Showing papers on "Sample size determination published in 1993"

Simulation Study of Confounder-Selection Strategies

Abstract: In the absence of prior knowledge about population relations, investigators frequently employ a strategy that uses the data to help them decide whether to adjust for a variable. The authors compared the performance of several such strategies for fitting multiplicative Poisson regression models to cohort data: 1) the "change-in-estimate" strategy, in which a variable is controlled if the adjusted and unadjusted estimates differ by some important amount; 2) the "significance-test-of-the-covariate" strategy, in which a variable is controlled if its coefficient is significantly different from zero at some predetermined significance level; 3) the "significance-test-of-the-difference" strategy, which tests the difference between the adjusted and unadjusted exposure coefficients; 4) the "equivalence-test-of-the-difference" strategy, which significance-tests the equivalence of the adjusted and unadjusted exposure coefficients; and 5) a hybrid strategy that takes a weighted average of adjusted and unadjusted estimates. Data were generated from 8,100 population structures at each of several sample sizes. The performance of the different strategies was evaluated by computing bias, mean squared error, and coverage rates of confidence intervals. At least one variation of each strategy that was examined performed acceptably. The change-in-estimate and equivalence-test-of-the-difference strategies performed best when the cut-point for deciding whether crude and adjusted estimates differed by an important amount was set to a low value (10%). The significance test strategies performed best when the alpha level was set to much higher than conventional levels (0.20).

Biostatistics: A Methodology for the Health Sciences

Abstract: Partial table of contents: Biostatistical Design of Medical Studies. Descriptive Statistics. Statistical Inference: Populations and Samples. Counting Data. Categorical Data: Contingency Tables. Nonparametric, Distribution-Free and Permutation Models: Robust Procedures. Analysis of Variance. Association and Prediction: Multiple Regression Analysis, Linear Models with Multiple Predictor Variables. Multiple Comparisons. Discrimination and Classification. Rates and Proportions. Analysis of the Time to an Event: Survival Analysis. Sample Sizes for Observational Studies. A Personal Postscript. Appendix. Indexes.

Standard Errors and Sample Sizes for Two-Level Research:

Abstract: The hierarchical linear model approach to a two-level design is considered, some variables at the lower level having fixed and others having random regression coefficients. An approximation is derived to the covariance matrix of the estimators of the fixed regression coefficients (for variables at the lower and the higher level) under the assumption that the sample sizes at either level are large enough. This covariance matrix is expressed as a function of parameters occurring in the model. If a research planner can make a reasonable guess as to these parameters, this approximation can be used as a guide to the choice of sample sizes at either level.

The Effect of Sample Size on Estimated Limits for and X Control Charts

Abstract: The results of this study indicate that charts with subgroups of size n require about 400/(n-1) samples, and X charts require about 300 values to estimate control limits that perform like known limits. The results also indicate that using estimated con..

Two Programs to Estimate Significance of χ2 Values Using Pseudo-Probability Tests

Abstract: where o, and e, are observed and expected (under the null hypothesis) numbers of the fth category (see any textbook on biometry or population genetics, e.g., Ayala and Kiger 1984; Sokal and Rohlf 1981). An unfortunate requirement of the test is that the expected numbers (e,) should not be small. Different authors give different recommendations; common opinion is that e, should not be less than 4 (see cited books). Introduction into population genetics of molecular techniques revealed a great wealth of genetic variation—allozymic, DNA restriction fragment length polymorphisms, etc.—in both plants and animals. Hence, samples of practical size (say, hundreds of individuals) will very often contain rare phenotypic or allelic categories. To obtain reliable x estimates one should then pool these rare categories, otherwise the calculated x will be inflated. Unfortunately, this causes loss of information, which is undesirable. An alternative is to use Fisher's exact probability test, but in the case of many categories and considerable total sample size, this is impractical. Roff and Bentzen (1989) suggested another practical alternative (without any pooling of data) for testing heterogeneity in R x C contingency tables containing rare categories. They used a Monte Carlo procedure, which was termed by Hernandez and Weir (1989) a pseudo-probability test, to test Hardy-Weinberg equilibrium. The procedure consists of (1) generating a sample of all possible data sets having the same marginal totals as the original data set and (2) computing x for each derived data set and counting all the sets for which x is larger than that of the original sample. The ratio of the obtained number to the overall number of generated data sets is the estimate of probability of the null hypothesis. We present here two programs, CHIRXC and CHIHW, which estimate the significance of x statistics using pseudo-probability tests. Thus, our programs permit analysis of sparse table data without pooling rare categories. This saves time and prevents loss of information. The CHIRXC analyzes R x C contingency tables. For the 2 x 2 case, it can perform Fisher's exact probability test as well. The CHIHW estimates conformity of genotypic proportions in a sample to Hardy-Weinberg expectations. It also computes an index of heterozygote deficiency or excess [D = (Ho He)/He] (Koehn et al. 1973) and estimates its significance through the pseudoprobability test. The programs are written in C (Turbo C, ver. 2, Copyright Borland International 1988). They will run on an IBM PC and compatibles. Sample sizes and dimensionality of R x C tables under analysis are limited only by the available computer memory. The approach of Roff and Bentzen (1989) was used in the MONTE program in REAP (McElroy et al. 1991). Our algorithm of randomization is different from theirs and much faster (Pudovkin Al and Zaykin DV, unpublished). The programs are available from the authors. To receive a copy, send a nonformatted 5.25-in diskette, and we will supply the disk with the programs (executables and listings), README files with user instructions, and input file formats.

