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PubMedDate not supplied

Autocorrelation and variability of indoor air quality measurements.

Measurements of gaseous and particulate concentrations are used to characterize the indoor environment, but such measurements may reflect temporary conditions that are not representative of longer time periods. Moreover, indoor air quality (IAQ) measurements are autocorrelated, a result of limited mixing and air exchange, cyclic emissions, HVAC operation, and other factors. This article analyzes the autocorrelation and variability of IAQ measurements using time series analysis techniques in conjunction with a simple IAQ model. Autocorrelations may be estimated using the air exchange rate (alpha) and ventilation effectiveness (epsilon) of the building or room under study, or estimated from pollutant measurements. From this, the variability, required sample size, and other sampling parameters are estimated. The method is tested in a case study in which particle number, fungi, bacteria, and carbon dioxide concentrations were continuously measured in an office building over a 1-week period. The estimated air exchange rate (1.4/hr) for area studied was predicted to yield autocorrelation coefficients of approximately 0.5 for measurements collected on 30-min intervals. Autocorrelation coefficients based on airborne measurements (lag 0.5 hr) ranged from 0.5 to 0.7 for 1-25 microm diameter particles, fungi, and CO2, but near zero for particles < or =1 microm diameter and bacteria. As expected, the variability of measurements with the lowest autocorrelation decreased the most at long sampling times. The implications for spaces with low alpha * epsilon products are that measurements may not benefit significantly from longer averaging periods, measurements on any single day may not be representative, and day-to-day variability may be significant. Steps to determine sample sizes, averaging times, and sampling strategies that can improve the representativeness of IAQ measurements are discussed.

Air Pollutants↗
PubMed2006

Parasite prevalence and sample size: misconceptions and solutions.

Parasite prevalence (the proportion of infected hosts) is a common measure used to describe parasitaemias and to unravel ecological and evolutionary factors that influence host-parasite relationships. Prevalence estimates are often based on small sample sizes because of either low abundance of the hosts or logistical problems associated with their capture or laboratory analysis. Because the accuracy of prevalence estimates is lower with small sample sizes, addressing sample size has been a common problem when dealing with prevalence data. Different methods are currently being applied to overcome this statistical challenge, but far from being different correct ways of solving a same problem, some are clearly wrong, and others need improvement.

Animals↗
PubMed1998

Regression-based reference limits: determination of sufficient sample size.

Regression analysis is the method of choice for the production of covariate-dependent reference limits. There are currently no recommendations on what sample size should be used when regression-based reference limits and confidence intervals are calculated. In this study we used Monte Carlo simulation to study a reference sample group of 374 age-dependent hemoglobin values. From this sample, 5000 random subsamples, with replacement, were constructed with 10-220 observations per sample. Regression analysis was used to estimate age-dependent 95% reference intervals for hemoglobin concentrations and erythrocyte counts. The maximum difference between mean values of the root mean square error and original values for hemoglobin was 0.05 g/L when the sample size was > or = 60. The parameter estimators and width of reference intervals changed negligibly from the values calculated from the original sample regardless of what sample size was used. SDs and CVs for these factors changed rapidly up to a sample size of 30; after that changes were smaller. The largest and smallest absolute differences in root mean square error and width of reference interval between sample values and values calculated from the original sample were also evaluated. As expected, differences were largest in small sample sizes, and as sample size increased differences decreased. To obtain appropriate reference limits and confidence intervals, we propose the following scheme: (a) check whether the assumptions of regression analysis can be fulfilled with/without transformation of data; (b) check that the value of v, which describes how the covariate value is situated in relation to both the mean value and the spread of the covariate values, does not exceed 0.1 at minimum and maximum covariate positions; and (c) if steps 1 and 2 can be accepted, the reference limits with confidence intervals can be produced by regression analysis, and the minimum acceptable sample size will be approximately 70.

Child, Preschool↗
PubMed1978

Sample size needed for student ratings of instruction.

The number of evaluation forms students are asked to complete is multiplying. To reduce that number, the present study determines the minimum sample size needed for accurate student ratings of instruction. Typical questionnaire items using four- and seven-category ratings scales were studied. Data for four class sizes (40, 60, 100, 140) were sampled in graduated sizes, and a standard error of the mean was computed for each sample size. A permissible error index was computed to estimate the accuracy of ratings obtained from any sample size needed for the four different class sizes. Figures are presented from which minimum sample sizes necessary for accurate student evaluation of instruction can be computed. The figures show that sampling only one-third of classes of 100-140 students is sufficient to obtain accurate evaluations.

Evaluation Studies as Topic↗
PubMed1993

Estimating and testing autocorrelation with small samples: a comparison of the C-statistic to a modified estimator.

