scispace - formally typeset
Search or ask a question

Showing papers on "Sample size determination published in 1990"


Journal ArticleDOI
TL;DR: In this article, the sample size and power equations for these designs are shown to be special cases of two generic formulae for sample sizes and power calculations, and a computer program is available that can be used for studies with dichotomous, continuous, or survival response measures.

1,858 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the effect of sample size on structural equation fit measures and examined the current debate on sample size influences in the context of covariance structure models. But their focus was not on the statistical properties of the covariance matrix of a model.
Abstract: A controversial area in covariance structure models is the assessment of overall model fit. Researchers have expressed concern over the influence of sample size on measures of fit. Many contradictory claims have been made regarding which fit statistics are affected by N. Part of the confusion is due to there being two types of sample size effects that are confounded. The first is whether N directly enters the calculation of a fit measure. The second is whether the means of the sampling distributions of a fit index are associated with sample size. I explain these types of sample size effects and illustrate them with the major structural equation fit indices. In addition, I examine the current debate on sample size influences in light of this distinction. Structural equation models, including confirmatory factor analyses, are becoming increasingly popular in psychology. Key to these procedures is the hypothesis that the population covariance matrix of observed variables is a function of the unknown free parameters of a model. Many measures of overall model fit have been proposed to assess the degree to which this hypothesis holds (e.g., Rentier B Bollen, 1986;Hoelter, 1983; Joreskog & Sorbom, 1986; Tucker & Lewis, 1973).

865 citations


Journal ArticleDOI
TL;DR: Numerical examples covering a variety of sample sizes and proportions of events display the closeness of this relationship in situations typical of the Framingham Study.
Abstract: A standard analysis of the Framingham Heart Study data is a generalized person-years approach in which risk factors or covariates are measured every two years with a follow-up between these measurement times to observe the occurrence of events such as cardiovascular disease. Observations over multiple intervals are pooled into a single sample and a logistic regression is employed to relate the risk factors to the occurrence of the event. We show that this pooled logistic regression is close to the time dependent covariate Cox regression analysis. Numerical examples covering a variety of sample sizes and proportions of events display the closeness of this relationship in situations typical of the Framingham Study. A proof of the relationship and the necessary conditions are given in the Appendix.

755 citations


Book
14 Jan 1990
TL;DR: In this paper, the authors propose a statistical method for sample size determination in case-control studies and cohort studies, based on sampling distribution characteristics of estimates of population parameters hypothesis testing two sample confidence intervals and hypothesis tests epidemiologic study design basis sampling concepts.
Abstract: Part 1 Statistical methods for sample size determination: the one sample problem the two sample problem sample size for case-control studies sample size determination for cohort studies lot quality assurance sampling the incidence density sample size for continuous response variables sample size for sample surveys. Part 2 Foundations of sampling and statistical theory: the population the sample sampling distribution characteristics of estimates of population parameters hypothesis testing two sample confidence intervals and hypothesis tests epidemiologic study design basis sampling concepts.