Evaluating Results Using Corrected and Uncorrected Effect Size Estimates

Abstract: Magnitude-of-effect (ME) statistics, when adequately understood and correctly used, are important aids for researchers who do not want to place a sole reliance on tests of statistical significance in substantive result interpretation. We describe why methodologists encourage the use of ME indices as interpretation aids and discuss different types of ME estimates. We discuss correction formulas developed to attenuate statistical bias in ME estimates and illustrate the effect these formulas have on different sample and effect sizes. Finally, we discuss several cautions against the indiscriminate use of these statistics and offer reasons why ME statistics, like all substantive result interpretation aids, are useful only when their strengths and limitations are understood by researchers.

Sample size calculations for ordered categorical data

Abstract: Many clinical trials yield data on an ordered categorical scale such as very good, good, moderate, poor. Under the assumption of proportional odds, such data can be analysed using techniques of logistic regression. In simple comparisons of two treatments this approach becomes equivalent to the Mann-Whitney test. In this paper sample size formulae consistent with an eventual logistic regression analysis are derived. The influence on efficiency of the number and breadth of categories will be examined. Effects of misclassification and of stratification are discussed, and examples of the calculations are given.

Post-Stratification: A Modeler's Perspective

Abstract: Post-stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates. The basic technique divides the sample into post-strata, and computes a post-stratification weight w ih = rP h /r h for each sample case in post-stratum h, where r h is the number of survey respondents in post-stratum h, P h is the population proportion from a census, and r is the respondent sample size. Survey estimates, such as functions of means and totals, then weight cases by w h . Variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions. Literature on post-stratification is limited and has mainly taken the randomization (or design-based) perspective, where inference is based on the sampling distribution with population values held fixed. This article develops Bayesian model-based theory for the method. A basic normal post-stratification mod...

The power of sensory discrimination methods

Abstract: Difference testing methods are extensively used in a variety of applications from small sensory evaluation tests to large scale consumer tests. A central issue in the use of these tests is their statistical power, or the probability that if a specified difference exists it will be demonstrated as a significant difference in a difference test. A general equation for the power of any discrimination method is given. A general equation for the sample size required to meet Type I and Type II error specifications is also given. Sample size tables for the 2-alternative forced choice (2-AFC), 3-AFC, the duo-trio and the triangular methods are given. Tables of the psychometric functions for the 2-AFC, 3-AFC, triangular and duo-trio methods are also given.

X¯ chart with adaptive sample sizes

Abstract: Standard Shewhart control charts employ fixed sample sizes at equal sampling intervals. By varying the sample size depending on the current location of the process mean, the mean time to detect an off-target condition can be reduced. The adaptive-sample-size control chart is compared with the fixed-sample-size control chart in terms of average run length under shifts in the process mean of variable magnitude. Significant improvements have been obtained with the adaptive-sample-size charts, particularly for small shifts. These improvements are achieved without increasing the in-control average sample size beyond that of the fixed-sample-size approach. A fast initial response is suggested and advantages of the procedure over fixed-sample-size control are illustrated with two examples from discrete manufacturing processes.

The Use of Statistical Significance Tests in Research: Bootstrap and Other Alternatives

Abstract: Three of the various criticisms of conventional uses of statistical significance testing are elaborated. Three alternatives for augmenting statistical significance tests in interpreting results are then elaborated. These include emphasizing effect sizes, evaluating statistical significance tests in a sample size context, and evaluating result replicability. Ways of estimating result replicability from data in hand include crossvalidation, jackknife, and bootstrap logics. The bootstrap is explored in some detail.