Huitema and McKean (Psychological Bulletin, 110, 291-304, 1991) recently showed, in a Monte-Carlo study, that five conventional estimators of first-order autocorrelation perform poorly for small (< 50) sample sizes. They suggested a modified estimator and a test for autocorrelation. We examine an estimator not considered by Huitema and McKean: the C-statistic (Young, Annals of Mathematical Statistics, 12, 293-300, 1941). A Monte-Carlo study of the small sample properties of the C-statistic shows that it performs as well or better than the modified estimator suggested by Huitema and McKean (1991). The C-statistic is also shown to be closely related to the d-statistic of the widely used Durbin-Watson test.

Biometry↗
PubMed1989

Comparison of iced and room temperature injectate for thermodilution cardiac output.

Cardiac output estimation by thermodilution is carried out using room temperature or iced injectate, but the accuracy and variability of the two methods is not well documented. Room temperature and iced injectate were compared in 21 patients undergoing diagnostic cardiac catheterization. Dextrose injectate (10 ml) was administered in prefilled syringes left to stand either in iced water or in room air. Four injections were made sequentially with room temperature and iced injectate. Cardiac output by room temperature and iced injectate were not significantly different (4.70 +/- 1.22 for room temperature and 4.90 +/- 1.37 for iced injectate, n = 21, P = 0.155). There was a significant difference in the variance of the estimations by the two methods (room temperature = 0.296, iced = 0.120, P less than 0.005). From this variance the calculated number of measurements needed to estimate cardiac output to +/- 0.5 L/min with 95% confidence is seven for room temperature and four for iced injectate. For five patients with cardiac output less than 4.00 L/min with room temperature injectate, cardiac output with iced injectate was significantly higher (3.33 +/- 0.34 for room temperature vs. 3.69 +/- 0.49 for iced injectate, P = 0.05). Thus room temperature injectate generally gives a satisfactory cardiac output estimation but with significantly greater variability than iced injectate. Sample size for accurate cardiac output estimation must be greater with room temperature injectate. Iced injectate may over-estimate output when cardiac output is low.

Cardiac Catheterization↗
PubMedDate not supplied

Overview of important design issues for a National Human Exposure Assessment Survey.

Exposure issues have important consequences for regulatory decisions. Reliable answers to exposure questions are critical for site cleanup, model validation, and cumulative risk issues, as well as giving perspective on our risk estimates. This paper discusses some of the important issues in designing the National Human Exposure Assessment Survey (NHEXAS) and, by implication, other exposure-monitoring-based studies as well. Sampling design issues are discussed in terms useful to exposure assessors. These issues include simple random sample designs versus more complex multistage designs, design efficiency, how to determine the sample size for the desired precision of the estimate, and the effects of stratification and oversampling on the needed sample size. This paper also discusses several important nonsampling issues such as population definition, response rates, and several potential sources of error in interpreting the monitoring results.

Data Collection↗
PubMed1995

A meta-analysis of the relationship of child sexual abuse to adult psychological adjustment.

This paper reports on meta-analyses of the relations of child sexual abuse to adult psychological adjustment. Results indicated statistically significant relationships between the experience of child sexual abuse and subsequent difficulties in psychological adjustment as measured by psychological symptomatology, depression, and self-esteem. Significant heterogeneity occurred across studies using a variety of different subject populations, research designs, and assessment methods. Some explanation of the effect size variance was partially accounted for by certain identified study characteristics, most notable in regard to sample source used in the included studies. Student samples consistently generated smaller, more homogeneous effect size estimates than did community or clinical samples. This indicates that abused subjects drawn from student samples may experience fewer impairments in psychological adjustment, when compared to abused subjects drawn from community or clinical samples. The implications of these findings and suggestions for future research are discussed.

Adaptation, Psychological↗
PubMed2002

Dealing with competing risks: testing covariates and calculating sample size.

It is universally agreed that Kaplan-Meier estimates overestimate the probability of the event of interest in the presence of competing risks. Kalbfleisch and Prentice recommend using the cumulative incidence as an estimate of the probability of an event of interest. However, there is no consensus on how to test the effect of a covariate in the presence of competing risks. Using simulations, this paper illustrates that the Cox proportional hazards model gives valid results when employed in testing the effect of a covariate on the hazard rate and when estimating the hazard ratio. A method to calculate the sample size for testing the effect of a covariate on outcome in the presence of competing risks is also provided.

Breast Neoplasms↗
PubMed2003

Incorporating covariates into standard line transect analyses.

