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Showing papers on "Sample size determination published in 1987"


Journal ArticleDOI
TL;DR: In this article, two k-sample versions of the Anderson-Darling rank statistic are proposed for testing the homogeneity of samples, and their asymptotic null distributions are derived for the continuous as well as the discrete case.
Abstract: Two k-sample versions of an Anderson–Darling rank statistic are proposed for testing the homogeneity of samples. Their asymptotic null distributions are derived for the continuous as well as the discrete case. In the continuous case the asymptotic distributions coincide with the (k – 1)-fold convolution of the asymptotic distribution for the Anderson–Darling one-sample statistic. The quality of this large sample approximation is investigated for small samples through Monte Carlo simulation. This is done for both versions of the statistic under various degrees of data rounding and sample size imbalances. Tables for carrying out these tests are provided, and their usage in combining independent one- or k-sample Anderson–Darling tests is pointed out. The test statistics are essentially based on a doubly weighted sum of integrated squared differences between the empirical distribution functions of the individual samples and that of the pooled sample. One weighting adjusts for the possibly different s...

670 citations


Journal ArticleDOI
TL;DR: The existence and uniqueness of a limiting form of a Huber-type $M$-estimator of multivariate scatter is established under certain conditions on the observed sample as discussed by the authors.
Abstract: The existence and uniqueness of a limiting form of a Huber-type $M$-estimator of multivariate scatter is established under certain conditions on the observed sample. These conditions hold with probability one when sampling randomly from a continuous multivariate distribution. The existence of the estimator is proven by showing that it is the limiting point of a specific algorithm. Hence, the proof is constructive. For continuous populations, the estimator of multivariate scatter is shown to be strongly consistent and asymptotically normal. An important property of the estimator is that its asymptotic distribution is distribution-free with respect to the class of continuous elliptically distributed populations. This distribution-free property also holds for the finite sample size distribution when the location parameter is known. In addition, the estimator is the "most robust" estimator of the scatter matrix of an elliptical distribution in the sense of minimizing the maximum asymptotic variance.

635 citations


Journal ArticleDOI
TL;DR: In this paper, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed, and the asymptotic distribution of the test statistic is derived assuming uni-dimensionality.
Abstract: Assuming a nonparametric family of item response theory models, a theory-based procedure for testing the hypothesis of unidimensionality of the latent space is proposed. The asymptotic distribution of the test statistic is derived assuming unidimensionality, thereby establishing an asymptotically valid statistical test of the unidimensionality of the latent trait. Based upon a new notion of dimensionality, the test is shown to have asymptotic power 1. A 6300 trial Monte Carlo study using published item parameter estimates of widely used standardized tests indicates conservative adherence to the nominal level of significance and statistical power averaging 81 out of 100 rejections for examinee sample sizes and psychological test lengths often incurred in practice.

519 citations


Journal ArticleDOI
TL;DR: In this paper, a method for statistical analysis of two independent samples with respect to difference in location is investigated, using the partial least squares projections to latent structures (PLS) with cross-validation.
Abstract: A method for statistical analysis of two independent samples with respect to difference in location is investigated. The method uses the partial least squares projections to latent structures (PLS) with cross-validation. The relation to classical methods is discussed and a Monte Carlo study is performed to describe how the distribution of the test-statistic employed depends on the number of objects, the number of variables, the percentage variance explained by the first PLS-component and the percentage missing values. Polynomial approximations for the dependency of the 50 per cent and the 5 per cent levels of the test-statistic on these factors are given. The polynomial for the 50 per cent level is complicated, involving several first-, second- and third-degree terms, whereas the polynomial for the 5 per cent level is dependent only on the number of objects and the size of the first component. A separate Monte Carlo experiment indicates that a moderate difference in sample size does not affect the distribution of the test-statistic. The multi-sample location problem is also studied and the effect of increasing the number of samples on the test-statistic is shown in simulations.

