True Population Mean Research Articles

Indirect early generation selection for yield in winter wheat

Early generation selection (EGS) aims to accelerate genetic yield gain by applying selection pressure for desirable traits at early generations within breeding programmes. This study was designed to evaluate single plant yield (SPY), harvest index (HI; SPY divided by aboveground biomass) and estimated fruiting efficiency (FE m ; kernels per unit chaff weight) as EGS traits in predominantly F3 populations of winter wheat. Lines were sown as single plants and in plots of pooled family seed in northwest Victoria, Australia in 2018. From the single plant populations, 21–23 lines were selected for each EGS trait and 52 lines were selected at random to estimate true population mean; 25 lines were selected visually from pooled plots. Selected lines were sown in partially replicated plots in 2019. Lines selected for HI yielded 24% more than lines selected at random and 22% more than lines selected visually; selections made for SPY and FE m yielded the equivalent of HI selections, but not significantly higher than the random or visual treatments. In 2020, the 7 highest-yielding lines from the HI, random and visual selection treatments were sown in replicated plots. There was no significant difference in yield between treatments. Nevertheless, EGS for HI successfully culled low yielding lines, and enriched populations with high yielding lines prior to plot-level yield testing. Advancements in high-throughput phenotyping are required before widespread adoption but are anticipated in the near future.

Intra-subject sample size effects in plantar pressure analyses.

BackgroundRecent work using large datasets (>500 records per subject) has demonstrated seemingly high levels of step-to-step variation in peak plantar pressure within human individuals during walking. One intuitive consequence of this variation is that smaller sample sizes (e.g., 10 steps per subject) may be quantitatively and qualitatively inaccurate and fail to capture the variance in plantar pressure of individuals seen in larger data sets. However, this remains quantitatively unexplored reflecting a lack of detailed investigation of intra-subject sample size effects in plantar pressure analysis.MethodsHere we explore the sensitivity of various plantar pressure metrics to intra-subject sample size (number of steps per subject) using a random subsampling analysis. We randomly and incrementally subsample large data sets (>500 steps per subject) to compare variability in three metric types at sample sizes of 5–400 records: (1) overall whole-record mean and maximum pressure; (2) single-pixel values from five locations across the foot; and (3) the sum of pixel-level variability (measured by mean square error, MSE) from the whole plantar surface.ResultsOur results indicate that the central tendency of whole-record mean and maximum pressure within and across subjects show only minor sensitivity to sample size >200 steps. However, <200 steps, and particularly <50 steps, the range of overall mean and maximum pressure values yielded by our subsampling analysis increased considerably resulting in potential qualitative error in analyses of pressure changes with speed within-subjects and in comparisons of relative pressure magnitudes across subjects at a given speed. Our analysis revealed considerable variability in the absolute and relative response of the single pixel centroids of five regions to random subsampling. As the number of steps analysed decreased, the absolute value ranges were highest in the areas of highest pressure (medial forefoot and hallux), while the largest relative changes were seen in areas of lower pressure (the midfoot). Our pixel-level measure of variability by MSE across the whole-foot was highly sensitive to our manipulation of sample size, such that the range in MSE was exponentially larger in smaller subsamples. Random subsampling showed that the range in pixel-level MSE only came within 5% of the overall sample size in subsamples of >400 steps. The range in pixel-level MSE at low subsamples (<50) was 25–75% higher than that of the full datasets of >500 pressure records per subject. Overall, therefore, we demonstrate a high probability that the very small sample sizes (n < 20 records), which are routinely used in human and animal studies, capture a relatively low proportion of variance evident in larger plantar pressure data set, and thus may not accurately reflect the true population mean.

