Nominal Error Research Articles

Using Priors to Improve Multiple Animal Carcinogenicity Tests

This article reviews and summarizes methods for controlling false positives in animal carcinogenicity studies and promotes an alternative that incorporates historical control information via Bayesian methods. The Bayesian paradigm is used as a procedure generator; however, frequentist multisample, age-stratified exact trend tests are used in the ultimate analysis. Critical values for the exact tests are chosen to maximize total expected power, conditional on tumor totals, by using prior distributions. To control the risk of a false-positive finding for one or more tumor types, the sum of the individual critical levels is constrained to be less than a nominal familywise error rate, such as .05. The resulting tests give more power to tumor types with higher-than-expected tumor totals. We use historical control data from animal carcinogenicity studies obtained from a large pharmaceutical company to train and evaluate the tests. There is greatly enhanced power of the proposed method, with concurrent error rate control, because the targeting procedure gives higher power to affected sites, and the procedure tends to produce critical values that are as small as possible overall (implying higher power), subject to the overall risk level constraint. Randomly sampling from real historical animal populations, we compare operating characteristics of various methods proposed in the literature and requested by regulatory agencies. Commonly used methods can have greatly inflated false-positive rates, particularly with larger studies. In some cases, we find greater power for the proposed method, even compared to methods that do not control false positives.

On the minimum expected quantity for the validity of the chi-squared test in 2 2 2 tables

A 2 2 2 contingency table can often be analysed in an exact fashion by using Fisher's exact test and in an approximate fashion by using the chi-squared test with Yates' continuity correction, and it is traditionally held that the approximation is valid when the minimum expected quantity E is E S 5. Unfortunately, little research has been carried out into this belief, other than that it is necessary to establish a bound E>E*, that the condition E S 5 may not be the most appropriate (Martín Andrés et al., 1992) and that E* is not a constant, but usually increasing with the growth of the sample size (Martín Andrés & Herranz Tejedor, 1997). In this paper, the authors conduct a theoretical experimental study from which they ascertain that E* value (which is very variable and frequently quite a lot greater than 5) is strongly related to the magnitude of the skewness of the underlying hypergeometric distribution, and that bounding the skewness is equivalent to bounding E (which is the best control procedure). The study enables estimating the expression for the above-mentioned E* (which in turn depends on the number of tails in the test, the alpha error used, the total sample size, and the minimum marginal imbalance) to be estimated. Also the authors show that E* increases generally with the sample size and with the marginal imbalance, although it does reach a maximum. Some general and very conservative validity conditions are E S 35.53 (one-tailed test) and E S 7.45 (two-tailed test) for alpha nominal errors in 1% h f h 10%. The traditional condition E S 5 is only valid when the samples are small and one of the marginals is very balanced; alternatively, the condition E S 5.5 is valid for small samples or a very balanced marginal. Finally, it is proved that the chi-squared test is always valid in tables where both marginals are balanced, and that the maximum skewness permitted is related to the maximum value of the bound E*, to its value for tables with at least one balanced marginal and to the minimum value that those marginals must have (in non-balanced tables) for the chi-squared test to be valid.

Improved digital tachometer with reduced sensitivity to sensor nonideality

A constant sample-time digital tachometer, similar to Ohmae's "M/T" method, is described. This system is capable of accurate determination of shaft velocity, based on the outputs of an incremental encoder. Previous error analyses of such devices which consider only the asynchronous nature of counter operation are shown to be specious. It is highlighted that sensor nonidealities, including variations in the transition locations from their nominal values and phasing errors between encoder channels, can produce much larger tachometer errors. An estimate is made of the actual RMS output error, based on a simple encoder model and simplified analysis. It is shown that the error can be significantly reduced by operating four sub-circuits in parallel, each dealing with either a low-to-high or high-to-low transition of a single incremental encoder signal. A field-programmable-gate-array/digital-signal processor-based practical implementation is described. Both simulation and experimental results are presented which confirm the utility of the enhanced digital tachometer.

Performance enhancement on the basis of identified model uncertainty sets with application to a CD mechanism

We address the design of robust feedback controllers based on nominal models and model error bounds that are obtained from measurement data. In order to keep controller complexity limited an approach is adopted where controller synthesis is performed on the basis of a low order (approximate) nominal model; prior to controller implementation the robust performance of the controller is evaluated based on a (highly accurate) system uncertainty set employing a dual Youla uncertainty structure. The procedure is based on an iterative scheme of identification and control design and is experimentally verified on the radial tracking control of a Compact Disc mechanism.