415 citations


Journal ArticleDOI
Blair Wheaton1
TL;DR: In this article, the authors discuss the logic of the fit problem, review the analytical intentions of six measures, with emphasis on their dependence on sample size, and compare the operational behavior of these measures in three-model situations: in a confirmatory factor model based on small N, and in two covariance structure models, one based on a slightly larger N and the other based on large N.
Abstract: In recent years a number of measures have been suggested for the assessment of fit of overidentified models with latent variables (i.e., covariance structure models). This article discusses the logic of the fit problem, reviews the analytical intentions of six of these measures, with emphasis on their dependence on sample size, and compares the operational behavior of these measures in three-model situations: in a confirmatory factor model based on small N, and in two covariance structure models, one based on a slightly larger N and the other based on a large N. Given that these models and data are “typical,” results suggest that certain measures are both more stable across sample sizes and more sensitive to important variation in fit across substantively plausible models. The article concludes by suggesting a three-component approach to fitting: use of multiple measures, strategical overfitting, and comparison of parameter estimates in borderline versus more clearly sufficient models in terms of fit.

322 citations


Journal ArticleDOI
TL;DR: The efficiency of using a simulated critical point for exact intervals, which has been suggested before but never put to serious test, is investigated and is found to be completely reliable and essentially exact.
Abstract: A frequently encountered problem in practice is that of simultaneous interval estimation of p linear combinations of a parameter beta in the setting of (or equivalent to) a univariate linear model. This problem has been solved adequately only in a few settings when the covariance matrix of the estimator is diagonal; in other cases, conservative solutions can be obtained by the methods of Scheffe, Bonferroni, or Sidak (1967, Journal of the American Statistical Association 62, 626-633). Here we investigate the efficiency of using a simulated critical point for exact intervals, which has been suggested before but never put to serious test. We find the simulation-based method to be completely reliable and essentially exact. Sample size savings are substantial (in our settings): 3-19% over the Sidak method, 4-37% over the Bonferroni method, and 27-33% over the Scheffe method. We illustrate the efficiency and flexibility of the simulation-based method with case studies in physiology and marine ecology.

294 citations


Journal ArticleDOI
TL;DR: In this article, the authors used a rating curve to predict unmeasured river loads from continuous discharge data but relatively infrequent sampling of sediment, solute, or pollutant concentrations.
Abstract: River loads often have to be estimated from continuous discharge data but relatively infrequent sampling of sediment, solute, or pollutant concentrations. Two standard ways of doing this are to multiply mean concentration by mean discharge, and to use a rating curve to predict unmeasured concentrations. Both methods are known from previous empirical studies to underestimate true load. Statistical considerations explain these biases and yield correction factors which can be used to obtain unbiased estimates of load. Simulation experiments with normally-distributed scatter about log-linear trends, and sampling experiments using a natural data set, show that the corrected rating curve method has lower sampling variability than other unbiased methods based on average instantaneous load and is thus the recommended procedure when the rating plot is of the assumed form. The precision of all methods increases with sample size and decreases with increasing rating-curve slope and scatter.

293 citations


Journal ArticleDOI
TL;DR: In this paper, an efficient recursive algorithm was proposed to generate the joint and conditional distributions of the sufficient statistics for logistic regression with binary response variables, and the algorithm was shown to be computationally feasible except in a few special situations.
Abstract: Logistic regression is a commonly used technique for the analysis of retrospective and prospective epidemiological and clinical studies with binary response variables. Usually this analysis is performed using large sample approximations. When the sample size is small or the data structure sparse, the accuracy of the asymptotic approximations is in question. On other occasions, singularity of the covariance matrix of parameter estimates precludes asymptotic analysis. Under these circumstances, use of exact inferential procedures would seem to be a prudent alternative. Cox (1970) showed that exact inference on the parameters of a logistic model with binary response requires consideration of the distribution of sufficient statistics for these parameters. To date, however, resorting to the exact method has not been computationally feasible except in a few special situations. This article presents an efficient recursive algorithm that generates the joint and conditional distributions of the sufficient...

289 citations


Journal ArticleDOI
TL;DR: In this article, the problem of determining the number of observations required by some common nonparametric tests, so that the tests have power at least 1 − β against alternatives that differ sufficiently from the hypothesis being tested is discussed.
Abstract: The article discusses the problem of determining the number of observations required by some common nonparametric tests, so that the tests have power at least 1 – β against alternatives that differ sufficiently from the hypothesis being tested. It is shown that the number of observations depends on certain simple probabilities. A method is suggested for fixing the value of the appropriate probability when determining sample size.

