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.
Dawn M. VanLeeuwen, Rolston St. Hilaire and Emad Y. Bsoul
Matthew H. Kramer, Ellen T. Paparozzi and Walter W. Stroup
primarily on research questions that require inferential statistics. Typically, using designed experiments when addressing a research question requires experiment planning, data collection, and subsequent statistical analysis, and the following
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.
Benjamin G. Mullinix and R. E. Worley
Three out of many pecan cultivars (Gloria, Pabst, & Stuart) were examined over long periods of time. The latter two cultivars have been planted since 1921 when the first pecan orchard was established. One tree of each of these cultivars were removed because of overcrowding. Gloria and Pabst were planted in 1954. Best production practices known were used until 1962. Fertilization and insecticide sprays were adopted. In 1970, spraying for disease was adopted. In 1974, drip irrigation and selective limb pruning were adopted. GrowSeason (GS) [(Year-Planted+l)-mean GS] was used in a linear (L), quadratic (Q), or cubic (C) model where the best model was chosen (significant F-test). Yield was expressed as cumulative yield. Older trees tended to produce more after 1962 (C trend), mid-aged trees more after 1970 (Q/C trend), and younger trees more after 1974 (L/Q trend). Younger trees had the greatest average yearly cumulative yield.
George C.J. Fernandez
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.
Benjamin G. Mullinix, Dean R. Evert and Kerry Harrison
Two peach cultivars (Flordaking & Junegold) were planted in wheel-spoke design under a center pivot irrigation system. Main plots were sprays (Blast, Cheek, & Piggy-back) and cultivars. Sub-plots were training systems (Inside, Outside, & Standard). Sub-sub-plots were tree areas. Four rows were planted with two Inside rows and two Outside rows. Middle two rows of the standard plots were harvested. Intra-row spacing increased the further they were from the center. All trees harvested in 1990, standard plots were harvested every year, and Inside/Outside were harvested in alternate years. Most sources of variation in the model failed to be homogeneous among the 3 years. Since the number of trees harvested each year varied, all mean comparisons were done using the unequal N - unequal variance t-test.
A. Plotto, A. N. Azarenko, M. R. McDaniel and J.P. Mattheis
`Gala' apples were harvested at weekly intervals for 6 weeks, refrigerated at 0C, and evaluated by a consumer panel monthly over a 6 month period for overall liking, firmness, sweetness, tartness and flavor intensities. Firmness, titratable acidity and soluble solids concentration were also measured. Initial analysis of sensory data revealed multicollinearity for overall liking, sweetness, and flavor. The five descriptors explained 75 % of the dataset variation in the first two factors. An orthogonal rotation separated overall liking, flavor and sweetness, and firmness and tartness into two independent factors. The distribution of mean scores along these independent factors showed that panelists could perceive changes due to ripening and maturation. The multivariate factor analysis was better than univariate ANOVA at illustrating how apple maturity stages were apparent to untrained panelists. Firmness was the only instrumental variable correlated to firmness ratings in the sensory tests. None of the analytical measurements could explain overall liking.
Theodore Kisha, Richard Johnson, Dan Skinner and Stephanie Greene
Three alfalfa populations were compared using four molecular marker systems. Population differences were analyzed using Prevosti's distance coefficient, which is a measurement over all loci of the proportion of unshared alleles. The variance of this sample distance is related to the genetic diversities used in calculating F-statistics and can be easily generated using a spreadsheet. The simplicity of statistical testing using Prevosti's distance, and its accuracy at small distances compared with other coefficients, are unique and useful characteristics of this measurement.