An implicit assumption of standard line transect methodology is that detection probabilities depend solely on the perpendicular distance of detected objects to the transect line. Heterogeneity in detection probabilities is commonly minimized using stratification, but this may be precluded by small sample sizes. We develop a general methodology which allows the effects of multiple covariates to be directly incorporated into the estimation procedure using a conditional likelihood approach. Small sample size properties of estimators are examined via simulations. As an example the method is applied to eastern tropical Pacific dolphin sightings data.

Analysis of Variance↗
PubMed2004

Bayesian sample size determination for prevalence and diagnostic test studies in the absence of a gold standard test.

Planning studies involving diagnostic tests is complicated by the fact that virtually no test provides perfectly accurate results. The misclassification induced by imperfect sensitivities and specificities of diagnostic tests must be taken into account, whether the primary goal of the study is to estimate the prevalence of a disease in a population or to investigate the properties of a new diagnostic test. Previous work on sample size requirements for estimating the prevalence of disease in the case of a single imperfect test showed very large discrepancies in size when compared to methods that assume a perfect test. In this article we extend these methods to include two conditionally independent imperfect tests, and apply several different criteria for Bayesian sample size determination to the design of such studies. We consider both disease prevalence studies and studies designed to estimate the sensitivity and specificity of diagnostic tests. As the problem is typically nonidentifiable, we investigate the limits on the accuracy of parameter estimation as the sample size approaches infinity. Through two examples from infectious diseases, we illustrate the changes in sample sizes that arise when two tests are applied to individuals in a study rather than a single test. Although smaller sample sizes are often found in the two-test situation, they can still be prohibitively large unless accurate information is available about the sensitivities and specificities of the tests being used.

Bayes Theorem↗
PubMed2003

In vitro evaluation of ultrasound Doppler strain rate imaging: modification for measurement in a slowly moving tissue phantom.

Doppler strain rate imaging (SRI) was evaluated in vitro using a silicone strip phantom mimicking slowly moving tissue. A test apparatus was developed that enabled controlled strain experiments with variable strain and strain rate to be performed. SRI strain was measured at eight different calculated strains (range 5.7 to 63.4 %) at three different pump speeds with tissue velocity 0.1, 0.5 and 1.0 mm/s. The effect of varying tissue velocity and strain sample size on the measured SRI strain was elaborated. SRI strains agreed well with calculated values for strain when SRI strain was measured as the average over the whole strip cross-section and the strain sample size was 1.9 mm (mean difference = 2.78%, limits of agreement +/- 9.97% for tissue velocity 1.0 mm/s, n = 8). The variance was substantial if single central samples were used, especially for strain sample size of 0.8 mm (mean difference = -7.47%, limits of agreement +/- 20.90 for tissue velocity 0.5 mm/s, n = 24). Increasing the strain sample size to 1.9 mm removed some of the underestimation (giving mean difference of -4.46%, n = 24). We found low intra- and interobserver variation. This study indicates that, for the SRI method to give accurate estimates of strain, strain sample size should be in the region of 2 mm. Averaging over several ultrasound (US) beams increased the accuracy further.

Elasticity↗
PubMed2000

Validity and coverage of estimates of relative accuracy.

PURPOSE: Studies comparing test accuracy often restrict the confirmation procedure to subjects classified as positive by either test. Relative sensitivity (RSN) and relative false-positive rate (RFP) are two estimable comparative measures of accuracy. This article evaluates the influence of sample size, disease prevalence, and test accuracy on the validity of point estimates of RSN and RFP, and on the coverage of their confidence intervals (CI). METHODS: For each combination of sample size, disease prevalence, test accuracy, and interdependence between tests 1,000 samples were generated using computer simulations. The percent bias in the RSN and RFP estimates was measured by comparing the means of the 1,000 values computed in each simulation (log-transformed) with their theoretical values. Coverage of the estimated CI was measured by computing the proportion that actually included the theoretical values. Application of these methods was illustrated with data from a study comparing mammography and physical examination in screening for breast cancer. RESULTS: RSN estimates were valid if the true number of diseased cases exceeded 30, and RFP estimates were valid if the number of nondiseased subjects exceeded 200. When the numbers of diseased and nondiseased subjects exceeded 150 each, the 95% CI of RSN and RFP provided adequate coverage of the parameters (95 +/- 2%). CONCLUSION: Sample size is the most important variable for the validity and coverage of RSN and RFP estimates. For small samples, validity and coverage of RSN and RFP also depend on the accuracy of each test and on the degree of interdependence between the tests.

Adult↗
PubMed1995

Design and feasibility of a national Medicaid Access Survey with state-specific estimates.