285 citations


Journal ArticleDOI
TL;DR: In this paper, the design aspect of this procedure is explored in terms of the maximum sample size needed to achieve a desired level of power and the expected stopping times under both null and alternative hypotheses.
Abstract: SUMMARY Lan & DeMets (1983) devised a method of constructing discrete group sequential boundaries by using the type I error spending rate function. It is extended so as to generate asymmetric as well as symmetric two-sided boundaries for clinical trials. The design aspect of this procedure is explored in terms of the maximum sample size needed to achieve a desired level of power and the expected stopping times under both null and alternative hypotheses. Finally, these properties are employed in search of appropriate type I error spending rate functions for differing situations.

261 citations


Journal ArticleDOI
TL;DR: In this paper, the authors derived and used easily computable expressions for the mean and variance of R2 in the standard linear regression model with fixed regressors, and showed that R2 is seriously biased upward in small samples; the 0 "adjusted" R2 does much better.

Journal ArticleDOI
01 May 1987
TL;DR: For measuring the degree of association or correlation between two nominal variables, a measure based on informational entropy is presented as being preferable to that proposed recently by Horibe.
Abstract: For measuring the degree of association or correlation between two nominal variables, a measure based on informational entropy is presented as being preferable to that proposed recently by Horibe [1]. Asymptotic developments are also presented that may be used for making approximate statistical inferences about the population measure when the sample size is reasonably large. The use of this methodology is illustrated using a numerical example.

Journal ArticleDOI
TL;DR: In this article, a procedure and a table for selecting sample size for simultaneously estimating the parameters of a multinomial distribution is presented, analogous to the case in which a binomial parameter equals one-half.
Abstract: This article presents a procedure and a table for selecting sample size for simultaneously estimating the parameters of a multinomial distribution. The results are obtained by examining the “worst” possible value of a multinomial parameter vector, analogous to the case in which a binomial parameter equals one-half.

Journal ArticleDOI
TL;DR: In many cases, the sample size for the independent-sample case provides a conservative approximation for the matched-pair design, and a simple alternative approximation is presented here.
Abstract: Miettinen (1968, Biometrics 24, 339-352) presented an approximation for power and sample size for testing the differences between proportions in the matched-pair case. Duffy (1984, Biometrics 40, 1005-1015) gave the exact power for this case and showed that Miettinen's approximation tends to slightly overestimate the power or underestimate the sample size necessary for the design power. A simple alternative approximation that is more conservative is presented here. In many cases, the sample size for the independent-sample case provides a conservative approximation for the matched-pair design.

Journal ArticleDOI
TL;DR: In this paper, a discussion of how various equating methods are affected by sampling error, sample characteristics, and sample characteristics of anchor test items is presented, and the question of whether an equating transformation remains the same regardless of the group used to define it is also reviewed.
Abstract: This paper focuses on a discussion of how various equating methods are affected by (1) sampling error, (2) sample characteristics, and (3) characteristics of anchor test items. Studies that examine the effect of analytic techniques for smoothing or modeling mar ginal and bivariate frequency distributions on the ac curacy of equipercentile equating are reviewed. A need for simulation and empirical studies designed to evaluate the effectiveness of analytic smoothing tech niques for recovering the underlying distribution when sample size, test length, and distributional shape are varied is identified. Studies that examine the question of whether an equating transformation remains the same regardless of the group used to define it are also reviewed. The results of some studies suggested that this may not be a problem for forms of a homogene ous test constructed to be similar in all respects. Re sults of other studies indicated that examinees who take a test on different administration dates may vary in system...

