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Burton J. Hoyle

Environmental analysis (EA) is described as a simplified system for determining significant differences between individual and groups of treatments within a test plot. It is based on recognizing and using the fact that each data point comes from a different environment in the soil. So called effects of blocks, rows and columns are ignored and replicates are ranked. Ranges of treatments are compared at corresponding levels of most to least favorable environment. The magnitude of a replicate is used only to indicate equal or better of one to another treatment. Significance levels are calculated or looked up in tables. EA is hundreds of times faster than ANOVA or regression analysis; results can often be obtained quickly by hand. Examples of EA are compared to ANOVA plus LSD and regression analysis. In all cases, results obtained by EA were nearly the same for the examples discussed. The predictive value of EA appears to be superior to the other methods. Techniques are shown for atypical ranking and other characteristics.

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Li-Chun Huang and Li-Chun Chen

were excluded, leaving 1629 posts for the subsequent statistical analyses. Afterward, this study adopted the ANOVA approach to test whether post content and media format had significant effects on the number of likes, comments, and shares from users. If

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Dawn M. VanLeeuwen, Rolston St. Hilaire, and Emad Y. Bsoul

Statistical analysis of data from repeated measures experiments with missing factor combinations encounters multiple complications. Data from asynchronous cyclic drought experiments incorporate unequal numbers of drought cycles for different sources and provide an example of data both with repeated measures and missing factor combinations. Repeated measures data are problematic because typical analyses with PROC GLM do not allow the researcher to compare candidate covariance structures. In contrast, PROC MIXED allows comparison of covariance structures and several options for modeling serial correlation and variance heterogeneity. When there are missing factor combinations, the cross-classified model traditionally used for synchronized trials is inappropriate. For asynchronous data, some least squares means estimates for treatment and source main effects, and treatment by source interaction effects are inestimable. The objectives of this paper were to use an asynchronous drought cycle data set to 1) model an appropriate covariance structure using mixed models, and 2) compare the cross-classified fixed effects model to drought cycle nested within source models. We used a data set of midday water potential measurements taken during a cyclic drought study of 15 half-siblings of bigtooth maples (Acer grandidentatum Nutt.) indigenous to Arizona, New Mexico, Texas, and Utah. Data were analyzed using SAS PROC MIXED software. Information criteria lead to the selection of a model incorporating separate compound symmetric covariance structures for the two irrigation treatment groups. When using nested models in the fixed portion of the model, there are no missing factors because drought cycle is not treated as a crossed experimental factor. Nested models provided meaningful F tests and estimated all the least squares means, but the cross-classified model did not. Furthermore, the nested models adequately compared the treatment effect of sources subjected to asynchronous drought events. We conclude that researchers wishing to analyze data from asynchronous drought trials must consider using mixed models with nested fixed effects.

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Richard P. Marini

Experiments with factorial arrangements of treatments plus one or more other treatment(s) are sometimes analyzed with a one-way analysis of variance (ANOVA) and means are separated with a multiple comparison. A set of single degree-of-freedom contrasts in a one-way ANOVA, provides formal tests for main effects and interactions. Data from a 2 × 3 factorial experiment that also contained a control were analyzed with a one-way ANOVA with a multiple comparison. Results from this analysis were compared to results obtained from a two-way ANOVA, a one-way ANOVA with pre-planned contrasts, a two-way ANOVA with least squares means comparisons obtained with SAS/general linear models procedure, and a regression model with an indicator variable and random blocks obtained with SAS/Mixed procedure. Results and interpretation differed depending on how the data were analyzed and these differences are discussed.

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Cheryl A. Parris, Clinton C. Shock, and Michael Qian

material was weighed, dried, and separated into leaves and stems, and reweighed to calculate leaf yield in Mg·ha −1 . Differences in leaf yield and steviol glycoside content by varying rates of SWT were determined by ANOVA and regression statistics ( Hintze

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D. Michael Glenn

The minirhizotron approach for studying the dynamics of root systems is gaining acceptance; however, problems have arisen in the analysis of data. The purposes of this study were to determine if analysis of variance (ANOVA) was appropriate for root count data, and to evaluate transformation procedures to utilize ANOVA. In peach, apple, and strawberry root count data, the variance of treatment means was positively correlated with the mean, violating assumptions of ANOVA. A transformation based on Taylor's power law as a first approximation, followed by a trial and error approach, developed transformations that reduced the correlation of variance and mean.

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Ryan W. Dickson, Paul R. Fisher, Sonali R. Padhye, and William R. Argo

iron concentration. Statistical and cluster analysis. PROC GLIMMIX ANOVA in SAS 9.4 (SAS Institute, Cary, NC) was used to evaluate genotype and substrate pH effects on absolute values at high and low pH for leaf SPAD, shoot dry weight, flower index

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Lisa J. Rowland, Elizabeth L. Ogden, Fumiomi Takeda, David Michael Glenn, Mark K. Ehlenfeldt, and Bryan T. Vinyard

the true LT 50 for the replicate. Both a one-way and a two-way ANOVA was fit to the median 200 (LT 50 bootstrap estimates) for each replicate. In the one-way ANOVA, pairwise means comparisons were conducted among the combinations of method

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Shuyin Liang, Xuan Wu, and David Byrne

the interaction of the flower diameter corresponds to a significant interaction in the ANOVA which indicates flower diameter is the better trait, as compared with petal number or flower dry weight, to select for heat-stable flower size. Table 3

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Kent M. Eskridge

Breeders need powerful and simply understood statistical methods when analyzing disease reaction data. However, many disease reaction experiments result in data which do not adhere to the classical analysis of variance (ANOVA) assumptions of normality, homogeneity variance and a correctly specified model. Nonparametric statistical methods which require fewer assumptions than classical ANOVA, are applied to data from several disease reaction experiments. It is concluded that nonparametric methods are easily understood, can be productively applied to plant disease experiments and many times result in improved chances for detecting differences between treatments.