Maximum likelihood estimation of K distribution parameters for SAR data

Abstract: The K distribution has proven to be a promising and useful model for backscattering statistics in synthetic aperture radar (SAR) imagery. However, most studies to date have relied on a method of moments technique involving second and fourth moments to estimate the parameters of the K distribution. The variance of these parameter estimates is large in cases where the sample size is small and/or the true distribution of backscattered amplitude is highly non-Rayleigh. The present authors apply a maximum likelihood estimation method directly to the K distribution. They consider the situation for single-look SAR data as well as a simplified model for multilook data. They investigate the accuracy and uncertainties in maximum likelihood parameter estimates as functions of sample size and the parameters themselves. They also compare their results with those from a new method given by Raghavan (1991) and from a nonstandard method of moments technique; maximum likelihood parameter estimates prove to be at least as accurate as those from the other estimators in all cases tested, and are more accurate in most cases. Finally, they compare the simplified multilook model with nominally four-look SAR data acquired by the Jet Propulsion Laboratory AIRSAR over sea ice in the Beaufort Sea during March 1988. They find that the model fits data from both first-year and multiyear ice well and that backscattering statistics from each ice type are moderately non-Rayleigh. They note that the distributions for the data set differ too little between ice types to allow discrimination based on differing distribution parameters. >

Application and testing of a procedure to evaluate transferability of habitat suitability criteria

Abstract: A procedure designed to test the transferability of habitat suitability criteria was evaluated in the Cache la Poudre River, Colorado. Habitat suitability criteria were developed for active adult and juvenile rainbow trout in the South Platte River, Colorado. These criteria were tested by comparing microhabitat use predicted from the criteria with observed microhabitat use by adult rainbow trout in the Cache la Poudre River. A one-sided X2 test, using counts of occupied and unoccupied cells in each suitability classification, was used to test for non-random selection for optimum habitat use over usable habitat and for suitable over unsuitable habitat. Criteria for adult rainbow trout were judged to be transferable to the Cache la Poudre River, but juvenile criteria (applied to adults) were not transferable. Random subsampling of occupied and unoccupied cells was conducted to determine the effect of sample size on the reliability of the test procedure. The incidence of type I and type II errors increased rapidly as the sample size was reduced below 55 occupied and 200 unoccupied cells. Recommended modifications to the procedure included the adoption of a systematic or randomized sampling design and direct measurement of microhabitat variables. With these modifications, the procedure is economical, simple and reliable. Use of the procedure as a quality assurance device in routine applications of the instream flow incremental methodology was encouraged.

Group sequential tests for bivariate response: interim analyses of clinical trials with both efficacy and safety endpoints

Abstract: We describe group sequential tests for a bivariate response. The tests are defined in terms of the two response components jointly, rather than through a single summary statistic. Such methods are appropriate when the two responses concern different aspects of a treatment; for example, one might wish to show that a new treatment is both as effective and as safe as the current standard. We present a formulation of the bivariate testing problem, introduce group sequential tests that satisfy Type I error conditions, and show how to find the sample size guaranteeing a specified power. We describe how properties of group sequential tests for bivariate normal observations can be computed by numerical integration.

Using fixed-effects model multivariate analysis of variance in marine biology and ecology

Abstract: The robustness and power of four commonly used MANOVA statistics (the Pillai-Bartlett trace (V), Wilks' Lambda (W), Hotelling's trace (1), Roy's greatest root (R)) are reviewed and their behaviours demonstrated by Monte Carlo simulations using a one-way fixed effects design in which assumptions of the model are violated in a systematic way under different conditions of sample size (n), number of dependent variables (P), number of groups (k), and balance in the data. The behaviour of Box's M statistic, which tests for covariance heterogeneity, is also examined. The behaviours suggest several recommendations for multivariate design and for application of MANOVA in marine biology and ecology, viz. (1) Sample sizes should be equal. (2) p, and to a lesser extent k, should be kept to a minimum insofar as the hypothesis permits. (3) Box's M statistic is rejected as a test of homogeneity of covariance matrices. A suitable alternative is Hawkins' (1981) statistic that tests for heteroscedasticity and non-normality simultaneously. (4) To improve agreement with assumptions, and thus reliability of tests, reduction of p (e.g. by PCA or MDS methods) and/or transforming data to stabilise variances should be attempted. (5) The V statistic is recommended for general use but the others are more appropriate in particular circumstances. For Type I errors, the violation of the assumption of homoscedasticity is more serious than is nonnormality and the V statistic is clearly the most robust to variance heterogeneity in terms of controlling level. Kurtosis reduces the power of all statistics considerably. Loss of power is dramatic if assumptions of normality and homoscedasticity are violated simultaneously. (6) The preferred approach to multiple comparison procedures after MANOVA is to use Bonferroni-type methods in which the total number of comparisons is limited to the fewest possible. If all possible comparisons are required an alternative is to use the V statistic in the overall test and the R statistic in a follow-up simultaneous test procedure. We recommend following a significant MANOVA result with a canonical discriminant analysis. (7) Classical parametric MANOVA should not be used with data in which high levels of variance heterogeneity cannot be rectified or in which sample sizes are unequal and assumptions are not satisfied. We discuss briefly alternatives to parametric MANOVA.