True mean value discovery over multiple data sources with unknown reliability degrees

In the era of big data, we are committed to obtaining the observations of target objects from a wider range of data sources. As the number of data sources increases, we expect that more trustworthy statistical parameters can be estimated from the multi-source observations, for example, the population mean. However, the reliability of data sources rarely attracts our attention, because the hypothesis testing seems to be an effective tool for determining whether a given estimate is acceptable. In practice, the noisy observations from different unreliable data sources may have different statistical characteristic parameters, and these parameters are unknown. It makes the condition that observations should be identically distributed in hypothesis testing no longer tenable. Therefore, a poor estimate of the population mean may be accepted, as the hypothesis testing is performed over the multi-source observations. To address this issue, in this paper, we propose a true mean value discovery algorithm in which we can use multi-source observations to determine whether an estimated population mean should be rejected. Additionally, the reliability degree of each data source can be estimated using the proposed algorithm. By removing incorrect observations provided by unreliable sources, we can obtain more reliable estimates of true population means. Experiments on three real-world tasks demonstrate that the proposed method outperforms state-of-the-art approaches.

Watermelon bug (Aspongopus viduatus) full‐fat meals as an alternative dietary protein on broiler chickens’ growth performance, meat, and blood

Insects were considered a sufficient sustainable and alternative source of nutrients for poultry, watermelon bug is the main pest ofwatermelons in Sudan. The insect meal contain high protein with relatively cheap price. This study was conducted to evaluate using watermelon bug meal as protein source on broiler chickens’ diet. 144 one-day-old chicks were distributed in a completely randomized experimental design with 4 treatments and 3 replicates of 12 birds. A control, B, C and D, (treatments), the powder of insects 0, 10, 20, and 30g/kg rations, was carried for 6 weeks. Weekly record of feed intake, weight gain and feed conversion ratio were taken. Data were analyzed by ANOVA the standard error of the mean (SEM) was used to measure how far the sample mean of the data is likely to be from the true population mean. Adding watermelon bug meal (WMBM) to the diet at 10, 20, and 30 % WMBM of feed essentially increased the body weight of chickens from 395.87g in the first week with concentration of 10 % to 1715.00g in the fifth week, followed by C (20 %) inclusion of WMBM which increased the body weight from 380.13g to 1773.33g, respectively. The highest FCR was recorded in D (30 %) WMBM feed. There was a significant difference in the means weight of heart, and gizzard. The blood analysis revealed no increase in the percentage of cholesterol while there were significant (p < 0.05) differences in total protein and triglycerides. Significant differences were observed in flavor, texture and juiciness values among all treatments. In conclusion, the current results confirmed that the addition of WMBM to the diet of broiler chickens can improve growth and meat performance.

How Reliably Can We Measure a Child's True IQ? Socio-Economic Status Can Explain Most of the Inter-Ethnic Differences in General Non-verbal Abilities.

Roma children have been discriminated against for many years as they are denied access to high-quality education based on their scores on general non-verbal IQ tests. Rushton et al. (2007) showed that Roma perform more poorly than non-Roma on one such test (i.e., Raven Progressive Matrices), but suggest that this underperformance could be explained by Roma’s low socio-economic status. In this paper, we tested the non-verbal abilities of Roma children and expanded on the research of Rushton et al. (2007) by investigating empirically the potential mediating effects of socio-economic status on children’s performance on Raven Progressive Matrices. Results showed that the performance of Roma children was, on average, significantly lower than the performance of their non-Roma peers; however, the effect of ethnicity was partially mediated by the parents’ education and living conditions (while the parents’ income had no significant effect). As hypothesized by Rushton et al. (2007) some socio-economic factors can explain important variability in the performance of Roma children on general non-verbal tests, and their poor performance on such tests may lead to an underestimation of the true population mean.