A goodness-of-fit test for capture-recapture model Mt under closure.

A new, fully efficient goodness-of-fit test for the time-specific closed-population capture-recapture model Mt is presented. This test is based on the residual distribution of the capture history data given the maximum likelihood parameter estimates under model Mt, is partitioned into informative components, and is based on chi-square statistics. Comparison of this test with Leslie's test (Leslie, 1958, Journal of Animal Ecology 27, 84-86) for model Mt, using Monte Carlo simulations, shows the new test generally outperforms Leslie's test. The new test is frequently computable when Leslie's test is not, has Type I error rates that are closer to nominal error rates than Leslie's test, and is sensitive to behavioral variation and heterogeneity in capture probabilities. Leslie's test is not sensitive to behavioral variation in capture probabilities but, when computable, has greater power to detect heterogeneity than the new test.

Asset Market and Balance of Payments Characteristics: An Eclectic Exchange Rate Model for the Dollar, Mark and Yen

In this paper we use an exchange rate model, which combines asset market characteristics with balance of payments interactions, to examine the nominal effective exchange rates of the German mark, Japanese yen and US dollar for the recent experience with floating exchange rates. Our approach may be interpreted as one which attempts to flesh out the missing links that arise in conditioning an exchange rate solely on relative prices, as occurs in a standard PPP analysis. Amongst the results reported in this paper are: significant, and sensible, long-run relationships for the currencies studied; complex short-run dynamics; a variance decomposition analysis which apportions nominal exchange rate error variances into real and nominal elements.

Mechanical Behaviors of Bolted Joint in Various Clamping Configurations

In a bolted joint, failures usually initiate at the first root of the bolt thread. However, rupture around the bolt head is sometimes reported for a tap bolt because of high stresses produced by tightening torque applied to the bolt head. It is also well known that manufacturing errors of internal threads in a tapped hole are generally much larger than those of external threads, thus leading to the failures concerned. In this paper, mechanical behaviors of bolted joints in various clamping configurations are analyzed using FEM as multi-body elastic contact problem, and the effects of nominal diameter, friction and pitch error upon stress concentrations are evaluated for through bolts, studs, and tap bolts. It is then quantitatively estimated on the effectiveness of “recessed internal threads” for reducing the stress concentration occurred around the far end of bolt hole. In addition, the tightening process and strength of a bottoming stud, which have seldom been studied despite favorable performance in preventing stress concentration at the runout of threads, are also investigated.

Calibration of the Lenth Test for Unreplicated Factorial Designs

The Lenth test is a simple procedure to test for significant factorial effects in unreplicated 2k factorial experiments. Estimated factorial effects are standardized and compared to critical values from a t distribution with (2k − 1)/3 degrees of freedom. However, the procedure does not maintain its nominal Type I error rates in small experiments. This article presents a simulation study in which the Lenth procedure error rates are found for several common values of k under numerous specified nominal error rates. This procedure is then calibrated and critical values are revised to produce a variety of common Type I error rates.

Model Set Determination and its Application to the Control of Compact Disc Players

This paper deals with the problem of obtaining a plant nominal model and its error uncertainty bound when a batch of plant models is provided. While the selection of model set structure is essential and probably depends on the model intended application, in this paper it is assumed that a nominal model is perturbed by its error through a homographic transformation. A necessary and sufficient condition is obtained for a nominal model to be suboptimal. Moreover, an algorithm is proposed to obtain a nominal model which is suboptimal and has a low complexity. Furthermore, the extraction of structured nominal model errors is discussed. The efficiency of the proposed model set determination algorithm is verified through the application to the simultaneous spiral control of two compact disc players.

Detecting Overdispersion in Large Scale Surveys: Application to a Study of Education and Social Class in Britain (with Comments)

SUMMARY A practical problem with large scale survey data is the potential for overdispersion. Overdispersion occurs when the data display more variability than is predicted by the variance–mean relationship for the assumed sampling model. This paper describes a simple strategy for detecting and adjusting for overdispersion in large scale survey data. The method is primarily motivated by data on the relationship between social class and educational attainment obtained from a 2% sample from the 1991 census of the population of Great Britain. Overdispersion can be detected by first grouping the data into a number of strata of approximately equal size. Under the assumption that the observations are independent and there is no variability in the parameter of interest, there is a direct relationship between the nominal standard errors and the empirical or sample standard deviation of the parameter estimates obtained from each of the separate strata. With the 2% sample from the British census data, quite a discernible departure from this relationship was found, indicating overdispersion. After allowing for overdispersion, improved and more realistic measures of precision of the strength of the social class–education associations were obtained.