748 citations


Journal ArticleDOI
01 Aug 1990-Ecology
TL;DR: In an effort to encourage rigorous analysis of response data, this work addresses statistical treatment of response curves and illustrates the correct alternatives that are available.
Abstract: Physiological ecologists often analyze the responses of physiological or bio- chemical traits to environmental factors such as temperature, irradiance, water potential, or the concentrations of CO2, 0, and inorganic nutrients. The data for such a response curve typically are gathered by sequential sampling of the same plant or animal, and their analysis should explicitly allow for this repeated-measures design. Unfortunately, the sta- tistical analysis of response curves in ecology generally has either been ignored or incorrectly done. In an effort to encourage rigorous analysis of response data, we address statistical treatment of response curves and illustrate the correct alternatives that are available. Four different statistical methods for analyzing response curves are considered: analysis of vari- ance with repeated measures (ANOVAR), multivariate analysis of variance with repeated measures (MANOVAR), a nonparametric split-plot analysis (NP split-plot) and parametric comparison of models fitted to the data by nonlinear regression. Analyses of the CO2 dependence of photosynthesis in the C4 grass Echinochloa crus-galli following chilling are used as examples of these different methods. ANOVAR, potentially the most powerful analysis, makes stringent assumptions about the variance-covariance structure of the data. Within limits these assumptions can be relaxed and a corrected significance level used. When the variance-covariance structure badly violates the ANOVAR assumptions, MANOVAR or NP split-plot are viable alter- natives. In physiological ecology, however, the use of MANOVAR frequently is limited by small sample sizes and the tendency for the number of levels of the treatment factor to exceed the sample size. Greater attention to experimental design can avoid this problem. The NP split-plot is based on simple assumptions and could be widely used. The comparison of curves fitted by nonlinear regression is also distribution free and provides an interesting alternative when the responses are amenable to fitting. For any of these analyses to be viable the thoughtful choice of experimental protocols and design is essential.

668 citations


Journal ArticleDOI
02 Feb 1990-JAMA
TL;DR: The hypothesis that lead impairs children's IQ at low dose is strongly supported by this quantitative review, and the effect is robust to the impact of any single study.
Abstract: We identified 24 modern studies of childhood exposures to lead in relation to IQ. From this population, 12 that employed multiple regression analysis with IQ as the dependent variable and lead as the main effect and that controlled for nonlead covariates were selected for a quantitative, integrated review or metaanalysis. The studies were grouped according to type of tissue analyzed for lead. There were 7 blood and 5 tooth lead studies. Within each group, we obtained jointPvalues by two different methods and average effect sizes as measured by the partial correlation coefficients. We also investigated the sensitivity of the results to any single study. The sample sizes ranged from 75 to 724. The sign of the regression coefficient for lead was negative in 11 of 12 studies. The negative partial r's for lead ranged from —.27 to —.003. The power to find an effect was limited, below 0.6 in 7 of 12 studies. The jointPvalues for the blood lead studies were (JAMA. 1990;263:673-678)

619 citations


Journal ArticleDOI
TL;DR: This paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non-zero difference or non-unity relative risk.
Abstract: When it is required to establish a materially significant difference between two treatments, or, alternatively, to show that two treatments are equivalent, standard test statistics and sample size formulae based on a null hypothesis of no difference no longer apply. This paper reviews some of the test statistics and sample size formulae proposed for comparative binomial trials when the null hypothesis is of a specified non-zero difference or non-unity relative risk. Methods based on restricted maximum likelihood estimation are recommended and applied to studies of pertussis vaccine.

580 citations


Journal ArticleDOI
TL;DR: The "activities of daily living," or ADLs, are the basic tasks of everyday life, such as eating, bathing, dressing, toileting, and transferring.
Abstract: The "activities of daily living," or ADLs, are the basic tasks of everyday life, such as eating, bathing, dressing, toileting, and transferring. Reported estimates of the size of the elderly population with ADL disabilities differ substantially across national surveys. Differences in which ADL items are being measured and in what constitutes a disability account for much of the variation. Other likely explanations are differences in sample design, sample size, survey methodology, and age structure of the population to which the sample refers. When essentially equivalent ADL measures are compared, estimates for the community-based population vary by up to 3.1 percentage points; and for the institutionalized population, with the exception of toileting, by no more than 3.2 percentage points. As small as these differences are in absolute terms, they can be large in percent differences across surveys. For example, the National Medical Expenditure Survey estimates that there are 60 percent more elderly people with ADL problems than does the Supplement on Aging.

