Robust effect sizes and their confidence intervals for group difference between trajectories in hierarchical linear growth model

Hierarchical linear growth model (HLGM), as a flexible and powerful analytic method, has played an increased important role in psychology, public health and medical sciences in recent decades. Mostly, researchers who conduct HLGM are interested in the treatment effect on individual trajectories, which can be indicated by the cross-level interaction effects. However, the statistical hypothesis test for the effect of cross-level interaction in HLGM only show us whether there is a significant group difference in the average rate of change, rate of acceleration or higher polynomial effect; it fails to convey information about the magnitude of the difference between the group trajectories at specific time point. Thus, reporting and interpreting effect sizes have been increased emphases in HLGM in recent years, due to the limitations and increased criticisms for statistical hypothesis testing. However, most researchers fail to report these model-implied effect sizes for group trajectories comparison and their corresponding confidence intervals in HLGM analysis, since lack of appropriate and standard functions to estimate effect sizes associated with the model-implied difference between grouping trajectories in HLGM, and also lack of computing packages in the popular statistical software to automatically calculate them. ^ The present project is the first to establish the appropriate computing functions to assess the standard difference between grouping trajectories in HLGM. We proposed the two functions to estimate effect sizes on model-based grouping trajectories difference at specific time, we also suggested the robust effect sizes to reduce the bias of estimated effect sizes. Then, we applied the proposed functions to estimate the population effect sizes (d ) and robust effect sizes (du) on the cross-level interaction in HLGM by using the three simulated datasets, and also we compared the three methods of constructing confidence intervals around d and du recommended the best one for application. At the end, we constructed 95% confidence intervals with the suitable method for the effect sizes what we obtained with the three simulated datasets. ^ The effect sizes between grouping trajectories for the three simulated longitudinal datasets indicated that even though the statistical hypothesis test shows no significant difference between grouping trajectories, effect sizes between these grouping trajectories can still be large at some time points. Therefore, effect sizes between grouping trajectories in HLGM analysis provide us additional and meaningful information to assess group effect on individual trajectories. In addition, we also compared the three methods to construct 95% confident intervals around corresponding effect sizes in this project, which handled with the uncertainty of effect sizes to population parameter. We suggested the noncentral t-distribution based method when the assumptions held, and the bootstrap bias-corrected and accelerated method when the assumptions are not met.^

Magnetic properties, grain sizes, XRF Scanner Data of sediment core GeoB9307-3

Geochemical and mineralogical proxies for paleoenvironmental conditions have the underlying assumption that climate variations have an impact on terrestrial weathering conditions. Varying properties of terrigenous sediments deposited at sea are therefore often interpreted in terms of paleoenvironmental change. Also in gravity core GeoB9307-3 (18° 33.99' S, 37° 22.89' E), located off the Zambezi River, environmental changes during Heinrich Stadial 1 (HS 1) and the Younger Dryas (YD) are accompanied by changing properties of the terrigenous sediment fraction. Our study focuses on the relationship of variability in the hydrological system and changes in the magnetic properties, major element geochemistry and granulometry of the sediments. We propose that changes in bulk sedimentary properties concur with environmental change, although not as a direct response of climate driven pedogenic processes. Spatial varying rainfall intensities on a sub-basin scale modify sediment export from different parts of the Zambezi River basin. During humid phases, such as HS 1 and the YD, sediment was mainly exported from the coastal areas, while during more arid phases sediments mirror the hinterland soil and lithological properties and are likely derived from the northern Shire sub-basin. We propose that a de-coupling of sedimentological and organic signals with variable discharge and erosional activity can occur.

