Sample Standard Error Research Articles

Meta-analysis of 2-treatment clinical trials including both continuous and dichotomous results.

To expedite the timely creation of medical practice guidelines, a meta-analytic method was developed to combine both dichotomous survival data and continuous physiologic data from multiple studies of differing experimental design, which compare the same innovative clinical intervention to standard care. An aggregate ratio, R*, of the observed treatment effect to a clinically optimal treatment effect for studies in a series is computed and compared to the 95% confidence limit for R* under the null hypothesis. Input data for continuous variables include sample means, standard errors, and sample sizes. Input data for dichotomous variables include group proportions and sizes. The analysis can be done using a simple, 1-page spreadsheet. It allows one to judge biological significance, to test for statistical significance, to compare subgroups of studies, to test for outliers, and to compute the power of the meta-analysis. These features are demonstrated for studies of interposed abdominal compression-cardiopulmonary resuscitation.

Estimating Asset Class Standard Deviations and Correlations

The authors present a robust method for estimating the asset class covariance matrix for use in a mean variance optimizer. The article is based on the work of Ledoit [1997] who proposes a technique for combining the sample covariance matrix with the single index covariance matrix to yield an estimate that has a lower out of sample standard error than does either of the two inputs when used alone. Using data from 1990 through 2001, the authors apply this methodology, with a few of additional modifications, to the AMG Guaranty Trust N.A. universe and present covariance, correlation, and standard deviation estimates.

Kappa statistics in the assessment of observer variation: the significance of multiple observers classifying ankle fractures

Studies using kappa statistics have been conducted with a varied but limited number of observers. The aim of this study was to evaluate the significance of multiple observers on kappa as a measure of observer variation. One hundred orthopedic specialists were asked to assess a random sample of ten sets of standard radiographs of 94 consecutive patients with ankle fractures. The observers were randomly allocated into four groups, which again were divided into subgroups with an increasing number of observers. Random subgroups of three observers revealed kappa values from 0.20 to 0.64 in the Lauge-Hansen and 0.27 to 0.90 in the Weber classification system. With an increasing number of observers in the subgroups, kappa stabilizes around a mean value, indicating that the sampling variation and standard error decrease. The standard error found in this study makes kappa questionable as a measure for agreement among a small number of observers. Thus, kappa values obtained for a given diagnostic tool at one department are not directly comparable with results from other departments. We conclude that kappa cannot stand alone as a simple measure of observer variation.

Multidimensional Item Response Theory Modeling of Binary Data: Large Sample Properties of NOHARM Estimates

NOHARM is a program that performs factor analysis for dichotomous variables assuming that these arise from an underlying multinormal distribution. Parameter estimates are obtained by minimizing an unweighted least squares function of the first- and second-order marginal proportions. Here, large sample standard errors for restricted as well as rotated unrestricted factor solutions are given. Also a test of the goodness of fit of the model to the first- and second-order marginals of the contingency table is proposed. In a simulation study, it was found that for small models, accurate parameter estimates, standard errors, and goodness-of-fit tests can be obtained with as few as 100 observations. Furthermore, NOHARM estimates, standard errors, and goodness-of-fit tests are comparable to those obtained using a related LISREL procedure.

The intracluster gas fraction in X-ray clusters: constraints on the clustered mass density

The mean intracluster gas fraction of X-ray clusters within their hydrostatic regions is derived from recent observational compilations of David, Jones & Forman and White & Fabian. At radii encompassing a mean density 500 times the critical value, the individual sample bi-weight means are moderately ($2.4 \sigma$) discrepant; revising binding masses with a virial relation calibrated by numerical simulations removes the discrepancy and results in a combined sample mean and standard error $\fbargas(r_{500}) = (0.060 \pm 0.003) \h^{-3/2}$. For hierarchical clustering models with an extreme physical assumption to maximize cluster gas content, this value constrains the universal ratio of total, clustered to baryonic mass $\Omega_m/\Omega_b \le 23.1 \h^{3/2}$; combining with the primordial nucleosynthesis upper limit on $\Omega_b$ results in $\Omega_m \h^{1/2} < 0.60$. A less conservative, physically plausible approach based on low D/H inferences from quasar absorption spectra and accounting for baryons within cluster galaxies yields an estimate $\Omega_m \h^{2/3} = 0.28 \pm 0.07$ with sources of systematic error involved in the derivation providing approximately $35%$ uncertainty. Additional effects which could provide consistency with the Einstein-deSitter case $\Omega_m \se 1$ are presented, and their observable signatures discussed.