476 citations


Journal ArticleDOI
TL;DR: In this article, the authors describe sampling designs in which, whenever an observed value of a selected unit satisfies a condition of interest, additional units are added to the sample from the neighborhood of that unit, if any of these additional units satisfies the condition, still more units may be added.
Abstract: In many real-world sampling situations, researchers would like to be able to adaptively increase sampling effort in the vicinity of observed values that are high or otherwise interesting. This article describes sampling designs in which, whenever an observed value of a selected unit satisfies a condition of interest, additional units are added to the sample from the neighborhood of that unit. If any of these additional units satisfies the condition, still more units may be added. Sampling designs such as these, in which the selection procedure is allowed to depend on observed values of the variable of interest, are in contrast to conventional designs, in which the entire selection of units to be included in the sample may be determined prior to making any observations. Because the adaptive selection procedure introduces biases into conventional estimators, several estimators are given that are design unbiased for the population mean with the adaptive cluster designs of this article; that is, the ...

420 citations


Journal ArticleDOI
TL;DR: The results indicate that both new tests performed as well as the D test for reasonable sample sizes and a combination of both LM and W tests seemed to provide a fairly satisfactory outcome in the process of model modification.
Abstract: Model comparisons in covariance structure modeling have traditionally been carried out by the likelihood ratio difference (D) test. Two more convenient approaches are reviewed and evaluated. The Lagrange Multiplier (LM) test evaluates the impact of model modification from a more limited model whereas the Wald (W) test makes the evaluation from a more general model. The empirical performance of the D, LM, and W tests under null and alternative hypotheses are compared in this study. The results indicate that both new tests performed as well as the D test for reasonable sample sizes. The nonmonotonicity of power function for the W test was discovered; however, it is not severe in this study. The LM test behaved as a central or noncentral X[SUP2] variate under null or alternative hypotheses, as expected. However, when a correct null hypothesis was embedded in a composite hypothesis which was false, an incremental LM test tended to suggest more parameters than needed to be freed, especially at larger sample si...

398 citations


Journal ArticleDOI
TL;DR: In this article, a bootstrap method for estimating mean squared error and smoothing parameter in nonparametric problems is described, which involves using a resample of smaller size than the original sample.

Book
12 Dec 1990

Journal ArticleDOI
TL;DR: In this paper, the MULTILOG computer program under default conditions was used for parameter recovery in the graded response model, and 36 simulated data sets were generated that varied on true θ distribution, true item discrimination distribution, and calibration sample size.
Abstract: The graded response model can be used to describe test-taking behavior when item responses are classified into ordered categories. In this study, parameter recovery in the graded response model was investigated using the MULTILOG computer program under default conditions. Based on items having five response categories, 36 simulated data sets were generated that varied on true θ distribution, true item discrimination distribution, and calibration sample size. The findings suggest, first, the correlations between the true and estimated parameters were consistently greater than 0.85 with sample sizes of at least 500. Second, the root mean square error differences between true and estimated parameters were comparable with results from binary data parameter recovery studies. Of special note was the finding that the calibration sample size had little influence on the recovery of the true ability parameter but did influence item-parameter recovery. Therefore, it appeared that item-parameter estimation error, due to small calibration samples, did not result in poor person-parameter estimation. It was concluded that at least 500 examinees are needed to achieve an adequate calibration under the graded model.

Journal ArticleDOI
01 Oct 1990-Ecology
TL;DR: In this article, the authors used papers which reported little evidence of the effect of acid deposition on forest ecosystems to point out the problems of statistical reporting practices in ecology and suggest that often we are not given the information necessary to judge the strength of the evidence in these reports; i.e., their data analyses or experiments may have had power too low to warrant being used as evidence.
Abstract: The author uses papers which reported little evidence of the effect of acid deposition on forest ecosystems to point out the problems of statistical reporting practices in ecology. He suggests that often we are not given the information necessary to judge the strength of the evidence in these reports; i.e., their data analyses or experiments may have had power too low to warrant being used as evidence. Low power could result from sample sizes too small or data sets too variable to have a high chance of finding a statistically significant effect of acid deposition. Risk assessments relevant to natural resource management should be based on concepts of probability of type II error, power and detectable effect size.