Tab. 2: Grain-sizes of cobble on the surface of sanderwurzel

yResults of 13 field investigations between 1966 and 1990 of the southwestern to eastern margin of Kötlujökull and its proglacial area are summarized with respect to sandar and their formation. Generally, the results are based on sedimentological examinations in the field and laboratory, on analyses of aerial photographs, and investigations of the glacier slope. The methods permitted a more detailed reconstruction of sandar evolution in the proglacial area of Kötlujökull since 1945, of tendencies in development and of single data going back until the last decades of the 19th century. Accordingly, there existed special periods of "flachsander"-formations with raised coarsegrained "sanderwurzels" resultant from the outbreak of subglacial meltwater tunneloutlets and other periods with "hochsander-"formations by supraglacial drainage. At present the belts of hochsanders in front of the glacier come up to more than 4 m in thickness and 1000 m in width, therefore containing perhaps more sediment direct in front of Kötlujökull than the old belts of flachsanderwurzels. In one case the explosion-like subglacial meltwater outburst combined with the genesis of a sanderwurzel could be observed for a time and is thoroughly discussed. The event is referred to the outburst of a sub- to inglacial meltwater body being under extreme hydrostatic press ures which is combined with the genesis of a new subglacial tunneloutlet as a new flachsander. Often these outbursts led to the destruction of a morainic belt more than 1000 m in width. Presumably the whole event was finished in not more than a few days. In addition to a characteristic pear-shaped form and water-moved stones up to diameters of 1 m the wurzels possess a single "main-channel" with rectangular cross-sections as far as 4 m deep and 50 m wide just as small flat channels resembling fish bones in connection with the main channel. Presumably, they have been active only in the last stage of wurzel formation. With regard to the subglacial tunnel gates long-living L-meltwater outlets are distinguished from short-living K-meltwater outlets. These are always combined with a raised coarse-grained sanderwurzel, but its meltwater discharge is generally decreasing and ceases after some years, whereas the discharge of L-meltwater outlets continues unchanged for long times (except seasonal differences). The material of flachsanders is preponderantly composed of mugearitic and andesitic cobble extending at least for some kilometres from the glacier margin, whereas the hochsanders correspond to medium to coarse sands without clay and without alternations into the direction of flow. The hochsander fans are covered with small braidet channels. Their sedimentary structures are determined by the short time changing of supraglacial meltwater discharge and the upper flow regime combined with the development of antidunes, which rule the channel-flows during the main activity periods in summer. Unlike the subglacial drainage the supraglacial drainage led to only weak effects of erosion on the glacier foreland. So the hochsanders refilled depressions of morainic areas or grew up on older flachsanderwurzels. Whereas all large flachsanders developed in front of approximate stationary glacier margins, the evolution of coherent belts of hochsanders were combined with progressive glacier fronts. On the other hand, there was obviously no evolution at all of large sandar in front of back-melting margins of Kötlujökull. Based on examinations of the glacier surface and on analyses of aerial photographs the different types of sandar are referred to different structures of the glacier snout. Finally chances of surviving of sandar in the proglacial area of Kötlujökull are shortly discussed just as the possibility of an application of the Islandic research results on Pleistocene sandar in northern Germany.

Magnetic properties, grain sizes and minerals at DSDP Site 83-504B

Twenty-seven samples from the Leg 83 section of Hole 504B have been investigated using magnetic, optical, and electron optical methods. The primary magnetic mineral to crystallize was titanomagnetite of approximate composition Fe2.4Ti0.6O4 (TM60), but none survives, nor is there evidence of titanomaghemite produced by oxidation of TM60. The average measured magnetic properties can be interpreted in terms of magnetite, Fe3O4, having average grain size of <1 µm and present in average volume concentration of - 0.5%. The intensity of the natural remanent magnetization (NRM) of the rocks could also be accounted for as being a thermoremanence carried by this mineral. Although the heterogeneity of the titanomagnetite grains could be detected optically, the texture of the intergrown phases is poorly developed. In some samples from the massive units of the lower part of the section, trellis patterns were visible. The Fe3O4 present in the intergrowths is too intimately mixed with the other intergrown phases to be revealed by electron microprobe analysis that simply returns the bulk composition of the intergrowth (oxidized TM60). The path by which the mineral assemblage evolved from TM60 to an Fe304-containing intergrowth, under the temperature and pressure conditions obtaining in the Leg 83 section, makes interesting speculation. Deuteric oxidation, maghemitization/inversion, or some hypothetical low-temperature/high-pressure oxidation by a leaching-of-iron process may all play roles.

Abundance and sizes of European oak species (Quercus petraea (Matt.) Liebl., Quercus robur L.) in dependence of neighborhood and environmental factors