Journal ArticleDOI
TL;DR: Examination of 10 carefully compiled large data sets reveals that the species-occurrence frequency distribution of each fits the log series distribution well and therefore sample size effects can be predicted.
Abstract: Few paleontological studies of species distribution in time and space have adequately considered the effects of sample size. Most species occur very infrequently, and therefore sample size effects may be large relative to the faunal patterns reported. Examination of 10 carefully compiled large data sets (each more than 1,000 occurrences) reveals that the species-occurrence frequency distribution of each fits the log series distribution well and therefore sample size effects can be predicted. Results show that, if the materials used in assembling a large data set are resampled, as many as 25% of the species will not be found a second time even if both samples are of the same size. If the two samples are of unequal size, then the larger sample may have as many as 70% unique species and the smaller sample no unique species. The implications of these values are important to studies of species richness, origination, and extinction patterns, and biogeographic phenomena such as endemism or province boundaries. I provide graphs showing the predicted sample size effects for a range of data set size, species richness, and relative data size. For data sets that do not fit the log series distribution well, I provide example calculations and equations which are usable without a large computer. If these graphs or equations are not used, then I suggest that species which occur infrequently be eliminated from consideration. Studies in which sample size effects are not considered should include sample size information in sufficient detail that other workers might make their own evaluation of observed faunal patterns.

Book
01 Jan 1987
TL;DR: In this paper, the authors discuss the importance of selecting the correct statistical test to evaluate the effectiveness of a program and the importance to consider when selecting a statistical test when evaluating individual practitioners' effectiveness.
Abstract: All chapters conclude with "Concluding Thoughts" and "Study Questions" Preface 1 Introduction to Statistical Analysis Uses of Statistical AnalysisGeneral Methodological TermsLevels of MeasurementLevels of Measurement and Analysis of DataOther Measurement ClassificationsCategories of Statistical Analyses 2 Frequency Distributions and Graphs Frequency DistributionsGrouped Frequency DistributionsUsing Frequency Distributions to Analyze DataMisrepresentation of DataGraphical Presentation of DataA Common Mistake in Displaying Data 3 Central Tendency and Variability Central TendencyVariability 4 Normal Distributions Skewed DistributionsNormal DistributionsConverting Raw Scores to Z Scores and PercentilesDeriving Raw Scores From Percentiles 5 Introduction to Hypothesis Testing Alternative ExplanationsProbabilityRefuting Sampling ErrorResearch HypothesesTesting the Null HypothesisStatistical SignificanceErrors in Drawing Conclusions About RelationshipsStatistically Significant Relationships and Meaningful Findings 6 Sampling Distributions and Hypothesis Testing Sample Size and Sampling ErrorSampling Distributions and InferenceSampling Distribution of MeansEstimating Parameters From StatisticsOther Distributions 7 Selecting a Statistical Test The Importance of Selecting the Correct Statistical TestFactors to Consider When Selecting a Statistical TestParametric and Nonparametric TestsMultivariate Statistical TestsGeneral Guidelines for Test SelectionGetting Help With Data Analyses 8 Correlation Uses of CorrelationPerfect CorrelationsNonperfect CorrelationsInterpreting Linear CorrelationsUsing Correlation For InferenceComputation and Presentation of Person's RNonparametric AlternativesUsing Correlation With Three or More VariablesOther Multivariate Tests that Use Correlation 9 Regression Analyses What is Prediction?What is Simple Linear Regression?Computation of the Regression EquationMore About the Regression LineInterpreting ResultsUsing Regression Analyses in Social Work PracticeRegression With Three or More VariablesOther Types of Regression Analyses 10 Cross-Tabulation The Chi-Square Test of AssociationUsing Chi-Square in Social Work PracticeChi-Square With Three or More VariablesSpecial Applications of the Chi-Square Formula 11 t Tests and Analysis of Variance The Use of t TestsThe One-Sample t TestThe Dependent t TestThe Independent t TestSimple Analysis of Variance (One-Way Anova) Appendix A Using Statistics to Evaluate Practice Effectiveness Evaluating ProgramsEvaluating Individual Practitioner Effectiveness Glossary Index

Journal ArticleDOI
TL;DR: A method is proposed which incorporates resolving power as a primary factor and expended effort (feasibility) as a secondary factor and the greatest limiting factor on sample size is used as a measure of sample effort.