Surface Sampling in Gravel Streams

Abstract: The accuracy of studies concerning the characteristics of gravel‐bed waterways is often dependent upon the techniques used to sample and quantify the material found on the channel boundary. Due to the vertical stratification present in the riverbed, the use of sampling techniques that remove only the particles within a thin surface layer is often necessary. Attributes of clay and grid sampling are considered in the present work. Criteria for determining the minimum sample size for a desirable level of accuracy are also presented. Many of the current surface sampling techniques truncate either the upper or lower size range of particles. Truncation of part of a size distribution not only limits the available information, but can also bias the rest of the distribution. The present work rectifies this problem by proposing the use of a hybrid technique that can sample the entire size range of either dry or submerged bed material. Results of field tests that utilize this new method are described in detail.

Extremal Index Estimation for a Weakly Dependent Stationary Sequence

Abstract: Under stationarity and weak dependence, the statistical significance and the estimation of the extremal index are considered. It is shown that the distribution of the sample maximum can be uniformly approximated given the extremal index and the marginal distribution as the sample size increases. An adaptive procedure is proposed for estimating the extremal index. The procedure is shown to be asymptotically optimal in a class of estimators.

Factors Influencing Cross-Validation of Confirmatory Factor Analysis Models.

Abstract: This study investigated, by means of a Monte Carlo study, the use of four cross-validation indices with confirmatory factor analysis models. The influence on the cross-validation indices of three design factors: sample size, loading size, and the degree of model misspecification, was studied. Sample size was varied at 200 and 600, and loading size at .4, .6, and .8. Model misspecifications were introduced by setting nonzero factor loadings to equal zero. A modified version of the Akaike Information Criterion (AIC) obtained very accurate estimates of the two-sample index under all sets of conditions. As expected, larger sample sizes and better specified models resulted in better cross-validation results. The presence of larger factor loadings increased the number of times the cross-validation indices yielded optimal values for the correctly specified model.

Historical Origins of Statistical Testing Practices: The Treatment of Fisher versus Neyman-Pearson Views in Textbooks.

Abstract: Textbook discussion of statistical testing is the topic of interest. Some 28 books published from 1910 to 1949, 19 books published from 1990 to 1992, plus five multiple-edition books were reviewed in terms of presentations of statistical testing. It was of interest to discover textbook coverage of the P-value (i.e., Fisher) and fixed-alpha (i.e., Neyman-Pearson) approaches to statistical testing. Also of interest in the review were some issues and concerns related to the practice and teaching of statistical testing: (a) levels of significance, (b) importance of effects, (c) statistical power and sample size, and (d) multiple testing. It is concluded that it is not statistical testing itself that is at fault; rather, some of the textbook presentation, teaching practices, and journal editorial reviewing may be questioned.

Use of previous experience to estimate precision uncertainty of small sample experiments

Abstract: The determination of precision uncertainty is described for experiments where the test measurements are obtained from single readings or from a limited number of independent readings. For these cases, the limits of precision uncertainty are best determined from previous experience based on larger sample sizes over the full range of variations that occur for a specific test. We describe the appropriate procedures to determine the limits of precision uncertainty based on previous experience for small sample experiments. A Monte Carlo simulation technique is used to model the experiments to demonstrate the effectiveness of using the precision uncertainty to determine the range that covers the true test result

Computer-Intensive Methods for Tests about the Mean of an Asymmetrical Distribution

Abstract: For one-sided tests about the mean of a skewed distribution, the t test is asymptotically robust for validity; however, it can be quite inaccurate and inefficient with small sample sizes. Results presented here confirm that a procedure due to Johnson should be preferred to the t test when the parent distribution is asymmetrical, because it reduces the probability of type I error in cases where the t test has an inflated type I error rate and it is more powerful in other situations. But if the skewness is severe and the sample size is small, then Johnson's test can also be appreciably inaccurate. For such situations, computer-intensive test procedures using bootstrap resampling are proposed, and with an extensive Monte Carlo study it is shown that these procedures are remarkably robust and can result in reduced probabilities of type I and type II errors compared to Johnson's test.

