EXTENDED STATISTICAL ANALYSIS OF RANKED DATA FROM BALANCED INCOMPLETE BLOCK AND PAIRED COMPARISON DESIGNS

The usual Durbin analysis for ranked data obtained from a balanced incomplete block design is extended to allow for (1) dispersion effects, (2) a predetermined ordering of products and (3) more general trends. An application to paired comparison data is given. Calculation of p-values via Monte Carlo simulation is suggested.     

STATISTICAL ANALYSIS OF HETEROZYGOSITY DATA: INDEPENDENT SAMPLE COMPARISONS

The distribution of mean heterozygosities under an infinite allele model with constant mutation rate was examined through simulation studies. It was found that, although the variance of the distribution decreases with increasing numbers of loci examined as expected, the shape of the distribution may remain skewed or bimodal. The distribution becomes symmetrical for increasing mean heterozygosity levels and numbers of loci. As a result, parametric statistical tests may not be valid for making comparisons among populations or species. Independent sample t-tests were examined in detail to determine the frequency of rejection of the null hypothesis when pairs of samples are drawn from populations with the same mean heterozygosity. Differing numbers of loci and levels of mean heterozygosity were examined. For mean heterozygosity levels above 7.5%, t-tests provide the proper rejection rate, with as few as five loci. When mean heterozygosity is as low as 2.5%, the t-test is conservative even when 40 loci are examined in each population. Independent sample t-tests were then examined for their power to detect true differences between populations as the degree of difference and number of loci vary. Although large differences can be found with high certainty, differences on the order of 5% heterozygosity may require that large numbers of loci (>40) be examined in order to be 80% or more certain of detecting them. In addition, it is emphasized that, for small numbers of loci (<25), the statistical detection of differences of interesting magnitude requires that relatively rare sampling events occur and that much larger differences be observed among the samples than exist for the population means. Two reasons exist for the lack of sensitivity of the test procedures. First, when mean heterozygosity levels are low, the non-normality of the sample means is perhaps most important. Second, even when mean heterozygosity levels are high or when sample sizes are large enough so sample means are approximately normally distributed, the intrinsically high interlocus variance of heterozygosity estimates makes the tests insensitive to the presence of heterozygosity differences that might be biologically meaningful. Finally, the implications of the results of this study are discussed with regard to observed low levels of correlation between heterozygosity and other explanatory variables.     

COMPARISON OF SIGMPLOT, PROBIT, AND EXTREME-VALUE METHODS FOR THE ANALYSIS OF THRESHOLD DATA

Two panels consisting of 12 and of 14 members, respectively,evaluated solutions of ethyl caprylate at different concentrationsto establish flavor detection thresholds. The resulting frequenciesof success at each concentration level were analyzed by a probitmethod and Drake's procedure (1975). These two methods in turnwere compared with extreme-value analysis. Agreement among thethree methods was good. The lowest threshold observed was 0.00069ppm and the highest, 26.9 ppm. An extreme-value plot is presentedfor 59 determinations obtained in prior studies and the 26 valuesof this study. The limitations and advantages of each methodof calculation are discussed as are precautions relative tothe way the extreme-value data should be accumulated or arrayedfor analysis. ^*Station Statistician, Georgia Agricultural Experiment Station.     

多元方差分析中的单一自由度独立比较

本文根据一元方差分析的单一自由度比较原理提出了多元方差分析中的单一自由度比较方法,以用于各种平衡试验设计中具多个变量的处理间多重比较．     

A PHYLOGENETIC ANALYSIS OF THE SYNUROPHYCEAE USING MOLECULAR DATA AND SCALE CASE MORPHOLOGY

The phylogeny of the Synurophyceae was investigated by parsimony analysis of scale case characters and small-sub unit (18S) ribosomal RNA (rRNA) sequence data. Analysis of 1 eustigmatophycean (outgroup), 3 chrysophycean, and 10 synurophycean 18S rRNA sequences corroborated the inference from ultrastructural information that the Synurophyceae is a monophyletic assemblage . Tessellaria vol-vocina, which had been tentatively proposed as a member of the Synurophyceae, was confirmed as the earliest lineage within the Synurophyceae by both the molecular analysis and an evaluation of published ultrastructural data. A second set of analyses investigated the relationships among Tessellaria volvocina, 6 Synura species, and 10 Mallomonas species/varieties, with particular reference to the validity of current classifications of the Synurophyceae and the characters upon which they are based. The molecular and scale case phylogenies were not totally resolved but were largely congruent. The data sets were combined to produce another phylogeny, which showed greater resolution. The combined phylogeny weakly supported our representatives of Synura and Mallomonas as monophyletic groupings and also upheld several of the sections within these genera that are recognized by current classifications. However, some changes to the classification and delineation of these genera are recommended and predicted. Both our 18S rRNA sequence and scale case data sets were more appropriate for examining the branching order among the more closely related text rather than resolving the deeper branching points of the synurophycean phylogeny .     

复合四倍体异育银鲫的血红蛋白和红细胞的同工酶分析

用聚丙烯酰胺梯度凝胶电泳,分析了银鲫、复合四倍体异育银鲫和红鲁的血红蛋白及红细胞中的４种不同的同工酶。结果表明复合四倍体异育银鲫的一些座位,除了银鲫的基因表达外还观察到红鲤基因的表达,出现了银鲫原来所没有的区带或原有的区带受到抑制等现象,显示出复合四倍体异育银鲫具有类似于杂种的遗传性状,另一方面从４种不同的 同工酶表型分析,表明复合四倍体异育银鲫的同工酶基因表达较接近银鲫。     

AN EXAMINATION OF SOME BASIC ASSUMPTIONS OF DNA DISTRIBUTION ANALYSIS USING BIOLOGICAL DATA

An examination is made of how the observed DNA distributions spread from their original biological distributions. Using distributions from testicular and hepatic tissue we find that the current assumptions for DNA distribution analysis need re-examination and suggest how this might be done.     

A COMPARISON OF TWO MULTIVARIATE METHODS FOR THE ANALYSIS OF SENSORY PROFILE DATA

Tables of means, over assessors, are often used to summarize the results of sensory profile experiments. These tables are sometimes further summarized by Principal Components Analysis (PCA) to give plots of the samples in the principal sensory dimensions. An alternative procedure is to use Generalized Procrutes Analysis (GPA) on the assessor data to allow for differences in usage of the vocabulary and in the proportion of the scale used. It is shown that these methods give different configurations in the principal sensory dimensions when applied to the data from a study of cheeses (Muir et al. 1995). Using a Jackknife method to calculate the variability of the samples in the principal sensory dimensions, the results from the GPA method are shown to have a higher dimensionality than from the PCA method. Jackknife estimates of variability are used to calculate confidence ellipses to attach to the sensory space maps.