Journal ArticleDOI
TL;DR: In this paper, the applicability of the large sample theory to maximum likelihood estimates of total indirect effects in sample sizes of 50, 100, 200, 400, and 800 was examined using Monte Carlo methods and the results suggest that sample szes of 200 or more and 400 or more are required for models such as Model 1 and Model 2, respectively.
Abstract: The large sample distribution of total indirect effects in covariance structure models in well known. Using Monte Carlo methods, this study examines the applicability of the large sample theory to maximum likelihood estimates oftotal indirect effects in sample sizes of 50, 100, 200, 400, and 800. Two models are studied. Model 1 is a recursive model with observable variables and Model 2 is a nonrecursive model with latent variables. For the large sample theory to apply, the results suggest that sample szes of 200 or more and 400 or more are required for models such as Model 1 and Model 2, respectively.

Posted Content
TL;DR: In this article, the authors derived the asymptotic distribution for a vector of sample autocorrelations of regression residuals from a quite general linear model, which forms the basis for a test of the null hypothesis that the regression error follows a moving average of order q [greater than or equal] 0 against the general alternative that auto-correlations of the regression regression error are non-zero at lags greater than q. By allowing for endogenous, predetermined and/or exogenous regressors, for estimation by either ordinary least squares or a number of instrumental variables
Abstract: This paper derives the asymptotic distribution for a vector of sample autocorrelations of regression residuals from a quite general linear model. The asymptotic distribution forms the basis for a test of the null hypothesis that the regression error follows a moving average of order q [greaterthan or equal] 0 against the general alternative that autocorrelations of the regression error are non-zero at lags greater than q. By allowing for endogenous, predetermined and/or exogenous regressors, for estimation by either ordinary least squares or a number of instrumental variables techniques, for the case q>0, and for a conditionally heteroscedastic error term, the test described here is applicable in a variety of situations where such popular tests as the Box-Pierce (1970) test, Durbin's (1970) h test, and Godfrey's (1978b) Lagrange multiplier test are net applicable. The finite sample properties of the test are examined in Monte Carlo simulations where, with a sample sizes of 50 and 100 observations, the test appears to be quite reliable.

Journal ArticleDOI
TL;DR: In this article, the authors considered a continuous idealization of the PET reconstruction problem, considered as an example of bivariate density estimation based on indirect observations, and established exact minimax rates of convergence of estimation, for all possible estimators, over suitable smoothness classes of functions.
Abstract: Several algorithms for image reconstruction in positron emission tomography (PET) have been described in the medical and statistical literature. We study a continuous idealization of the PET reconstruction problem, considered as an example of bivariate density estimation based on indirect observations. Given a large sample of indirect observations, we consider the size of the equivalent sample of observations, whose original exact positions would allow equally accurate estimation of the image of interest. Both for indirect and for direct observations, we establish exact minimax rates of convergence of estimation, for all possible estimators, over suitable smoothness classes of functions. A key technical device is a modulus of continuity appropriate to global function estimation. For indirect data and (in practice unobservable) direct data, the rates for mean integrated square error are $n^{-p/(p + 2)}$ and $(n/\log n)^{-p/(p + 1)}$, respectively, for densities in a class corresponding to bounded square-integrable $p$th derivatives. We obtain numerical values for equivalent sample sizes for minimax linear estimators using a slightly modified error criterion. Modifications of the model to incorporate attenuation and the third dimension effect do not affect the minimax rates. The approach of the paper is applicable to a wide class of linear inverse problems.

Journal ArticleDOI
TL;DR: In this paper, the statistical properties of estimates of pointwise dimension and their errors have been investigated for some maps and for some random variables, and substantial bias in the estimates is detected and modelled as a function of the sample size and the embedding dimension.
Abstract: The statistical properties of estimates of pointwise dimension and their errors have been investigated for some maps and for some random variables. Substantial bias in the estimates is detected and modelled as a function of the sample size and the embedding dimension. The usual methods for calculating error bars are shown to underestimate the actual error bars by factors of ten and more. Procedures to improve the estimation of dimension in the cases studied are discussed, as are methods to improve the ability to distinguish noise from an attractor when using small data sets. Some idea of small is given when the attractors are similar to the ones studied.