Posted Content
01 Jan 1987
TL;DR: In this article, the authors considered the consistency property of some test statistics based on a time series of data and provided Monte Carlo evidence on the power of the tests in Finite Samples.
Abstract: This Paper Considers the Consistency Property of Some Test Statistics Based on a Time Series of Data. While Th Eusual Consistency Criterion Is Based on Keeping the Sampling Interval Fixed, We Let the Sampling Interval Take Any Path As the Sample Size Increases to Infinity. We Consider Tests of the Null Hypotheses of the Random Walk and Randomness Against Positive Autocorrelation We Show That Tests of the Unit Root Hypothesis Based on the First-Order Correlation Coefficient of the Original Data Are Consistent As Long As the Span of the Data Is Increasing. Tests of the Same Hypothesis Based on the First-Order Correlation Coefficient Using the First-Differenced Data Are Consistent Only If the Span Is Increasing At a Rate Greater Than Square Root of 'T'. on the Other Hand Tests of the Randomness Hypotheses Based on the First-Order Correlation Coefficient Applied to the Original Data Are Consistent As Long As the Span Is Not Increasing Too Fast. We Provide Monte Carlo Evidence on the Power, in Finite Samples, of the Tests Studied Allowing Various Combinations of Span and Sampling Frequencies. It Is Found That the Consistency Properties Summarize Well the Behavior of the Power in Finite Samples. the Power of Tests for a Unit Root Is More Influenced by the Span Than the Number O Observations While Tests of Randomness Are More Powerfull When a Small Sampling Frequency Is Available.

Journal ArticleDOI
TL;DR: Probability inequalities for the supremum of a weighted empirical process indexed by a Vapnik-Cervonenkis class C of sets were obtained in this article for the assumption P(∪{C∈C:P(C)
Abstract: Probability inequalities are obtained for the supremum of a weighted empirical process indexed by a Vapnik-Cervonenkis class C of sets. These inequalities are particularly useful under the assumption P(∪{C∈C:P(C)

Journal ArticleDOI
TL;DR: The power and required sample size are studied for Gaussian and log-Gaussian distributions of diagnostic test values and the results may be useful for the planning phase of studies to evaluate quantitative diagnostic tests.
Abstract: For a quantitative laboratory test the 0.975 fractile of the distribution of reference values is commonly used as a discrimination limit, and the sensitivity of the test is the proportion of diseased subjects with values exceeding this limit. A comparison of the estimates of sensitivity between two tests without taking into account the sampling variation of the discrimination limits can increase the type I error to about seven times the nominal value of 0.05. Correct statistical procedures are considered, and the power and required sample size are studied for Gaussian and log-Gaussian distributions of diagnostic test values. The results may be useful for the planning phase of studies to evaluate quantitative diagnostic tests.

Journal ArticleDOI
TL;DR: In this article, Monte Carlo evidence on the fixed sample size properties of adaptive maximum likelihood estimates of a linear regression is reported, where the focus is on the problem of selecting the smoothing and trimming parameters used in estimating the score function.
Abstract: This paper reports Monte Carlo evidence on the fixed sample size properties of adaptive maximum likelihood estimates of a linear regression. The focus is on the problem of selecting the smoothing and trimming parameters used in estimating the score function. We examine the performance of adaptive maximum likelihood estimators when these parameters are preselected or, alternatively, are determined by a data-based bootstrap method.

Journal ArticleDOI
TL;DR: Calculation of confidence intervals demonstrated that 50 to 450 subjects are needed for a precise parametric estimation of the 95% reference interval, and a goodness-of-fit test to transformed values shows that one should accept gaussianity only for p-values greater than 0.05.
Abstract: In two-stage transformation systems for normalization of reference distributions, the asymmetry is first corrected, and any deviation of kurtosis is then adjusted. The simulation studies reported here show that these systems have previously been assessed too optimistically because the sample variation of the transformation parameters was neglected. Applying a goodness-of-fit test to transformed values shows that one should accept gaussianity only for p-values greater than 0.15 instead of those greater than 0.05. Further, the calculated 90% confidence intervals of reference limits should be expanded by 25%. When the correct level of significance is used, only real reference distributions that deviate moderately from the gaussian form are normalized. Calculation of confidence intervals demonstrated that 50 to 450 subjects are needed for a precise parametric estimation of the 95% reference interval. For the nonparametric approach, 125 to 700 reference subjects are necessary. The larger sample sizes are needed when distributions show pronounced skewness.