Estimating standard errors of accuracy assessment statistics under cluster sampling

Cluster sampling is a viable sampling design for collecting reference data for the purpose of conducting an accuracy assessment of land-cover classifications obtained from remotely sensed data. The formulas for estimating various accuracy parameters such as the overall proportion of pixels correctly classified, the kappa coefficient of agreement, and user's and producer's accuracy are the same under cluster sampling and simple random sampling, but the formulas for estimating standard errors differ between the two designs. If standard error formulas appropriate for cluster sampling are not employed in an accuracy assessment based on this design, the reported variability of map accuracy statistics is likely to be grossly misleading. The proper standard error formulas for common map accuracy statistics are derived for one-stage cluster sampling. The validity of these standard error formulas is verified by a small simulation study, and the standard errors computed according to the usual simple random sampling formulas are shown to underestimate the true cluster sampling standard errors by 20–70% if the intracluster correlation is moderate.

An Analysis of Sampling Errors for the Demographic and Health Surveys

"Sampling errors and design effects from 48 nationally representative surveys conducted under the Demographic and Health Surveys Program for a large number of variables concerning fertility, family planning, fertility intentions, child health and mortality etc. are analysed for the total sample, and for urban-rural domains, sub-national regions and various demographic and socio-economic subclasses.... At the country level, overall design effect (the ratio of actual to simple random sampling standard error) averaged over all variables and countries is around 1.5. Variation among countries is high, but less so than among variables. Urban-rural and regional differentials in design effects are small, and can be attributed to the fact that similar sample designs and cluster sizes were used across those domains within each country. Design effects for estimates over other subclasses are smaller, and tend towards 1.0 for small subclasses and differences, apart from the effect of sample weights which tends to persist undiminished across variables and subclasses." (SUMMARY IN FRE)

Difficulties with the lognormal model in mean estimation and testing

A frequent assumption in environmental risk assessment is that the underlying distribution of an analyte concentration is lognormal. However, the distribution of a random variable whose log has a t-distribution has infinite mean. Because of the proximity of the standard normal and t-distribution, this suggests that a distribution such as the gamma or truncated normal, with smaller right tail probabilities, might make a better statistical model for mean estimation than the lognormal. In order to assess the effect of departures from lognormality on lognormal-based statistics, we simulated complete lognormal, truncated normal, and gamma data for various sample sizes and coefficients of variation. In these cases, departures from lognormality were not easily detected with the Shapiro-Wilk test. Various lognormal-based estimates and tests were compared with alternate methods based on the ordinary sample mean and standard error. The examples were also considered in the presence of random left censoring with the mean and standard error of the product limit estimate replacing the ordinary sample mean and standard error. The results suggest that in the estimation of or tests about a mean, if the assumption of lognormality is at all suspect, then lognormal-based approaches may not be as good as the alternative methods.

MIXED MODELS APPROACH TO ON-FARM TRIALS: AN ALTERNATIVE TO META-ANALYSIS FOR COMPARING ONE TREATMENT TO POSSIBLY DIFFERENT CONTROLS

The estimator of effect size, the sample mean difference divided by the sample standard error of the difference is studied in the context of mixed models and is related to the analysis of on-farm trials. A single treatment is compared against possibly different controls using a completely randomized design on each farm. A lower (1-α)100% confidence limit on mean difference of the treatment and the average control is obtained. The best linear unbiased predictors (BLUPs) of the mean difference of the treatment and the individual controls as well as the lower (1-α)100% prediction limits are provided. The effect of omitting or not omitting the farm-by-treatment interaction variance component in the weighting process is assessed using two numerical examples.

Sampling precision of plantation inventory in South Australia

Plantation inventory in South Australia is a continuing, stratified random sample by 0.1 ha plots. The inventory covers all areas that have already received at least one commercial production thinning and also some unthinned areas. Stratification is by age, site quality strata and sometimes stocking level. Similar strata are grouped into units for logging operations. This paper demonstrates that, based on the inventory currently practiced, the estimate of the volume expected to be cut in any particular year has a sampling standard error of less than 5%.

Effect Size Standard Errors for the Non-Normal Non-Identically Distributed Case

Suppose there are k independent studies and for each study the experimental and control groups have been sampled from independent but essentially arbitrary populations. The problem is to construct a plausible standard error of the effect size mean (effect sizes are standardized experimental-control group mean differences) when given only minimal sample statistic information. Standard errors based on the sample standard error, or bootstrap, will typically be much too large and have very large variance. A normal theory estimator may prove practically useful in more general settings. Asymptotic distribution-free estimators are provided for two cases.

Standard Errors of Tucker Equating

Large sample standard errors are derived for the Tucker linear test score equating method under the common item nonequivalent populations design. Stan dard errors are derived without the normality assump tion that is commonly made in the derivation of stan dard errors of linear equating. The behavior of the standard errors is studied using a computer simulation and a real data example. In the simulation, the derived standard errors were reasonably accurate. In the real data example, the derived standard errors agreed closely with standard errors estimated using Efron's (1982) bootstrap.