Journal ArticleDOI
TL;DR: The authors present a general formulation to compute sample size and power for case-control and cohort studies to investigate more complex patterns in the odds ratios, such as to distinguish between two different slopes of linear trend, to distinguishBetween two possible dose-response relations, or to distinguish different models for the joint effects of two important exposures.
Abstract: Estimates of sample size and statistical power are essential ingredients in the design of epidemiologic studies. Once an association between disease and exposure has been demonstrated, additional studies are often needed to investigate special features of the relation between exposure, other covariates, and risk of disease. The authors present a general formulation to compute sample size and power for case-control and cohort studies to investigate more complex patterns in the odds ratios, such as to distinguish between two different slopes of linear trend, to distinguish between two possible dose-response relations, or to distinguish different models for the joint effects of two important exposures or of one exposure factor adjusting for another. Such special studies of exposure-response relations may help investigators to distinguish between plausible biologic models and may lead to more realistic models for calculating attributable risk and lifetime disease risk. The sample size formulae are applied to studies of indoor radon exposure and lung cancer and suggest that epidemiologic studies may not be feasible for addressing some issues. For example, if the risk estimates from underground miners' studies are, in truth, not applicable to home exposures and overestimate the gradient of risk from home exposure to radon by, for example, a factor of 2, then enormously large numbers of subjects would be required to detect the difference. Furthermore, if the true interaction between smoking and radon exposure is less than multiplicative, only the largest investigations will have sufficient power to reject additivity. For the simple case of testing for no exposure effect, when exposure is either dichotomous or continuous, these methods yield well-known formulae.

Journal ArticleDOI
TL;DR: In this paper, two factors which are involved in sample size estimation are detailed—namely type I (α) and type II (β) error.

Journal ArticleDOI
TL;DR: Diversity indices, although designed for comparative purposes, often cannot be used as such, due to their sample-size dependence and it is argued here that this dependence is more pronounced in high diversity assemblages than in low diversity assembls and that indices more sensitive to rarer species require larger sample sizes to estimate diversity with reasonable precision.
Abstract: Diversity indices, although designed for comparative purposes, often cannot be used as such, due to their sample-size dependence. I t is argued here that this dependence is more pronounced in h~gh divers~ty than in low diversity assemblages and that indices more sensitive to rarer species require larger sample sizes to estimate diversity with reasonable precision than indices which put more weight on commoner species. This was tested for Hill's diversity numbers No to N, (Hill 1973) and some other commonly used diversity indices for a high-diversity nematode assemblage in the Mediterranean deep sea. Although diversity indices were introduced into the ecological literature more than 20 yr ago and have very often been criticized since, their use in applied ecological research, mainly in pollution impact studies, is still very popular ( e . g . Heip et al. 1988a). A fundamental drawback of many diversity indices is their sample-size dependence (Sanders 1968 and references therein), making comparison between studies difficult. Yet, the main purpose of quantifying diversity by a numerical index is to provide means for comparison between different communities. One way of avoiding incomparability of measurements resulting from different-sized samples was provided by the rarefaction method of Sanders (1968). In this method, one calculates the number of species expected from each sample if sampling size is standardized. Hurlbert (1971) showed that the rarefaction method generally overestimates the expected number of species present and h e introduced an exact computational formula for this index: the expected number of species in a sample with size n , drawn from a population of size N which had S species, is given by i' Inter-Research/Printed in F. R. Germany where Ni represents the number of individuals in the i th species in the full sample (Hurlbert 1971). This index was used by Heck et al. (1975) to estimate sufficient sample size for the calculation of the number of species in a sample. However, a mere species count, like ES (n), does not cover all information present in the community as it is not related to the way the individuals are divided among the species. Thus other diversity measures should be considered as well. Sample size dependence of diversity indices. Intuitively, one expects that not all diversity indices are equally influenced by sample size, and that also the type of community (with high or low diversity) plays a role. Let us consider the influence of sample size on Hill's diversity numbers (N,) of various orders (Hill 1973). Hill's diversity number of order a is given by: S Na = I C Pia I("l-al