This article presents the results of a study to design and assess the feasibility of conducting a national Medicaid Access Survey to generate timely, state-specific estimates of access to care for Medicaid enrollees. State-specific data on Medicaid access is especially relevant because state programs and environments vary considerably and are changing rapidly in ways that could influence access. We analyze (1) basic survey design parameters and instrument content, (2) alternative sampling approaches and their feasibility, (3) pilot test results, (4) the feasibility of using existing national surveys to generate comparison estimates for state-based surveys, and (5) estimates of the required sample size and costs for such a national Medicaid Access Survey. We conclude that a survey generating timely, state-specific estimates of Medicaid access is both feasible and affordable if attention is paid to key design challenges while keeping objectives and design simple.

Budgets↗
PubMed2001

Utility of semivariogram for spatial variation of soil nutrients and the robust analysis of semivariogram.

The spatial variation of soil nutrients in topsoil (0-20 cm) was analyzed using semivariogram in the Zunhua County of Hebei Province, China. The effect on semivariogram with randomly deleted data and kriged estimates using various reduced sample sizes was also analyzed. The semivariograms of available N, total N, available P, organic matter were best described by a spherical model, except for available K, which best fitted a complex structure of exponential model and linear with sill model. The ratio of nugget to total sample variance ranged from 34.4% to 68.4%, indicating the spatial correlation of tested soil nutrients on a large scale was moderately dependent. Among five soil nutrients, available nitrogen and available phosphorus had the shortest spatial correlation range (5 km and 5.5 km), available K had the longest range (25.5 km), whereas total nitrogen and organic matter had intermediate spatial correlation range (14.5 km and 8.5 km). The semivariograms of available N, total N, available P, and organic matter were insensitive to a 50%-60% reduction in original sampling density, while for available K, it is up to 70%. The estimated spatial distributions of total N by kriging, under various reduced sample sizes, all correlated significantly (P = 0.001) with those obtained from original data. The results showed that the semivariogram was a relatively robust tool when used in a large region and sufficient spatial variation information could be retained regardless of a higher deletion proportion of the original data. The original sample data could be reduced by kriging and the estimates showed no loss of spatial information, however, the results may be unreliable unless a clearly identified semivariogram model could be obtained. The results may provide useful information for determining the appropriate sampling densities for these scales of soil survey.

Environmental Monitoring↗
PubMed2003

Simple procedures for blinded sample size adjustment that do not affect the type I error rate.

For normally distributed data, determination of the appropriate sample size requires a knowledge of the variance. Because of the uncertainty in the planning phase, two-stage procedures are attractive where the variance is reestimated from a subsample and the sample size is adjusted if necessary. From a regulatory viewpoint, preserving blindness and maintaining the ability to calculate or control the type I error rate are essential. Recently, a number of proposals have been made for sample size adjustment procedures in the t-test situation. Unfortunately, none of these methods satisfy both these requirements. We show through analytical computations that the type I error rate of the t-test is not affected if simple blind variance estimators are used for sample size recalculation. Furthermore, the results for the expected power of the procedures demonstrate that the methods are effective in ensuring the desired power even under initial misspecification of the variance. A method is discussed that can be applied in a more general setting and that assumes analysis with a permutation test. This procedure maintains the significance level for any design situation and arbitrary blind sample size recalculation strategy.

Anxiety Disorders↗
PubMed1975

Proportions with extraneous variance: two dependent samples.

Data which appear to be binomial proportions sometimes exhibit heterogeneity which results in greater variation than would be exhibited under the binomial distribution. Previous work by the author (Kleinman [1973]) in which estimates of the heterogeneity variances are obtained and used in weighting is extended to the case of comparing means in two dependent samples. The resulting empirical weighting estimates are asymptotically equivalent to exact least squares estimates and Monte Carlo studies for sample size 10 indicate high efficiency relative to exact least squares estimates.

Analysis of Variance↗
PubMed2004

Who was student and why do we care so much about his t-test?

Statistics is the study of populations, how they relate to one another and what effect sampling has in terms of representing the original population. Use of statistical tools has been facilitated by modern computer technology; however, given the ease in which results are obtained, it is easy to overlook potentially incorrect use of the various statistical tests. Statistical tools are invaluable for investigators because they make it possible to determine if scientific results are important. When a test is used, it is important to know that the result of any statistical test is valid to avoid erroneous conclusions. To do so, the investigator must have a basic understanding of the test's assumptions and limitations. Modern statistical packages often include a variety of results relating to the test's applicability to the data analyzed. Not uncommonly, biologists are unfamiliar with these analyses. This review intends to improve the reader's understanding of t-tests by providing a history of Student's t-test, and its assumptions, applications, and limitations. Part 1 of the series ("The Mean and Standard Deviation: What Does It All Mean?") reviewed basic aspects of distributions, measures of central tendency, and dispersion assessment. Small sample size effects on accurate estimation of a population mean and group comparisons for continuous data are presented in this review.

Data Interpretation, Statistical↗