Journal ArticleDOI
TL;DR: In this article, Traugott et al. report on the results of a series of experiments designed to improve response rates for telephone surveys and assess the cost and error components of these designs.
Abstract: This article reports on the results of a series of experiments designed to improve response rates for telephone surveys. In three surveys telephone households were selected using both standard random digit dialing (RDD) techniques and lists of telephone numbers purchased from a commercial firm. In the RDD portions of the samples "cold contact" interviewing methods were used; in the list frame portions advance letters were mailed, and the listed household name was used in the introduction. Experiments were designed to test the effects on response rates of the advance letters and use of the listed household name as a means of establishing rapport. The advance letters increased response rates, but no difference could be attributed to the use of names. The mixture of RDD and list sampling techniques is also used to evaluate the effects of relative response rates on substantive findings. The cost consequences of these dual frame designs are assessed along a number of dimensions, and the cost and error components of these designs are discussed. Survey nonresponse error is partially a function of achieved response rates. The researcher's ability to increase response rates, in turn, depends on a number of survey design features-the topic of the survey, MICHAEL W. TRAUGOTT is Research Scientist in the Center for Political Studies, ROBERT M. GROVES is Associate Research Scientist in the Survey Research Center, and JAMES M. LEPKOWSKI is Assistant Research Scientist in the Survey Research Center, all at the University of Michigan. The data utilized in this paper were collected in conjunction with a contract with the Detroit News. Support for consideration of dual frame telephone survey designs was obtained from the U.S. Bureau of the Census. However, all of the analyses and interpretations presented here are the sole responsibility of the authors. The research assistance of Judy Connor and Kim Fridkin Kahn is gratefully acknowledged, as is the computing support of the University of Michigan. A version of this paper was presented at the annual meeting of the American Association for Public Opinion Research, St. Petersburg, Florida, 16-18 May 1986. Public Opinion Quarterly Volume 51:522-539 ? 1987 by the Amerncan Association for Public Opinion Research Published by The University of Chicago Press / 0033-362X/87/0051-04(1)/$2.50 This content downloaded from 157.55.39.180 on Mon, 25 Apr 2016 06:57:17 UTC All use subject to http://about.jstor.org/terms Dual Frame Designs to Reduce Nonresponse 523 the population studied, the efforts at refusal conversion, the duration of the interviewing period, information known about the sample persons, and a host of other factors. Inevitably, decisions regarding response rate goals require a balancing of the expected costs of these design attributes and the likely nonresponse error reduction which may result from them. When names, addresses, and telephone numbers are available on a frame, two techniques can be used to improve cooperation-advance letters or telephone calls informing sample persons that they have been selected for a study and indicating the need for cooperation in order to achieve accurate results. Brunner and Carroll (1967) found that an advance telephone call for a personal interview actually led to lower response rates. Groves and Magilavy (1981) observed that advance telephone calls for a telephone survey had no effect on final response rates in an RDD survey. Dillman, Gallegos, and Frey (1976) found that overall response rates were increased by about five percentage points using an advance letter, but that the content of the letter had little influence on the magnitude of the response rate increase. Sykes and Hoinville (1985) found no effect in a telephone survey in Great Britain. Brunner and Carroll (1969) found large increases in response rates to a telephone survey (30 percentage points) with a letter sent on university stationery, but a decline in response rates (6 percentage points) using one from a market research company. Response rates are also sensitive to the amount of effort used to contact sample households, but even this may be affected by characteristics of the sampling frame. The use of callbacks is a minimum condition for increasing response rates (Traugott, 1987), and refusal conversion techniques are also important for this purpose. In some surveys the number of callbacks is a fixed design feature, determined prior to the interviewing period. In other designs the maximum number of callbacks is determined by the length of the survey period. Since the time spent screening ineligible sample units detracts from time available for