This study formulates a property of a quantification method, the principle of equivalent partitioning (PEP). When the PEP is used together with Guttman's principle of internal consistency (PIC) in a simple way, the combination offers an interesting way of analyzing categorical data in terms of the variate(s) chosen by the investigator, a type of canonical analysis. The study discusses applications of the technique to multiple-choice, rank-order, and paired comparison data.

For analyses with missing data, some popular procedures delete cases with missing values, perform analysis with “missing value” correlation or covariance matrices, or estimate missing values by sample means. There are objections to each of these procedures. Several procedures are outlined here for replacing missing values by regression values obtained in various ways, and for adjusting coefficients (such as factor score coefficients) when data are missing. None of the procedures are complex or expensive.

Two coefficients are proposed for measuring the extent of overlap in distributions as a direct function of the variance between the arithmetic means (“disco” and “odisco”). They are designed to answer such questions as: “Given the value of a numerical variable x, to which population should an individual be assigned so that minimum error would be incurred?” This is just the reverse of the question addressed by ANOVA. These coefficients are shown to be analytic in x and they are related to Pearson's eta and Fisher's F. Extensions of these coefficients (designed for univariate, one-way discrimination) to k-way and multivariate discriminant analysis and measurement of “interaction” are suggested.

The clay mineral distributions in fault gouges from shear zones in several slates, phyllites, mica schists, and gneisses of the Eastern Alps were statistically analyzed for consistencies in their occurrence. Discriminant analyses suggested significant groupings of the most common minerals: illite, smectite, kaolinite, and chlorite. The clay mineral distributions in the fault gouges appeared to be related to regional geological units. No relationship, however, was found with the piles of nappes of the Alps. The influence of the mineralogical composition of the parent rock on the clay mineral assemblages appeared to be minor, but the shear behavior of the parent rocks, which is mainly a function of rock strength, was found to control the formation of the clay minerals. In hard rocks (e.g., gneisses), solution transfer at an early stage of the shear process was apparently extensive enough to favor kaolinite formation. As shearing continued, the rate of solution transfer gradually decreased and favored the formation of smectite. In softer rocks (e.g., phyllites), the extent of solution transfer during the shear process was less than in the gneisses and generated an environment that favored smectite formation, even during the early stages of shearing.

Use of a discriminant analysis has verified and grouped three suspected varieties of kaolinite found in kaolin-rich clay strata of late Paleocene to early Eocene age across north-central Mississippi. Initial identification of each type of kaolinite was based on clay-texture characteristics observed on scanning electron micrographs and the differences in pattern configurations of X-ray diffractograms. The discriminant function used for data treatment clearly segregated and grouped each variety. The discrimination variables were found to be the Hinckley index and, to a lesser extent, the Si4+ content relative to the Al3+ content.

The oldest variety is the Blue Mountain clay, composed of preserved hexagonal plates usually clustered into booklets with a vermiform texture. The Ashland variety, stratigraphically younger than the Blue Mountain clay, appears to have been derived from the erosion of the Blue Mountain clay. The Ashland cannot be recognized by any type of diagnostic texture, as it is made up of individual plates that have been corroded and abraded to the point where a hexagonal outline can no longer be recognized. The Sardis variety is the stratigraphically youngest of the three varieties and is at least a second, or possibly a third generation detrital product. The Sardis clay can be recognized by a distinct “ribbon” or “swirl” texture commonly found in ball clays.

Data from this study are not sufficient for complete petrogenetic interpretation. However, speculation on possible differences in depositional environments and modes of deposition can be based on the data at hand. The Blue Mountain variety is considered from previous studies to be primary. The Ashland variety is probably a first generation alluvial clay. The Sardis variety appears to be a multiple generation, detrital product that accumulated as part of overbank swamp deposits.

Multivariate analysis of variance and discriminant analysis were used to establish the crystal chemistry of several Al-rich smectites. The statistical analyses were carded out on 78 samples taken from the literature which were classified on the basis of their physicochemical properties. A strong discrimination exists between beidellites and montmorillonites, ‘non-ideal’ montmorillonites and ‘ideal’ montmorillonites, and Wyoming-type and Cheto-type montmorillonites. Of the Cheto-type montmorillonites, the Tatatilla-type samples are strongly discriminated, whereas the distinction between Chambers- and Otay-types is not strong. AlIV, AlVI, Fe, Mg, and Ca are generally important discriminating variables, whereas the tetrahedral portion of the layer charge, commonly used as a discriminating factor among these minerals, is only moderately significant.