Journal ArticleDOI
TL;DR: In this paper, the authors present a simple but effective procedure for determining whether a reasonably large sample comes from a stable population against the alternative of a population with finite higher moments, using the fact that the stable population sample has moments of the fourth and sixth order whose magnitudes increase very rapidly as the sample size increases.
Abstract: We present a simple but effective procedure for determining whether a reasonably large sample comes from a stable population against the alternative that it comes from a population with finite higher moments. The procedure uses the fact that a stable population sample has moments of the fourth and sixth order whose magnitudes increase very rapidly as the sample size increases. This procedure shows convincingly that stock returns, when taken as a group, do not come from stable populations. Even for individual stocks, our results show that the stable-population-model null hypothesis can be rejected for more than 95% of the stocks.

Journal ArticleDOI
12 Jan 1990-JAMA
TL;DR: Using standard formulas, tables that provide the appropriate sample size in determining the performance characteristics of interest are designed, which should result in better studies of laboratory tests and fewer meaningless negative studies.
Abstract: Test performance characteristics are important in assessing the clinical usefulness of laboratory tests and serve as a basis for comparing one test to another. Statistical comparisons of performance characteristics are meaningful only when they can detect medically important differences; that is, when they provide adequate statistical power. This requires choosing the appropriate sample size in determining the performance characteristics of interest. Using standard formulas, we designed tables that provide such sample size requirements. Example problems of sample size determination in laboratory test comparisons are given. Used appropriately, this approach should result in better studies of laboratory tests and fewer meaningless negative studies. ( JAMA . 1990;263:275-278)

Journal ArticleDOI
TL;DR: In this article, the authors test the robustness of a method for estimating abundance that assumes that the underlying distribution of the nonzero observations is lognormal (Pennington, 1983, Biometrics 39, 281-286).
Abstract: We test the robustness of a method for estimating abundance that assumes that the underlying distribution of the nonzero observations is lognormal (Pennington, 1983, Biometrics 39, 281-286). Violations in model assumptions that cannot reliably be detected with moderate sample sizes (-40) lead to biases and large reductions in efficiency. Unless it can be clearly demonstrated from repeated sampling that nonzero values follow a lognormal distribution, the sample mean and variance are more robust than lognormal-based estimators of mean and variance of population abundance.

Journal ArticleDOI
TL;DR: In this paper, the authors attempted to learn more about subjects' understanding of the importance of sample size by systematically changing aspects of the problems they gave to subjects, and they found that people understand that the means of larger samples are more likely to resemble the population mean but not the implications of this fact for the variability of the mean.

Journal ArticleDOI
TL;DR: Arguments are raised against Kaplan's (1990) view that fit indices other than the likelihood ratio test need not be used in covariance structure modeling except when sample size sensitivity is observed.
Abstract: Arguments are raised against Kaplan's (1990) view that fit indices other than the likelihood ratio test need not be used in covariance structure modeling except when sample size sensitivity is observed. Kaplan's criterion for the presence of sample size sensitivity is called into question. Furthermore, it is argued that the likelihood ratio test should not be relied on heavily because (a) it is inherently biased when sample size is large; (b) it is dependent on distributional assumptions as well as a large sample size; (c) the hypothesis that it tests, perfect fit of the model in the population, is not of central empirical interest; and (d) it does not provide information about the important issues of close (but imperfect) fit in the population, and cross-validity to other samples. Other measures of fit are available that overcome these problems, though they are likely to be subject to other problems. The general recommendation is that multiple approaches to assessment of fit be used in conjunction with Kaplan's recommended procedures.

