Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Shoot dieback in clipped young Golden Leyland (Cupressocyparis leylandii) trees - a physiological mechanism?

Shoot dieback is a problem in frequently trimmed Leyland hedges and is increasingly affecting gardeners’ choice of hedge trees, having a negative effect on a conifer nursery industry. Some damage can be attributed to the feeding by aphids, but it is unclear if there are also underlying physiological causes. In this study, we tested the hypothesis that shoot-clipping of conifer trees during adverse growing conditions (i.e. high air temperature and low soil moisture) could be leading to shoot ‘dieback’. Three-year-old Golden Leyland Cypress (x Cupressocyparis leylandii ‘Excalibur Gold’) plants were subjected to either a well-watered or droughted irrigation regime and placed in either a ‘hot’ (average day temperature = 40°C) or a ‘cool’ (average day temperature = 27°C) glasshouse compartment. Half of the plants from each glasshouse were clipped on Day 14 and again on Day 50. Measurements of soil moisture content (SMC), net CO2 assimilation rate (A), stomatal conductance (gs), branchlet xylem water potential (XWP), plant height and foliage colour were made. Within the clipped and unclipped treatments of both glasshouse compartments, plants from the droughted regime had significantly lower values for A, gs and XWP than those from the well-watered regime. However, there was no difference in these parameters between the hot and cool glasshouse compartments. The trends seen for A, gs and XWP of all treatments generally mirrored changes in SMC indicating a direct effect of water supply on these parameters. By the end of the experiment the overall foliage colour of plants from the hot glasshouse was darker than that of plants from the cool glasshouse and the overall foliage colour was also darker following shoot clipping. In general, shoot clipping led to increases in A, gs XWP and SMC. This may be due to the reduction in total leaf area leading to a greater supply of water for the remaining leaves. No shoot ‘dieback’ was observed in any treatment in response to drought stress or shoot-clipping.

Effect of forage type and proportion of concentrate in the diet on milk fatty acid composition in cows given sunflower oil and fish oil

Based on the potential benefits of cis-9, trans- 11 conjugated linoleic acid (CLA) for human health there is a need to develop effective strategies for enhancing milk fat CLA concentrations. In this experiment, the effect of forage type and level of concentrate in the diet on milk fatty acid composition was examined in cows given a mixture of fish oil and sunflower oil. Four late lactation Holstein-British Friesian cows were used in a 4 x 4 Latin-square experiment with a 2 x 2 factorial arrangement of treatments and 21-day experimental periods. Treatments consisted of grass (G) or maize (M) silage supplemented with low (L) or high (H) levels of concentrates (65: 35 and 35: 65; forage: concentrate ratio, on a dry matter (DM) basis, respectively) offered as a total mixed ration at a restricted level of intake (20 kg DM per day). Lipid supplements (30 g/kg DM) containing fish oil and sunflower oil (2: 3 w/w) were offered during the last 14 days of each experimental period. Treatments had no effect on total DM intake, milk yield, milk constituent output or milk fat content, but milk protein concentrations were lower (P<0.05) for G than M diets (mean 43.0 and 47.3 g/kg, respectively). Compared with grass silage, milk fat contained higher (P<0.05) amounts Of C-12: 0, C-14: 0, trans C-18:1 and long chain >= C20 (n-3) polyunsaturated fatty acids (PUFA) and lower (P<0.05) levels Of C-18:0 and trans C-18:2 when maize silage was offered. Increases in the proportion of concentrate in the diet elevated (P<0.05) C-18:2 (n-6) and long chain >= C20 (n-3) PUFA content, but reduced (P<0.05) the amount Of C-18:3 (n-3). Concentrations of trans-11 C-18:1 in milk were independent of forage type, but tended (P<0.10) to be lower for high concentrate diets (mean 7.2 and 4.0 g/100 g fatty acids, for L and H respectively). Concentrations of trans-10 C-18:1 were higher (P<0.05) in milk from maize compared with grass silage (mean 10.3 and 4.1 g/100 g fatty acids, respectively) and increased in response to high levels of concentrates in the diet (mean 4.1 and 10.3 g/100 g fatty acids, for L and H, respectively). Forage type had no effect (P>0.05) on total milk conjugated linoleic acid (CLA) (2.7 and 2.8 g/100 g fatty acids, for M and G, respectively) or cis-9, trans-11 CLA content (2.2 and 2.4 g/100 g fatty acids). Feeding high concentrate diets tended (P<0.10) to decrease total CLA (3.3 and 2.2 g/100 g fatty acids, for L and H, respectively) and cis-9, trans-11 CLA (2.9 and 1/7 g/100 g fatty acids) concentrations and increase milk trans-9, cis-11 CLA and trans-10, cis-12 CLA content. In conclusion, the basal diet is an important determinant of milk fatty acid composition when a supplement of fish oil and sunflower oil is given.

The relationship between absolute and proportion scores of serial order memory: simulation predictions and empirical data

The capability of a feature model of immediate memory (Nairne, 1990; Neath, 2000) to predict and account for a relationship between absolute and proportion scoring of immediate serial recall when memory load is varied (the list-length effect, LLE) is examined. The model correctly predicts the novel finding of an LLE in immediate serial order memory similar to that observed with free recall and previously assumed to be attributable to the long-term memory component of that procedure (Glanzer, 1972). The usefulness of formal models as predictive tools and the continuity between short-term serial order and longer term item memory are considered.