The unsolved systematics of the genus Cardiomya has led to a sequence of astonishing identification mistakes. This scenario is a result of the rarity of specimens and, more importantly, the lack of knowledge about which characters are relevant to the genus taxonomy. In this study, we developed a method based on standard linear discriminant analysis to identify the smallest number of morphological characters that efficiently distinguish individuals at the species level of Brazilian Cardiomya. Starting from 29 morphometric measurements obtained from photographed Cardiomya shells, we were able to identify only five characters: the dorsal inflection of the rostrum, the distance from the posterior most rib end to the umbonal posterior margin and the distance from the central point of the valve to the anterior margin at 45°, 15° and −30° angles. Surprisingly, all these characters are related to the shell outline and not the ornamentation, which is a remarkable character in Cardiomya. We performed a one-way ANOVA with post-hoc Tukey HSD test specifically using the total number of ribs to verify its discriminant power in species identification. Our analysis demonstrated that the number of ribs does not show a significant difference between the analysed species.

Compositional data for 464 clay minerals (2:1 type) were analyzed by statistical techniques. The objective was to understand the similarities and differences between the groups and subgroups and to evaluate statistically clay mineral classification in terms of chemical parameters. The statistical properties of the distributions of total layer charge (TLC), K, VIAl, VIMg, octahedral charge (OC) and tetrahedral charge (TC) were initially evaluated. Critical-difference (P = 1%) comparisons of individual characteristics show that all the clay micas (illite, glauconite and celadonite) differ significantly from all the smectites (montmorillonite, beidellite, nontronite and saponite) only in their TLC and K levels; they cannot be distinguished by their VIAl, VIMg, TC or OC values which reveal no significant differences between several minerals.

Linear discriminant analysis using equal prior was therefore performed to analyze the combined effect of all the chemical parameters. Using six parameters [TLC, K, VIAl, VIMg, TC and OC], eight minerals groups could be derived, corresponding to the three clay micas, four smectites (mentioned above) and vermiculite. The fit between predicted and experimental values was 88.1%. Discriminant analysis using two parameters (TLC and K) resulted in classification into three broad groups corresponding to the clay micas, smectites and vermiculites (87.7% fit). Further analysis using the remaining four parameters resulted in subgroup-level classification with an 85–95% fit between predicted and experimental results. The three analyses yielded D2 Mahalanobis distances, which quantify chemical similarities and differences between the broad groups, within members of a subgroup and also between the subgroups. Classification functions derived here can be used as an aid for classification of 2:1 minerals.

During a survey of soil nematodes in Iran, a population of a species belonging to the order Mononchida was recovered. The new species, Paramylonchulus iranicus sp. n. is characterized by body length (1292–1535 μm in females and 1476–1670 μm in males), c (20.2–29.0 in females and 19.9–27.4 in males), buccal cavity length (23.0–26.0 μm), post vulval uterine sac length (135–162 μm), spicule length (46.0–50.0 μm), gubernaculum length (8.0–11.0 μm), and tail length (49.0–70.0 μm in females and 55.0–73.0 μm in males). Canonical discriminant analysis clearly separated P. iranicus sp. n. from the closely related species Paramylonchulus based on the important morphometric characters of females and males. A molecular study of the 18S rDNA region of P. iranicus sp. n. places this population in a well-supported clade with other species of the genus.

The aim of the present study was to evaluate the physiological and morphological parameters of pregnant does for early prediction of prenatal litter size. In total, 33 does were screened using ultrasonography and further categorized into three groups based on does bearing twins (n = 12), a single fetus (n = 12), or non-pregnant does (n = 9). The rectal temperature °F (RT) and respiration rate (RR) as physiological parameters, while abdominal girth in cm (AG) and udder circumference in cm (UC) as morphological parameters were recorded at different gestation times, i.e. 118, 125, 132 and 140 days. In addition to this, age (years) and weight at service (kg) were also used. The statistical analyses included analysis of variance (ANOVA) and linear discriminant analysis (LDA). The results indicated that groups had significant (P < 0.05) differences among morphological parameters at each gestation time, with higher AG and UC in does bearing twins followed by a single fetus and non-pregnant does. However, both physiological parameters were non-significantly (P > 0.05) associated with litter size groups. It was also revealed that the studied parameters showed increasing trends over gestation time in single and twin fetus categories, but they were on par among non-pregnant does. The results of the LDA revealed that estimated function based on age, weight at service, RR, RT, AG and UC had greater (ranging from 75.00 to 91.70%) accuracy, sensitivity and specificity at different gestation times. It was concluded that using an estimated function, future pregnant does may be identified in advance for single or twin litter size, with greater accuracy.