interviewing, the percentage of units on the sampling frame that are eligible can also affect response rates. In this way, the choice of sampling frame can have a consequence for nonresponse error. The achievement of high response rates is a goal linked not only to improved estimation of descriptive statistics but also increased confidence in measured relationships. While there has been considerable research on increasing response rates, there has been little on their effects on measured relationships between variables. This is ordinarily complicated by an inability to measure relationships for nonrespondents. The literature that does exist compares relationships between variables among cooperative and reluctant respondents (O'Neil, 1979; Smith, 1984). This content downloaded from 157.55.39.180 on Mon, 25 Apr 2016 06:57:17 UTC All use subject to http://about.jstor.org/terms 524 M. W. Traugott, R. M. Groves, and J. M. Lepkowski Telephone surveys based upon random digit dialed (RDD) samples have offered substantial advantages in reducing data collection costs relative to personal interview surveys, in large part because travel costs can be eliminated and the number of interviewers required to complete a given sample size is often smaller. The RDD method has, however, also resulted in a reduction in survey response rates (Groves and Kahn, 1979). In some part these reduced rates may be attributed to "cold contacts" with respondents about whom the interviewers know little. In addition, the lower response rates may be attributed to features of the RDD sampling frame, including the relatively high percentages of nonworking and nonresidential numbers that are part of this frame. The time requirements for screening out such sample numbers reduces the time available to pursue eligible numbers. This article summarizes a series of experiments conducted across three telephone surveys designed to measure cost and nonresponse advantages of a sampling frame based on telephone directories (termed the "list frame") in comparison with RDD samples.1 In contrast to prior uses of directories as the sole frame or as a "seeding" mechanism for RDD work (Sudman, 1973), these experiments explored their use in a dual frame design, jointly employing RDD and directory based methods. The research reported here focuses not on the statistical design issues involved in dual frame telephone surveys but on those properties of the list frame that make it a desirable companion to the RDD frame. The major test described in this paper involved a comparison of the response rate among list frame households sent an advance letter with the rate for those in which cold contacts were made. Following previous results it was hypothesized that the use of the letter would increase response rates. A subsidiary experimental treatment involved the use upon initial contact of the name in the directory listing for a portion of the households that were sent the letter. Assuming that personalized approaches emphasize the unique attributes of the sample person, it was hypothesized that the use of names in conjunction with the letter would further increase response rates. Because of the anticipated higher proportions of working household numbers on the list frame, and possible differences in cooperation 1. The first two of these three surveys used the same basic dual frame sample design, while the third used a two-phase design described in Lepkowski and Groves (1986b). There were other elements of each study which differed. The first survey was conducted between 18 October and 10 November 1985, involved 753 interviews which averaged 23 minutes in length, and achieved an overall response rate of 61%. The second survey was conducted between 14 February and 3 March 1986, involved 668 interviews which averaged 13 minutes in length, and achieved an overall response rate of 61%. The third survey, conducted between 24 May and 15 June 1986, involved 789 interviews which averaged 22 minutes in length, and achieved an overall response rate of 63%. This content downloaded from 157.55.39.180 on Mon, 25 Apr 2016 06:57:17 UTC All use subject to http://about.jstor.org/terms Dual Frame Designs to Reduce Nonresponse 525 among respondents with listed and unlisted numbers, it was hypothesized that response rates would be higher in the list frame than in the RDD frame, for an equivalent level of effort at contacting respondents. The effects of these design features on survey costs, measured as efficiency in obtaining interviews, were evaluated under controlled conditions in a fixed field period and achievement of a designated final response rate. Examples are also presented of differences in observed bivariate relationships among respondents who were sent a letter (the "high response" sample) and those who were not (the "low response" sample). Elements of the Dual Frame Design for Telephone

