiments with Blocks
Published in Julian J. Faraway, Linear Models with Python, 2021
In a completely randomized design (CRD), the treatments are assigned to the experimental units at random. This is appropriate when the units are homogeneous, as has been assumed in the designs leading to the one- and two-way analyses of variances (ANOVAs). Sometimes, we may suspect that the units are heterogeneous, but we cannot describe the form the difference takes — for example, we may know that a group of patients are not identical, but we may have no further information about them. In this case, it is still appropriate to use a CRD. Of course, the randomization will tend to spread the heterogeneity around to avoid systematic bias, but the real justification lies in the randomization test discussed in Section 3.3. Under the null hypothesis, there is no link between a factor and the response. In other words, the responses have been assigned to the units in a way that is unlinked to the factor. This corresponds to the randomization used in assigning the levels of the factor to the units. This is why the randomization is crucial because it allows us to make this argument. Now if the difference in the response between levels of the factor seems too unlikely to have occurred by chance, we can reject the null hypothesis. The normal-based inference is approximately equivalent to the permutation-based test. Since the normal-based inference is much quicker, we usually prefer to use that.
Biostatistics and Bioaerosols
Published in Harriet A. Burge, Bioaerosols, 2020
Lynn Eudey, H. Jenny Su, Harriet A. Burge
Analogous nonparametric tests exist for various designs and analysis of variance tests. The test which is analogous to one-way analysis of variance for completely randomized design is the Kruskal-Wallis test. For a design with randomized blocks (i.e., the data are “matched” in k-tuples and the comparison is between the k populations) the Freidman test is used. In general, these nonparametric tests determine whether the k populations have the same distribution against the alternative hypothesis that at least one of the k distributions differs from the others. Hence, these tests are not only for detecting a difference in location, but a difference in shape of distribution as well.
Principles of Experimental Design
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Three basic experimental designs: completely randomized, randomized block, and factorial designs. A completely randomized design involves a single factor with a random assignment of the treatments to the experimental units.
Locally Optimal Design for A/B Tests in the Presence of Covariates and Network Dependence
Published in Technometrics, 2022
In its simplest form, the experimenter wants to compare the outcomes of two different treatments, labeled by A and B. A completely randomized design is commonly used, in which the treatment setting is randomly assigned to different test subjects. The randomization leads to unbiased estimates of certain estimands, typically, the average treatment (or causal) effect (Rubin 2005), under minimum assumptions. However, there is still room for improvement in the efficiency of the A/B test procedure when certain practical challenges are involved. Besides the treatment setting, many other variables can affect a user’s outcome, including the covariates information and social network connection of the user. Covariates, such as users’ demographic, educational, financial information, are usually available to the experimenter and can significantly contribute to the behaviors and opinions of users. In the aforementioned scenarios, the experimenter also possesses the network connections of the users. In Section 7, we simulate an A/B experiment for the music recommender system based on the real dataset collected from the music streaming service Deezer. The data contains the friendship network of users and their covariates information regarding preferences to different music genres, which should be highly influential to the music recommender system. Intuitively, the outcomes of two connected users might be correlated to some degree. This intuition is reflected in the model assumption of the outcome regarding the network structure, and referred to as the network-correlated outcomes in Basse and Airoldi (2018b). In Sections 2 and 3, we explain in details the assumption on the effects of the network to a user’s outcome.
Effect of wastewater quality parameters on coliform inactivation by tin oxide anodes
Published in Journal of Environmental Science and Health, Part A, 2018
Total coliform counts in the reactors after treatment were determined using the membrane filter technique.[16] The data obtained featured counts of coliform bacteria as a function of time affected by different concentrations of water quality constituents. These data were analyzed using completely randomized design analysis of variance (CRD ANOVA) with one way treatment structure and repeated measures using α=0.05 (95% confidence interval).
Comparative Study on Efficacy of Sanitizing Potential of Aqueous Ozone and Chlorine on Keeping Quality and Shelf-life of Minimally Processed Onion (Allium Cepa L.)
Published in Ozone: Science & Engineering, 2022
Raouf Aslam, Mohammed Shafiq Alam, Preetinder Kaur
All measurements were performed in duplicates for each treatment, and the data obtained were analyzed statistically for analyzing variance by ANOVA using completely randomized design and least significant difference at P < .05 with the SPSS software (version 20.0) (SPSS, Chicago, IL, USA). All data were presented as means ± standard deviation.