In this work we report a lipidomics approach to study the effects of two diet systems on the composition of ovine milk. Milk from two groups of Sarda sheep grazing on 40% (P40) and 60% (P60) of pasture were analyzed by a UHPLC-QTOF-MS analytical platform and data submitted to multivariate statistical analysis. Pairwise partial least square discriminant analysis of the lipid profile of the data was carried out to classify samples and to find discriminant lipids. The two dietary groups were characterized by differences in triacylglycerols, phosphocholines and phosphatidylethanolamines levels. Discriminants of the P40 group were TG and PC containing in their backbone saturated medium chain FA thus suggesting greater de novo fatty synthesis in the mammary gland. On the other hand, the P60 group was characterized by TG and PC formed by unsaturated long chain FA originating from the diet or from lipid mobilization.

Resistant starch can alter the intestinal nutrient availability and bulk of digesta, thereby modulating the substrate available for microbial metabolic activity along the gastrointestinal tract. This study elucidated the effect of transglycosylated starch (TGS) on the retention of digesta in the upper digestive tract, ileal flow and hindgut disappearance of nutrients, and subsequent bacterial profiles in pigs. Fourteen ileal-cannulated growing pigs were fed either the TGS or control (CON) diet in a complete crossover design. Each period consisted of a 10-d adaptation to the diets, followed by 3-d collection of faeces and ileal digesta. Consumption of TGS decreased the retention of digesta in the stomach and small intestine, and increased ileal DM, starch, Ca and P flow, leading to enhanced starch fermentation in the hindgut compared with CON-fed pigs. TGS increased ileal and faecal total SCFA, especially ileal and faecal acetate and faecal butyrate. Gastric retention time positively correlated to Klebsiella, which benefitted together with Selenomonas, Lactobacillus, Mitsuokella and Coriobacteriaceae from TGS feeding and ileal starch flow. Similar relationships existed in faeces with Coriobacteriaceae, Veillonellaceae and Megasphaera benefitting most, either directly or indirectly via cross-feeding, from TGS residuals in faeces. TGS, in turn, depressed genera within Ruminococcaceae, Clostridiales and Christensenellaceae compared with the CON diet. The present results demonstrated distinct ileal and faecal bacterial community and metabolite profiles in CON- and TGS-fed pigs, which were modulated by the type of starch, intestinal substrate flow and retention of digesta in the upper digestive tract.

The aim of this study was to analyse the morphology and allometry of larvae belonging to five potamodromous species. Five breeding species belonging to the order Characiformes [Salminus brasiliensis (Cuvier, 1816), Leporinus steindachneri, Eigenmann, 1907, Prochilodus lineatus (Valenciennes, 1837), Prochilodus vimboides (Kner,1859) and Brycon insignis, Steindachner, 1877] were used to obtain larvae samples during the pre-flexing, post-flexing, and juvenile developmental stages. When we observed the degree-hour (DH) amplitude time values, we found three developmental groups based on allometry and morphometrics within the period between the pre-flexing and post-flexing phases. Group 1 consists of the species S. brasiliensis and B. insignis, Group 2 consists of P. lineatus and P. vimboides, and Group 3 consists of L. steindachneri. Group 1 requires less development time and has more slender larvae. Group 2 has a moderate development time and larvae with a more rounded shape. Group 3 presents a greater development time and an intermediate larval morphology. It was possible to classify the larvae through cross-validated discriminant analyses based on seven morphometric variables with 90% accuracy in B. insignis, 83% in L. steindachneri, 91% in P. lineatus, 80% in P. vimboides, and 96% in S. brasiliensis. These results indicate larval characteristics that can be used for the taxonomic identification of the icthyoplankton.