Sampling of Atlantic salmon Salmo salar from tanks and sea cages is size-biased

Random samples of individual fish for the cause of estimating body size average and variation in fish groups is a widespread practice in scientific experiment as well as in fish production. Sample accuracy and precision naturally increases with sample size, but may very well depend on other factors such as fish size dependent success rate of capture method and spatial-behavioural size segregation. In 4 case studies with Atlantic salmon (Salmo salar) where the entire population was crowded and measured for length and weight, we show how the estimated mean weight and condition factor, and their deviation from the true population mean, evolve with number of sampled fish: 1) sampling of 3400 pre-smolts (77 g) netted by hand from a 5 m tank, 2) 466 post-smolts (711 g) netted by hand from a 5 m sea cage, 3) 5569 post-smolts (394 g) netted by hand from a 12 m sea cage, 4) the same fish as in 3, but 9 months later (3367 g, n = 5288) and netted out by using a crane mounted tarpaulin container. Sampling of cases 1, 3 and 4 took place over consecutive days. Cumulative mean, i.e. the mean for each new fish sampled, of weight and condition factor were calculated for each sampling day. To simulate a perfectly random sampling to compare with that observed, the order in which the individuals in the entire population were sampled were randomized, and cumulative means calculated in the same manner. With the randomized sampling order the cumulative mean values rapidly approached true population mean and remained at that level for both weight and condition factor in all days on all sampling events. In contrast, the cumulative mean weight and/or condition factor of the observed sampling order generally deviated from the true mean even after a large number of fish had been sampled, and the patterns in how cumulative mean values developed was inconsistent between days.

Covariate adjustment and estimation of mean response in randomised trials.

Analyses of randomised trials are often based on regression models which adjust for baseline covariates, in addition to randomised group. Based on such models, one can obtain estimates of the marginal mean outcome for the population under assignment to each treatment, by averaging the model-based predictions across the empirical distribution of the baseline covariates in the trial. We identify under what conditions such estimates are consistent, and in particular show that for canonical generalised linear models, the resulting estimates are always consistent. We show that a recently proposed variance estimator underestimates the variance of the estimator around the true marginal population mean when the baseline covariates are not fixed in repeated sampling and provide a simple adjustment to remedy this. We also describe an alternative semiparametric estimator, which is consistent even when the outcome regression model used is misspecified. The different estimators are compared through simulations and application to a recently conducted trial in asthma.

Sample size and its role in Central Limit Theorem (CLT)

It is very important to determine the proper or accurate sample size in any field of research. Sometimes researchers cannot take the decision that how many numbers of individuals or objects will they select for their study purpose. Also, a set of survey data is used to verify that central limit theorem (CLT) for different sample sizes. From the data of 1348 students, we got the average weight for our population of BRAC University students is 62.62 kg with standard deviation 11.79 kg. We observed that our sample means became better estimators of the true population mean. In addition, the shape of the distribution became more Normal as the sample size increased. So it is concluded that our simulation results were consistent with the central limit theorem.

Do small samples underestimate mean abundance? It depends on what type of bias we consider.

Former authors claimed that, due to parasites' aggregated distribution, small samples underestimate the true population mean abundance. Here we show that this claim is false or true, depending on what is meant by 'underestimate' or, mathematically speaking, how we define 'bias'. The 'how often' and 'on average' views lead to different conclusions because sample mean abundance itself exhibits an aggregated distribution: most often it falls slightly below the true population mean, while sometimes greatly exceeds it. Since the several small negative deviations are compensated by a few greater positive ones, the average of sample means approximates the true population mean.