Development and Validation of a Binomial Sequential Sampling Plan for Striped Cucumber Beetle (Coleoptera: Chrysomelidae) in Cucurbits

Adult striped cucumber beetles, Acalymma vittatum (F.), were sampled in 20 fields during 1994-1995 in southern Minnesota. Data in both years were collected using a fixed sample unit of 7 consecutive plants within a row and a fixed sample size of 48. Sample units of 1 through 7 plants were separated out from each data set, and data sets for each sample unit of 1, 2, 3,... 7 plants each, were used for analysis. The sampling plan was analyzed and validated using resampling software, Resampling validation for sampling plans, which uses the Wald sequential probability ratio test to develop a binomial sampling plan. Based on actual a (type I) and β (type II) error rates derived from the resampling analysis of 32-36 data sets, the optimum sample unit was determined to be 2 consecutive plants. Specifying nominal error rates of α = β = 0.10, with a tally threshold = 2 and an action threshold = 0.25, the sample plan required an average of 14, 2-plant sample units per field. Actual α and β error rates were 0.05 and 0.08, respectively. Analysis of the average sample number function indicated that a maximum of 29 samples would be required to classify A. vittatum populations near the action threshold of 0.25 proportion of samples infested with a tally threshold = 2. Binomial sampling plans should provide an efficient sampling program for use in managing A. vittatum infestations in cucurbits with minimal sampling costs.

Model uncertainty in frequency response based system identification

Determination of plant nominal model error bound is one of the most essential topics in robust control oriented identification. The objective of this paper is to investigate the structure of plant model uncertainties when a set of corrupted plant frequency response samples are supplied. It is shown that the plant model uncertainties, which result from the “partialness” and “corruptedness” of the provided plant information, can be represented by structure-fixed, norm-bounded but uncertain matrix-valued functions that perturb a plant nominal model through a linear fractional transformation. These results are very similar to those when plant time domain identification experiment data have been provided.

Sampling Whiteflies in Cotton: Validation and Analysis of Enumerative and Binomial Plans

We tested enumerative and binomial sampling plans developed for Bemisia tabaci (Gennadius) in 3,240 ha of commercial cotton as part of the implementation of a community-wide integrated pest management (IPM) program in Laveen and Tolleson, AZ, in 1994. We compared new field observations to sampling distribution models developed previously for all lifestages, and validated and analyzed die performance of 5 sampling plans based on these models by resampling field data from 129 to 284 sites. Mean–variance relationships for the new data differed statistically from mean-variance models previously developed for adults, but not for eggs or nymphs. Resampling analyses indicated that desired precision (SE to mean ratio) was rarely achieved, on average, by fixed-precision sequential sampling plans. These enumerative sampling plans provided better precision than desired at moderate to high densities of eggs and adults and worse precision than desired at most densities of nymphs. An empirical model relating mean density to the proportion of leaves infested with 3 or more adult B. tabaci was accurate at mean densities < 2 adults per leaf but over-predicted mean density at higher densities. Resampling analysis revealed that a sequential sampling plan based on this empirical model was accurate at classifying population density relative to an action threshold of 5 adults per leaf. At nominal α and β error rates of 0.10, population density was correctly classified ≍87% of the time. Accuracy was not improved by reducing nominal error rates to 0.05. Resampling analysis of a fixed-sample size plan based on n = 30 gave similar results and increasing sample size to 50 increased accuracy only 3%. Further resampling analyses that more closely approximated scouting protocols (15 sample units drawn from each of 2 quadrants in die field) resulted in an average accuracy of ≍70%. Accuracy declined when populations densities differed greatly among quadrants in a field. Most of this error was associated with making a decision to control when pest density was below the action threshold. Based on a robust validation technique using field observations representing a wide range of environmental and agronomic conditions, our sampling plans performed well and should be useful for estimating and classifying population densities of B. tabaci in cotton over a wide area.