Journal ArticleDOI
TL;DR: Results from simulations modeling the overlapping year-class pattern typical of chinook salmon indicate that the ratio of effective to actual sample size (Se/S) is determined primarily by the ratios of sample size to the effective number of breeders per year (S/Nb).
Abstract: The effects of temporal variation in allele frequency on mixed-stock fishery analysis of Pacific salmon (Oncorhynchus spp.) are examined. The concept of effective sample size (Se), which equates the precision obtained from a sample from a finite population with that from one with no temporal variability, is used to evaluate the magnitude of the problems introduced by genetic drift. Results from simulations modeling the overlapping year-class pattern typical of chinook salmon (O. tshawytscha) indicate that the ratio of effective to actual sample size (Se/S) is determined primarily by the ratio of sample size to the effective number of breeders per year (S/Nb). Unless Nb is large relative to S, effective sample size can be considerably less than the actual number of individuals sampled. Sampling in more than 1 yr results in a higher Se than does taking the same total number of individuals in 1 yr; furthermore, the advantages to multiple sampling are greatest in small populations, in which the effects of gen...

Journal ArticleDOI
TL;DR: In this article, ten nonparametric quantile estimators are compared with respect to small-sample performance characteristics including bias and mean squared error, and Graphical presentations are given for the case of a normal parent distribution, and comparisons with the minimum variance unbiased estimator for normal sampling.
Abstract: Ten nonparametric quantile estimators are compared with respect to small-sample performance characteristics including bias and mean squared error. The estimators considered are all linear functions of order statistics with properties that depend on sample size. Graphical presentations are given for the case of a normal parent distribution, and comparisons are made with the minimum variance unbiased estimator for normal sampling.

Proceedings ArticleDOI
16 Jun 1990
TL;DR: The authors discuss the effects of sample size on the feature selection and error estimation for several types of classifiers and give practical advice to today's designers and users of statistical pattern recognition systems.
Abstract: The authors discuss the effects of sample size on the feature selection and error estimation for several types of classifiers. In addition to surveying prior work in this area, they give practical advice to today's designers and users of statistical pattern recognition systems. It is pointed out that one needs a large number of training samples if a complex classification rule with many features is being utilized. In many pattern recognition problems, the number of potential features is very large and not much is known about the characteristics of the pattern classes under consideration: thus, it is difficult to determine a priori the complexity of the classification rule needed. Therefore, even when the designer believes that a large number of training samples has been selected, they may not be enough for designing and evaluating the classification problem at hand. It is further noted that a small sample size can cause many problems in the design of a pattern recognition system. >

Journal ArticleDOI
TL;DR: The authors investigate the implications of measurement error for the distribution of fat intake using a simple errors-in-measurement model and show how the inference of a more narrow distribution of true intakes affects the calculation of sample size for a cohort study.
Abstract: Dietary measurement error has two consequences relevant to epidemiologic studies: first, a proportion of subjects are misclassified into the wrong groups, and second, the distribution of reported intakes is wider than the distribution of true intakes. While the first effect has been dealt with by several other authors, the second effect has not received as much attention. Using a simple errors-in-measurement model, the authors investigate the implications of measurement error for the distribution of fat intake. They then show how the inference of a more narrow distribution of true intakes affects the calculation of sample size for a cohort study. The authors give an example of the calculation for a cohort study investigating dietary fat and colorectal cancer. This shows that measurement error has a profound effect on sample size, requiring a six- to eightfold increase over the number required in the absence of error, if the correlation coefficient between reported and true intakes is 0.65. Reliable detection of a relative risk of 1.36 between a true intake of greater than 47.5% calories from fat and less than 25% calories from fat would require approximately one million subjects.