Accuracy of torque-limiting devices: A comparative evaluation

Statement of problemTo prevent the loosening of implant screws, clinicians should be aware of the output torque values needed to achieve the desired preload. Accurate torque-control devices are crucial in this regard; however, little information is currently available comparing the accuracy of mechanical with that of electronic torque-control devices. PurposeThe purpose of this in vitro study was to identify and compare the accuracy of different types of torque-control devices. Material and methodsDevices from 5 different dental implant manufacturers were evaluated, including 2 spring-type (Straumann, Implance) mechanical devices (MTLD), 2 friction-type (Biohorizons, Dyna) MTLDs, and 1 (Megagen) electronic torque-control device (ETLD). For each manufacturer, 5 devices were tested 5 times with a digital torque tester, and the average for each device was calculated and recorded. The percentage of absolute deviations from the target torque values (PERDEV) were calculated and compared by using 1-way ANOVA. A 1-sample t test was used to evaluate the ability of each device to achieve its target torque value within a 95% confidence interval for the true population mean of measured values (α=.05 for all statistical analyses). ResultsOne-way ANOVAs revealed statistically significant differences among torque-control devices (P<.001). ETLD showed higher PERDEVs (28.33 ±9.53) than MTLDs (P<.05), whereas PERDEVS of friction-type (7.56 ±3.64) and spring-type (10.85 ±4.11) MTLDs did not differ significantly. In addition, devices produced by Megagen had a significantly higher (P<.05) PERDEV (28.33 ±9.53) other devices, whereas no differences were found in devices manufactured by Biohorizons (7.31 ±5.34), Dyna (7.82 ±1.08), Implance (8.43 ±4.77), and Straumann (13.26 ±0.79). However, 1-sample t tests showed none of the torque-control devices evaluated in this study were capable of achieving their target torque values (P<.05). ConclusionsWithin the limitations of this in vitro study, MTLDs were shown to be significantly more accurate than ETLDs. However, none of the torque-control devices evaluated were able to meet their target torque values successfully.

It's just a standard deviation!

It's just a standard deviation!

How do I interpret a confidence interval?

A 95% confidence interval (CI) of the mean is a range with an upper and lower number calculated from a sample. Because the true population mean is unknown, this range describes possible values that the mean could be. If multiple samples were drawn from the same population and a 95% CI calculated for each sample, we would expect the population mean to be found within 95% of these CIs. CIs are sensitive to variability in the population (spread of values) and sample size. When used to compare the means of two or more treatment groups, a CI shows the magnitude of a difference between groups. This is helpful in understanding both the statistical significance and the clinical significance of a treatment. In this article we describe the basic principles of CIs and their interpretation.

Inference from a sample mean--Part 1.

Inference from a sample mean--Part 1.

Reporting Confidence Interval Instead of a Point Estimate a Review

In medical studies, investigators try to find out whether the difference of a measured outcome between groups is statistically significant by reporting a p value to reject or retain a null hypothesis. Such reporting of p value from comparisons of mean of the two groups has its limitations. Hypothesis testing does not take into account the variability of an observed sample statistic or its precision. Hence, it is important to quantify the uncertainty in this estimate by means of a confidence interval around the mean difference rather than reporting the mean difference simply as a point estimate. The confidence interval provides a range within which the true population value of the mean difference would lie with a certain degree of probability. Thus, a 95% confidence interval provides a range of mean differences that would contain the true population mean difference at least 95 times out of 100 repeated studies. The width of this range is determined by the sampling error or standard error. Greater the standard error, wider the range of the confidence interval. Conversely, a narrow range of confidence interval reflects a more precise study.

Accuracy and precision of as-received implant torque wrenches

Previous implant torque evaluation did not determine if the target value fell within a confidence interval for the population mean of the test groups, disallowing determination of whether a specific type of wrench met a standardized goal value. The purpose of this study was to measure both the accuracy and precision of 2 different configurations (spring style and peak break) of as-received implant torque wrenches and compare the measured values to manufacturer-stated values. Ten wrenches from 4 manufacturers, representing a variety of torque-limiting mechanisms and specificity of use (with either a specific brand or universally with any brand of implant product). Drivers were placed into the wrench, and tightening torque was applied to reach predetermined values using a NIST-calibrated digital torque wrench. Five replications of measurement were made for each wrench and averaged to provide a single value from that instrument. The target torque value for each wrench brand was compared to the 95% confidence interval for the true population mean of measured values to see if it fell within the measured range. Only 1 wrench brand (Nobel Biocare) demonstrated the target torque value falling within the 95% confidence interval for the true population mean. For others, the targeted torque value fell above the 95% confidence interval (Straumann and Imtec) or below (Salvin Torq). Neither type of torque-limiting mechanism nor designation of a wrench to be used as a dedicated brand-only product or to be used as a universal product on many brands affected the ability of a wrench to deliver torque values where the true population mean included the target torque level.