A Monte Carlo study of Type I error rates for the two-sample Behrens-Fisher problem with and without rank transformation

This paper presents empirical Type I error rates when σ 1 2 ≠ σ 2 2 for the Student “pooled variance” t-test (ST), the Aspin-Welch “separate variance” t-test (AW), the Wilcoxon rank sum test (WX), and ST and AW computed on rank transformed (RT-1) data (STRK and AWRK, respectively). Eighteen different situations were simulated from two N(μ, σ 2) populations such that μ 1 = μ 2, σ 1 2 σ 2 2 = { 1 10 , 1 2 } , and n 1 n 2 = { 1 2 , 1, 2} for “small” {5, 10}, “moderate” {20, 40}, and “large” {50, 100} samples. When σ 1 2 σ 2 2 = 1 10 and n 1 ≠ n 2, ST exhibits the most severe deviations from nominal levels α = 0.05, 0.01, with conservative error rates for n 1 n 2 = 1 2 and inflated error rates for n 1 n 2 = 2 . STRK performs notably better than ST, as does WX, but neither ST nor WX maintains nominal error levels. AW is generally the best test to use. AWRK rejects H 0 more often than AW. For moderate sample sizes, AWRK is preferred over AW when n 1 n 2 = 2 , but its error rates are inflated when n 1 n 2 = 1 2 . When n 1 = n 2, ST and AW are most reasonable to use for moderate and large sample sizes; the tests based on ranks are not. When σ 1 2 σ 2 2 = 1 2 , the observed error rates differ less from nominal rates. The test(s) which maintain or approach nominal levels, the directions of the deviations from nominal levels, and the relative rankings of the tests' performances are not always consistent with those for σ 1 2 σ 2 2 = 1 10 , and differences between tests are less consistent.

USING RANKS TO PERFORM EXACT AND ESTIMATED EXACT TESTS IN DESIGNED EXPERIMENTS

A procedure is studied that uses rank transformed data to perform exact and estimated exact tests which is an alternative to the commonly used F-ratio test procedure. First, a common parametric test statistic is computed using rank transformed data, where two methods of ranking - ranks taken of the original observations, and ranks taken after aligning the observations - are studied. Significance is then determined using either the exact permutation distribution of the statistic or an estimate of this distribution based on a random sample of all possible permutations. Simulation studies compare the performance of this method to both the normal theory parametric F-test and the traditional rank transform procedure. Power and nominal type-I error rates are compared under conditions when normal theory assumptions are satisfied as well as when these assumptions are violated. The method is studied for a two factor factorial arrangement of treatments in a completely randomized design and also for a split-unit experiment.

On the thermal electron energy balance in the ionosphere in January 1993 and June 1990

This paper examines the electron energy balance in the F region of the ionosphere at Millstone Hill in January 1993 by comparing model electron temperatures with measurements from the incoherent scatter radar. Initial modeling indicated three problem areas for the electron temperature at the height of the peak electron density. First, the nighttime temperature was much too low. Second, the afternoon temperature was a little lower than the measured temperature. Third, the model temperature was too high in the morning just after sunrise. A new algorithm is presented for using the measured topside electron temperature to determine the amount of plasmaspheric heating. It was found that the plasmaspheric heating from photoelectrons escaping the ionosphere must be doubled in order for the model to reproduce the observed topside temperature. With this increased plasmaspheric heat flux, the model temperature at the peak height was also much closer to the measured temperature at night. The low temperature in the afternoon could be easily explained by nominal errors in the model inputs or the radar measurements, but the high model temperatures in the morning remain unexplained. Examination of the cooling rates showed that ion cooling is the main cooling rate and is clearly dominant in the afternoon, while O fine structure cooling is equally important in the morning and at night in January 1993. In order to provide a reference, model‐data comparisons were also for June 1990. In this case the agreement between model and data was excellent at all times without the need to adjust local heating and cooling rates. For these summer conditions, vibrationally excited N2 and ion cooling were the two main cooling mechanisms. As was the case in January 1993, doubling of the plasmaspheric heating rate was also needed for the model to match the topside electron temperatures in June 1990. The daytime peak plasmaspheric heat flow deduced from the topside electron temperature showed little variation between June 1990 and January 1993 despite the different seasons and levels of solar activity.