Measuring pairwise interobserver agreement when all subjects are judged by the same observers

Abstract An experiment is considered where each of a sample of subjects is rated on an L‐point scale by each of a fixed group of observers. Weighted kappa coefficients are defined to measure the degree of agreement among the observers, between two particular observers, or between a particular observer and the other observers. Attention is paid to the selection of one or more homogeneous subgroups of observers. A linearized Taylor series expansion is used to derive explicit formulas for the computation of large sample standard errors. The procedures are illustrated within the context of a study where seven pathologists separately classified 118 histological slides into five categories.

Linear structural equations with latent variables

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.

Microtest plates as a source of error in mixed lymphocyte cultures

We have determined that microtest plates supplied by 4 manufacturers are not equal in their support of lymphocyte stimulation in mixed lymphocyte cultures. Using lymphocytes isolated from the peripheral blood of normal donors by sedimentation and cotton column purification, we have found that Costar Tissue Culture Cluster plates and Nunclon-Delta Microtest plates consistently allowed the highest lymphocyte stimulation levels and the lowest sample standard errors. Falcon Microtest II plates, on the other hand, were lowest in terms of lymphocyte stimulation, and clearly produced the greatest sample standard error. When normal lymphocytes were isolated for culture using Ficoll-Hypaque gradients, Linbro Tissue Culture Multiwell plates tested superior in terms of lymphocyte stimulation, and equal to the others in sample standard error. It is hypothesized that the selection of an inappropriate microtest plate will introduce unacceptable error in human mixed lymphocyte cultures.

Measuring pairwise agreement among many observers

AbstractWeighted kappa is defined as a measure of pairwise inter observer agreement. A weighted intra class kappa coefficient is proposed to measure agreement on a particular response category. An interclass kappa coefficient is proposed for each pair of response categories. Simple estimation procedures are presented for the case where the observers judging one subject are not necessarily the same as those judging another subject. Large sample standard errors are derived and a numerical example is given.

Inference About Weighted Kappa in the Non-Null Case

The accuracy of the large sample standard error of weighted kappa appropriate to the non-null case was studied by computer simulation. Results indi cate that only moderate sample sizes are required to test the hypothesis that two independently de rived estimates of weighted kappa are equal. How ever, in most instances the minimal sample sizes re quired for setting confidence limits around a single value of weighted kappa are inordinately large. An alternative, but as yet untested procedure for set ting confidence limits, is suggested as being poten tially more accurate.

Large Sample Confidence Limits for Goodman and Kruskal's Proportional Prediction Measure Taub

Goodman and Kruskal's tb test statistic is frequently employed in measuring association between nominally-scaled polynomies. Because of an error in the published large sample standard error, the utility of tb has been severely circumscribed for many years. A recent published correction of the large sample standard error promises to increase its use. This paper describes a Fortran Extended computer program which computes tb, with column variable dependent, and its asymmetrical counterpart ta, with row variable dependent. The program also provides three sets of confidence limits for each coefficient under both full multinomial and proportional stratified sampling.

Trends and deviations in the yield of the English wheat crop during the last 750 years

The yield of wheat in England has increased more than six-fold during the last 750 years, from 0.5 tonne/ha in the first half of the 13th century to 3.4 tonne/ha in the third quarter of the 20th century. Present yields are nearly 4.5 tonne/ha/year representing a nine-fold increase from beginning to end of the period. Over this period the trend is best represented by a parabolic equation relating the logarithm of yield to year, which accounts for some 95% of the yield variation with time. Deviations of individual yearly yield from the long term trend are represented by a sample standard error of 0.25 tonne/ha. More than three quarters of the increase has occurred in the last 300 years when yields rose almost exponentially, doubling every 150 years. However, most of the increase was in two comparatively short periods, 1820–1860 and post-Second World War. In the last 30 years the national wheat yield has increased at 0.079 tonne/ha/year, twice as fast as in the accelerating phase of the previous century. Data on the short-term annual deviations from the long-term trends indicate that they are approximately proportional to the general yield level. After removing the long-term trend, the coefficient of variation is some 7% of the mean national yield.

Large sample standard errors of kappa and weighted kappa.

The statistics kappa (Cohen, 1960) and weighted kappa (Cohen, 1968) were introduced to provide coefficients of agreement between two raters for nominal scales. Kappa is appropriate when all disagreements may be considered equally serious, and weighted kappa is appropriate when the relative seriousness of the different possible disagreements can be specified. The papers describing these two statistics also present expressions for their standard errors. These expressions are incorrect, having been derived from the contradictory assumptions of fixed marginal totals and binomial variation of cell frequencies. Everitt (1968) derived the exact variances of weighted and unweighted kappa when the parameters are zero by assuming a generalized hypergeometric distribution. He found these expressions to be far too complicated for routine use, and offered, as alternatives, expressions derived by assuming binomial distributions. These alternative expressions are incorrect, essentially for the same reason as above. Assume that N subjects are distributed into k* cells by each of them being assigned to one of k categories by one rater and, independently, to one of the same k categories by a second