Are the Effects of Homeopathy Attributable to a Statistical Artefact? A Reanalysis of an Observational Study

Background. Cohort studies have reported that patients improve considerably after individualised homeopathic treatment. However, these results may be biased by regression to the mean (RTM). Objective. To evaluate whether the observed changes in previous cohort studies are due to RTM and to estimate RTM adjusted effects. Methods. SF-36 quality-of-life (QoL) data from a German cohort of 2827 chronically diseased adults treated by a homeopath were reanalysed by Mee and Chua's modified t-test. Results. RTM adjusted effects, standardized by the respective standard deviation at baseline, were 0.12 (95% CI: 0.06–0.19, P < 0.001) in the mental and 0.25 (0.22–0.28, P < 0.001) in the physical summary score. Small-to-moderate effects were confirmed for the most individual diagnoses in physical, but not in mental component scores. Under the assumption that the true population mean equals the mean of all actually diseased patients, RTM adjusted effects were confirmed for both scores in most diagnoses. Conclusions. Changes in QoL after treatment by a homeopath are small but cannot be explained by RTM alone. As all analyses made conservative assumptions, true RTM adjusted effects are probably larger than presented.

Spatial and seasonal variation in δ15N and δ13C values in a mesopredator shark, Squalus suckleyi, revealed through multitissue analyses

We used variance decomposition to explore the importance of body size, sex, location, and sampling period as predictors of intrapopulation variation in δ15N and δ13C values in spiny dogfish Squalus suckleyi from the Puget Sound–Strait of Georgia basin. Isotopes in two tissues with long (dorsal white muscle) and short (liver) isotopic turnover rates (~1 year and ~3–4 months, respectively) were sampled to evaluate whether the relative importance of each variable differed depending on the time span over which diet information was integrated. Significant spatial variation was observed in both muscle and liver isotopic composition, whereby location uniquely explained 25 and 17 % of the total variance, respectively. The remaining variables explained considerably less variation in both tissue types. Furthermore, evidence of seasonal isotopic shifts in δ15N and δ13C values was apparent, but differed widely in direction and magnitude among groups. These findings suggest that members of spiny dogfish schools may share a common feeding history, possibly by spending extended time periods (weeks to months) foraging in a spatially fixed region. Another explanation is that individuals may move and feed in aggregations that exist for extended periods. These complex group-level patterns suggest that even for large-bodied, motile predators such as sharks, population-level diet estimates derived from averaging isotope ratios of individuals collected from only a few locations may poorly reflect the true population mean.

Uncertainty of global warming potential for milk production on a New Zealand farm and implications for decision making