Quercus robur L. (pedunculate oak) and Quercus petraea (Matt.) Liebl. (sessile oak) are two European oak species of great economic and ecological importance. Even though both oaks have wide ecological amplitudes of suitable growing conditions, forests dominated by oaks often fail to regenerate naturally. The regeneration performance of both oak species is assumed to be subject to a variety of variables that interact with one another in complex ways. The novel approach of this research was to study the effect of many ecological variables on the regeneration performance of both oak species together and identify key variables and interactions for different development stages of the oak regeneration on a large scale in the field. For this purpose, overstory and regeneration inventories were conducted in oak dominated forests throughout southern Germany and paired with data on browsing, soil, and light availability. The study was able to verify the assumption that the occurrence of oak regeneration depends on a set of variables and their interactions. Specifically, combinations of site and stand specific variables such as light availability, soil pH and iron content on the one hand, and basal area and species composition of the overstory on the other hand. Also browsing pressure was related to oak abundance. The results also show that the importance of variables and their combinations differs among the development stages of the regeneration. Light availability becomes more important during later development stages, whereas the number of oaks in the overstory is important during early development stages. We conclude that successful natural oak regeneration is more likely to be achieved on sites with lower fertility and requires constantly controlling overstory density. Initially sufficient mature oaks in the overstory should be ensured. In later stages, overstory density should be reduced continuously to meet the increasing light demand of oak seedlings and saplings.

Stable carbon and oxygen isotope ratios for different test sizes of live benthic foraminifera from the Arabian Sea

We determined the stable oxygen and carbon isotopic composition of live (Rose Bengal stained) tests belonging to different size classes of two benthic foraminiferal species from the Pakistan continental margin. Samples were taken at 2 sites, with water depth of about 135 and 275 m, corresponding to the upper boundary and upper part of the core region of the oxygen minimum zone (OMZ). For Uvigerina ex gr. U. semiornata and Bolivina aff. B. dilatata, delta13C and delta18O values increased significantly with increasing test size. In the case of U. ex gr. U. semiornata, delta13C increased linearly by about 0.105 per mil for each 100-µm increment in test size, whereas delta18O increased by 0.02 to 0.06 per mil per 100 µm increment. For B. aff. B. dilatata the relationship between test size and stable isotopic composition is better described by logarithmic equations. A strong positive linear correlation is observed between delta18O and delta13C values of both taxa, with a constant ratio of delta18O and delta13C values close to 2:1. This suggests that the strong ontogenetic effect is mainly caused by kinetic isotope fractionation during CO2 uptake. Our data underline the necessity to base longer delta18O and delta13C isotope records derived from benthic foraminifera on size windows of 100 µm or less. This is already common practice in down-core isotopic studies of planktonic foraminifera.

Heavy mineral content and grain sizes of sediment samples from foreshore to dune around Skagen, north Denmark

Aufbau und Ausdehnung der Schwermineral-Anreicherungen (Ilmenit, Granat, Amphibol) am Strand südlich Skagens wurden in langen Schürfgräben untersucht. Die Seifenlagen ziehen durchgehend vom Kliff-Fuß bis zur mittleren Meereshöhe hin und liegen meist diskordant auf der alten Strandschichtung. Ihre strandparallele Ausdehnung beträgt bis zu 100 m. Aufgebaut werden sie aus dünnen Schwermineral-Lamellen, die in kleinerem Umfang überall in den Strandablagerungen zu finden sind und hier das Gefüge nachzeichnen (Rippeln, Strandwallschichtung, Schichtstörungen). Die Seifenbildung geht in einem Gebiet mit verstärktem Küstenabtrag vor sich (Lee-Erosion südlich der Hafenmolen von Skagen). Dieses deutet darauf hin, daß die Schwerminerale bei Aufarbeitung bereits vorhandener Sedimente infolge ihres unterschiedlichen hydraulischen Verhaltens Zurückbleiben und schließlich angereichert werden. Die Korngrößenverteilung der Minerale in verschiedenen Sedimentproben zeigen, daß mit steigender Schwermineral-Anreicherung eine Kornverfeinerung und Zunahme der spezifisch schwersten Minerale (opake Erzminerale und Zirkon) auftritt. In ähnlicher Weise werden die Sortierungswerte besser. Die Aufbereitung des Sedimentes wird, in Anlehnung an v. ENGELHARDT (1939), mit einem doppelten Sortierungsvorgang durch die Wasserbewegung am Strand erklärt. Beim Absinken des Sandes nach dem Brecherschwall tritt eine Vorsortierung ein, die den Abtransport der leichteren und größeren Minerale im Sog begünstigt. Verbindungen zu Vorstellungen der Aufbereitungstechnik (Rundherdverfahren) und Hydrodynamik ('laminare Unterschicht') werden hergestellt. Die Dünensande Skagens sind infolge ihres hohen Schwermineralgehaltes und günstiger Äquivalentgrößen der einzelnen Minerale besonders bedeutsam für die Seifenbildung am Strand.