Least-Squares Fitting A Smooth Curve to Radiocarbon Calibration Data

We Fourier transformed and filtered calibration curve data to compensate for the averaging effect of radiocarbon-dating sets of adjacent tree rings. A Wiener Filter was also applied to minimize the effects of the counting errors of the dates on the resulting calibration curve and to produce a least-squares curve through the data. The method is illustrated using a short 14C-dated tree-ring sequence from New Zealand to produce a calibration curve at yearly intervals for New Zealand matai (Prumnopitys taxifolia). The resulting curve has a nominal standard error of 10 ± 3 yr, which is ca. half the average standard error of the original raw data.

Consequences of [ITAL]H[/ITAL][TINF]0[/TINF] = 69 ± 8 km s[TSUP]−1[/TSUP] Mpc[TSUP]−1[/TSUP] from Cepheid Variables in the Leo I Group

We examine the consequences of the value of H0 = 69 ? 8 km s-1 Mpc-1 by Tanvir et al., which is based on the HST Cepheid observation of M96 in Leo I group and smaller by 10%-15% than those derived from surface brightness fluctuation method (SBF), planetary nebulae luminosity function method (PNLF), and Tully-Fisher relation. If we take the HST Cepheid distance of M96 as the correct distance of the Leo I group, there are discrepancies beyond the nominal error in the distance of the Leo I and the Virgo cluster among SBF, PNLF, Tully-Fisher relation, and Cepheids. We argue that the zero-point error of 10%-15% level in the SBF and PNLF distances is the most probable cause of the discrepancy.

Permutation Tests for Least Absolute Deviation Regression

A permutation test based on proportionate reduction in sums of absolute deviations when passing from reduced to full parameter models is developed for testing hypotheses about least absolute deviation (LAD) estimates of conditional medians in linear regression models. Sampling simulations demonstrated that the permutation test on full model LAD estimates had greater relative power (1.06-1.43) than normal theory tests on least squares estimates for asymmetric, chi-square error distributions and symmetric, double exponential error distributions for models with one (n = 35 and n = 63) and three (n 63) independent variables. Relative power was .77 -.84 for normal error distributions. Power simulations demonstrated the low sensitivity of LAD estimates and permutation tests to outlier contamination and heteroscedasticity that was a linear function of X, and increased sensitivity to heteroscedasticity that was a function of X2 for simple regression models. Three permutation procedures for testing partial models in multiple regression were compared: permuting residuals from the reduced model, permuting residuals from the full model, and permuting the dependent variable. Permuting residuals from the reduced model maintained nominal error rates best under the null hypothesis for all error distributions and for correlated and uncorrelated independent variables. Power under the alternative hypotheses for this partial testing procedure was similar to full LAD regression model tests. Four example applications of LAD regression are provided.

Binomial sampling plans for estimating and classifying population density of adult Bemisia tabaci in cotton

AbstractWe used an empirical relationship to develop models for estimating and for classifying the population density of adult Bemisia tabaci (Gennadius) (Homoptera: Aleyrodidae) in cotton based on the proportion of infested leaves. We examined models based on tally thresholds (the minimum number of insects present before a leaf is considered infested) of 1, 2, 3, 4, 5, and 6 adults per fifth mainstem node leaf from the terminal. For the estimation of density, sampling precision (SE/mean) increased with higher tally thresholds (T); however, there was negligible improvement in precision with T ≥ 3 adults per leaf. Using T = 3 as few as 30 samples were necessary to achieve a precision of 0.25 over a wide range of population densities. To evaluate these binomial models for the classification of population density for pest management application, we used simulation analyses to determine operating characteristic curves (error probabilities), and to estimate average sample size and cost functions. Error probabilities and average sample sizes declined with higher values of T, but there was negligible decline in error probabilities using T ≥ 3 adults per leaf, and the overall cost of sampling was lowest for T = 3. Wald's sequential probability ratio test was used to formulate sequential sampling stop lines for classifying population density relative to two nominal action thresholds, 5 or 10 adults per leaf. Simulation analysis indicated that by using T = 3, fewer than 30 samples, on average, were needed to classify populations relative to either action threshold. However, simulated error probabilities consistently exceeded the nominal error probabilities used to initially formulate sequential sampling stop lines regardless of the tally threshold. Comparing binomial models using T = 1 or T = 3 to independent data from four field sites, the model for T = 1 was generally biased towards overprediction of mean density, but the T = 3 model was a robust and relatively unbiased predictor of mean density. The binomial sampling plans presented here should permit the rapid estimation of population density and enhance the efficiency of pest management programs based on the prescriptive suppression of B. tabaci in cotton.