As a food exporting nation, New Zealand recognises that the Global Warming Potential (GWP) impact of agriculture has become important to food customers. Food production policy and industry analysts make GWP decisions based on greenhouse gas inventory and life cycle assessment (LCA) results. For decision making, the level of confidence associated with information is important. However, treatment of uncertainty has been problematic in LCA, especially in agricultural systems. In this paper, the GWP of 1 kg of milk was used as a case study to test the feasibility of quantifying uncertainties by Monte Carlo simulation in an LCA applied to an agriculture product. The study also contributes to the development of good practice and has implications for the incorporation of uncertainties into decision making. We distinguished between three sources of variation. First, there is variability amongst basic units such as dairy cattle, soils and farm characteristics which may be quantified by the standard deviation (SD). Second, there is uncertainty about true population means, which is typically provided by a sample and can be measured by the standard error of the mean (SEM). Third, choices, such as the time horizon for computing GWP, can strongly affect the LCA outcomes. The first two sources were analysed by compiling input variable statistics and undertaking Monte Carlo numerical simulations. The third source of variation was quantified by sensitivity analysis. Up to the farm-gate stage, the mean GWP of 1 kg of milk (computed over 100 years) was 0.96 kg CO2-eq. The associated SD was 38% of the mean when using the SD of input variables (and called “variability”) and 7% when using the SEM (and called “uncertainty”). The GWP was most sensitive to uncertainty of pasture dry matter intake by grazing cattle. The second and third key input variables were the cattle excreta nitrous oxide emission factor and the enteric fermentation methane emission factor, respectively. Changing the GWP from a 100-year computation to one of 20 years corresponded to GWP increasing by 92%, while for a change from 100 to 500 years GWP declined by 54%. Data compilation for the uncertainty analyses was challenging because the measurements available were made over smaller time and space scales than ideal, so observations had to be generalised and data gaps filled by expert judgement. Uncertainty analysis using the SEM of input variables was considered most adapted in LCA, so it is recommended as best practice. Identification of the key parameters responsible for uncertainty in the LCA revealed knowledge gaps where research should be directed, such as for methane digestion and nitrous oxide emissions from N excreted by ruminants. Moreover, richer information for those key parameters could be used to build a typology of more meaningful simulations instead of a single, virtual average for analysing environmental impacts of the agricultural system. The use of Monte Carlo simulations for uncertainty and sensitivity analyses of LCA estimates for an agricultural product was feasible and recommendations were made. Developing a typology of realistic simulations based on the key parameters identified in the sensitivity analysis could provide decision makers with more information. Furthermore, in comparative LCA studies, a probabilistic framework provides further information including the statistical significance of differences between technological options. This would represent considerable progress for the decision-making process. We recommend that uncertainty information such as SEM, when available, be part of inventory data for agriculture systems in public reports and databases including assessment of its statistical meaning and consistency.

Identifying Variables Responsible for Data not Missing at Random

When data are not missing at random (NMAR), maximum likelihood (ML) procedure will not generate consistent parameter estimates unless the missing data mechanism is correctly modeled. Understanding NMAR mechanism in a data set would allow one to better use the ML methodology. A survey or questionnaire may contain many items; certain items may be responsible for NMAR values in other items. The paper develops statistical procedures to identify the responsible items. By comparing ML estimates (MLE), statistics are developed to test whether the MLEs are changed when excluding items. The items that cause a significant change of the MLEs are responsible for the NMAR mechanism. Normal distribution is used for obtaining the MLEs; a sandwich-type covariance matrix is used to account for distribution violations. The class of nonnormal distributions within which the procedure is valid is provided. Both saturated and structural models are considered. Effect sizes are also defined and studied. The results indicate that more missing data in a sample does not necessarily imply more significant test statistics due to smaller effect sizes. Knowing the true population means and covariances or the parameter values in structural equation models may not make things easier either.

Bayesian predictive inference under informative sampling and transformation

AbstractWe consider the problem in which a biased sample is selected from a finite population (a random sample from a super‐population), and inference is required for the finite population mean and the super‐population mean. The selection probabilities are linearly related to the measurements, providing a non‐ignorable selection model. When all the selection probabilities are known, as in our problem, inference about the finite population mean and the super‐population mean can be made. As a practical issue, our method requires normality, but the measurements are not necessarily normally distributed. Thus, the key issue is the dilemma that a transformation to normality is needed, but this transformation will destroy the linearity between the selection probabilities and the measurements. This is the key issue we address in this work. We use the Gibbs sampler and the sample importance resampling algorithm to fit the non‐ignorable selection model to a simple example on natural gas production. Our non‐ignorable selection model estimates the finite population mean production much closer to the true finite population mean than a model which ignores the selection probabilities, and there is improved precision of the non‐ignorable selection model over this latter model. A naive 95% credible interval based on the Horvitz–Thompson estimator is too wide. Copyright © 2006 John Wiley &amp; Sons, Ltd.