Journal ArticleDOI
TL;DR: A simple approximate formula for sample sizes for detecting a linear trend in proportions is derived and some numerical results of a power study for small sample sizes show that the nominal power corresponding to the approximate sample size is a reasonably good approximation to the actual power.
Abstract: A simple approximate formula for sample sizes for detecting a linear trend in proportions is derived. The formulas for both the uncorrected and corrected Cochran-Armitage test are given. For two binomial proportions these reduce to those given by Casagrande, Pike, and Smith (1978, Biometrics 34, 483-486). Some numerical results of a power study for small sample sizes show that the nominal power corresponding to the approximate sample size is a reasonably good approximation to the actual power.

Journal ArticleDOI
TL;DR: There is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric, but the need for caution in the application of simulation studies to real problems is illustrated.
Abstract: We examine various methods to estimate the effective sample size for construction of confidence intervals for survival probabilities. We compare the effective sample sizes of Cutler and Ederer and Peto et al., as well as a modified Cutler-Ederer effective sample size. We investigate the use of these effective sample sizes in the common situation of many censored observations that intervene between the time point of interest and the last death before this time. We note that there is no a priori reason to treat upper and lower confidence intervals in a symmetric fashion since censored survival data are by nature asymmetric. We recommend the use of the Cutler-Ederer effective sample size in construction of upper confidence intervals and the Peto effective sample size in construction of lower confidence intervals. Two examples with real data demonstrate the differences between confidence intervals formed with different effective sample sizes. This study also illustrates the need for caution in the application of simulation studies to real problems.

Journal ArticleDOI
TL;DR: In this article, a new heuristic method for setting the limits of a control chart was proposed, which gives the same limits as the Shewhart method when the underlying population is symmetric.
Abstract: This paper proposes a new heuristic method for setting the limits of a control chart. The new method gives the same limits as the Shewhart method when the underlying population is symmetric. However, when the underlying population is skewed, the new limits are adjusted in accordance with the direction of skewness. The new method was compared with two other methods by simulation, when the underlying population was Weibull. The new method provides a higher probability of coverage between the chart limits than the other methods when the sample size and/or shape parameters vary.

Journal ArticleDOI
01 Jan 1987
TL;DR: In this article, the relationship between sample size and value estimation accuracy was examined for six terrain surfaces, and a functional relationship with consistent slope was found between sampling intensity and estimation error.
Abstract: Analysis and isometric mapping of continuous geographic surfaces often require estimation of values at points on the surface from a sample of known values. Five factors influence accuracy of these intermediate value estimates: data measurement accuracy, control point density, spatial distribution of sample points, intermediate value estimation procedures, and spatial variability of the surface represented. While holding data measurement, data location procedures, and interpolation methods constant, the relationship between sample size and value estimation accuracy was examined for six terrain surfaces. A functional relationship with consistent slope was found between sampling intensity and value estimation error. As sampling intensity increased, both the error of intermediate value estimates and the randomness of the spatial distribution of that error decreased at a decreasing rate. Absolute value of error varied with surface variability. These results were demonstrated to be applicable to determining min...

Journal ArticleDOI
TL;DR: In this paper, the number of trees to be sampled and an acceptable tree-ring response index should be dictated by the nature and geographical extent of the specific hazard under study, and three guidelines for choosing sample size, given variations in processes.
Abstract: Tree-ring dating is employed to reconstruct chronologies of occurrence for a variety of natural hazards. The number of trees sampled varies greatly as does the minimum number of tree-ring responses. The number of trees to be sampled and an acceptable tree-ring response index should be dictated by the nature and geographical extent of the specific hazard under study. Repetitive sampling of different numbers of 30 avalanche-damaged trees showed significant differences in number of tree-ring responses over a 55-year-period. More sampling and use of a higher minimum response index allowed greater confidence in the chronology constructed from tree-rings and compared to historical records. Three geographic scales of analysis that can confound tree-ring responses are identified, and three guidelines for choosing sample size, given variations in processes, are suggested.

Journal ArticleDOI
TL;DR: It is shown that when the dimensionality of the data is high, it may not be possible to estimate the asymptotic error simply by increasing the sample size, and a new procedure is suggested to alleviate this problem.
Abstract: The bias of the finite-sample nearest neighbor (NN) error from its asymptotic value is examined. Expressions are obtained which relate the bias of the NN and 2-NN errors to sample size, dimensionality, metric, and distributions. These expressions isolate the effect of sample size from that of the distributions, giving an explicit relation showing how the bias changes as the sample size is increased. Experimental results are given which suggest that the expressions accurately predict the bias. It is shown that when the dimensionality of the data is high, it may not be possible to estimate the asymptotic error simply by increasing the sample size. A new procedure is suggested to alleviate this problem. This procedure involves measuring the mean NN errors at several sample sizes and using our derived relationship between the bias and the sample size to extrapolate an estimate of the asymptotic NN error. The results are extended to the multiclass problem. The choice of an optimal metric to minimize the bias is also discussed.