Statistical analysis of in vivo tumor growth experiments.

Abstract: We review and compare statistical methods for the analysis of in vivo tumor growth experiments. The methods most commonly used are deficient in that they have either low power or misleading type I error rates. We propose a set of multivariate statistical modeling methods that correct these problems, illustrating their application with data from a study of the effect of alpha-difluoromethylornithine on growth of the BT-20 human breast tumor in nude mice. All the methods find significant differences between the alpha-difluoromethylornithine dose groups, but recommended sample sizes for a subsequent study are much smaller with the multivariate methods. We conclude that the multivariate methods are preferable and present guidelines for their use.

Efficiency of graphical perception

Abstract: The term graphical perception refers to the part played by visual perception in analyzing graphs. Computer graphics have stimulated interest in the perceptual pros and cons of different formats for displaying data. One way of evaluating the effectiveness of a display is to measure the efficiency (as defined by signal-detection theory) with which an observer extracts information from the graph. We measured observers' efficiencies in detecting differences in the means or variances of pairs of data sets sampled from Gaussian distributions. Sample size ranged from 1 to 20 for viewing times of 0.3 or 1 sec. The samples were displayed in three formats: numerical tables, scatterplots, and luminance-coded displays. Efficiency was highest for the scatterplots (approximately equal to 60% for both means and variances) and was only weakly dependent on sample size and exposure time. The pattern of results suggests parallel perceptual computation in which a constant proportion of the available information is used. Efficiency was lowest for the numerical tables and depended more strongly on sample size and viewing time. The results suggest serial processing in which a fixed amount of the available information is processed in a given time.

The Effect of Serial Correlation on Tests for Parameter Change at Unknown Time

Abstract: It is shown that serial correlation can produce striking effects in distributions of change-point statistics. Failure to account for these effects is shown to invalidate change-point tests, either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process, or through diminution of the power of the tests when high frequency mass predominates. These effects are characterized by the expression {2i- f(O)/fJr, f(A) dA), where f( ) is the spectral density of the noise process; in sample survey work this is known as the design effect or "deff." Simple precise adjustments to change-point test statistics which account for serial correlation are provided. The same adjustment applies to all commonly used regression models. Residual processes are derived for both stationary time series satisfying a moment condition and for general linear regression models with stationary error structure. 1. Introduction. Stochastic models for time sequenced data are generally characterized by several unknown parameters. These parameters may change over time, and if the changes, when they occur, do so unannounced and at unknown time points, then the associated inferential problem is referred to as the change-point problem. Various important application areas of statistics involve change detection in a central way; two of these areas are quality assurance and environmental monitoring. Most of the statistics commonly applied to the change-point problem involve cumulative sums or partial sums of regression residuals. The distribution theory for these statistics has been computed under the assumption that the error process for the regression model is white noise. In this paper we consider linear regression of a random variable against general nonstochastic functions of time, but with error variables that form a serially correlated time series. We then examine the large sample properties of the stochastic processes defined by the partial sums of the regression residuals. Large sample distribution theory for fixed sample size statistics used to detect changes in regression parameters is usually derived by computing the distributions of various functionals on

Nonparametric estimation of residual variance revisited

Abstract: SUMMARY Several difference-based estimators of residual variance are compared for finite sample size Since the introduction of a rather simple estimator by Gasser, Sroka & JennenSteinmetz (1986) other proposals have been made Here the one given by Hall, Kay & Titterington (1990) is of particular interest It minimizes the asymptotic variance Unfortunately it has severe problems with finite sample bias, and the estimator of Gasser et al (1986) proves still to be a good choice A new estimator is introduced, compromising between bias and variance

Nonparametric estimation for the difference or ratio of median failure times.

Abstract: A simple and purely nonparametric confidence interval procedure for the difference or ratio of two median failure times is proposed with censored observations. The new proposal does not involve unstable and complicated nonparametric density estimates and is valid asymptotically even when the two underlying distribution functions differ in shape. Extensive numerical studies are carried out to examine the appropriateness of the new procedure for practical sample sizes.