A study of sample size in making decisions about instructional materials /

Project No. 711151.01.

On sample size determination; informal report no. 2 to Systems Analysis Division, Chemical Research and Development Laboratories, Edgewood Arsenal, Md., under Contract DA-18-108-CML-7174.

Mode of access: Internet.

Statnote 8: statistical power and sample size

Statistical software is now commonly available to calculate Power (P') and sample size (N) for most experimental designs. In many circumstances, however, sample size is constrained by lack of time, cost, and in research involving human subjects, the problems of recruiting suitable individuals. In addition, the calculation of N is often based on erroneous assumptions about variability and therefore such estimates are often inaccurate. At best, we would suggest that such calculations provide only a very rough guide of how to proceed in an experiment. Nevertheless, calculation of P' is very useful especially in experiments that have failed to detect a difference which the experimenter thought was present. We would recommend that P' should always be calculated in these circumstances to determine whether the experiment was actually too small to test null hypotheses adequately.

Sample size estimation and statistical power analyses

The concept of sample size and statistical power estimation is now something that Optometrists that want to perform research, whether it be in practice or in an academic institution, cannot simply hide away from. Ethics committees, journal editors and grant awarding bodies are now increasingly requesting that all research be backed up with sample size and statistical power estimation in order to justify any study and its findings. This article presents a step-by-step guide of the process for determining sample sizeand statistical power. It builds on statistical concepts presented in earlier articles in Optometry Today by Richard Armstrong and Frank Eperjesi.

Estimation of Fraction of Distinguished Elements in Population Based on Partially Realized Random Sample

2000 Mathematics Subject Classi cation: 62D05.

Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

Calculation of sample size for stroke trials assessing functional outcome: comparison of binary and ordinal approaches

Background Many acute stroke trials have given neutral results. Sub-optimal statistical analyses may be failing to detect efficacy. Methods which take account of the ordinal nature of functional outcome data are more efficient. We compare sample size calculations for dichotomous and ordinal outcomes for use in stroke trials. Methods Data from stroke trials studying the effects of interventions known to positively or negatively alter functional outcome – Rankin Scale and Barthel Index – were assessed. Sample size was calculated using comparisons of proportions, means, medians (according to Payne), and ordinal data (according to Whitehead). The sample sizes gained from each method were compared using Friedman 2 way ANOVA. Results Fifty-five comparisons (54 173 patients) of active vs. control treatment were assessed. Estimated sample sizes differed significantly depending on the method of calculation (Po00001). The ordering of the methods showed that the ordinal method of Whitehead and comparison of means produced significantly lower sample sizes than the other methods. The ordinal data method on average reduced sample size by 28% (inter-quartile range 14–53%) compared with the comparison of proportions; however, a 22% increase in sample size was seen with the ordinal method for trials assessing thrombolysis. The comparison of medians method of Payne gave the largest sample sizes. Conclusions Choosing an ordinal rather than binary method of analysis allows most trials to be, on average, smaller by approximately 28% for a given statistical power. Smaller trial sample sizes may help by reducing time to completion, complexity, and financial expense. However, ordinal methods may not be optimal for interventions which both improve functional outcome

Treatment trials for neonatal seizures: the effect of design on sample size

Neonatal seizures are common in the neonatal intensive care unit. Clinicians treat these seizures with several anti-epileptic drugs (AEDs) to reduce seizures in a neonate. Current AEDs exhibit sub-optimal efficacy and several randomized control trials (RCT) of novel AEDs are planned. The aim of this study was to measure the influence of trial design on the required sample size of a RCT. We used seizure time courses from 41 term neonates with hypoxic ischaemic encephalopathy to build seizure treatment trial simulations. We used five outcome measures, three AED protocols, eight treatment delays from seizure onset (Td) and four levels of trial AED efficacy to simulate different RCTs. We performed power calculations for each RCT design and analysed the resultant sample size. We also assessed the rate of false positives, or placebo effect, in typical uncontrolled studies. We found that the false positive rate ranged from 5 to 85% of patients depending on RCT design. For controlled trials, the choice of outcome measure had the largest effect on sample size with median differences of 30.7 fold (IQR: 13.7–40.0) across a range of AED protocols, Td and trial AED efficacy (p<0.001). RCTs that compared the trial AED with positive controls required sample sizes with a median fold increase of 3.2 (IQR: 1.9–11.9; p<0.001). Delays in AED administration from seizure onset also increased the required sample size 2.1 fold (IQR: 1.7–2.9; p<0.001). Subgroup analysis showed that RCTs in neonates treated with hypothermia required a median fold increase in sample size of 2.6 (IQR: 2.4–3.0) compared to trials in normothermic neonates (p<0.001). These results show that RCT design has a profound influence on the required sample size. Trials that use a control group, appropriate outcome measure, and control for differences in Td between groups in analysis will be valid and minimise sample size.

Sample size for monitoring sirex populations and their natural enemies.

A vespa-da-madeira, Sirex noctilio Fabricius (Hymenoptera: Siricidae) foi introduzida no Brasil em 1988 e tornou-se a principal praga dos plantios de pínus. Encontra-se distribuída em aproximadamente 1.000.000 de ha em diferentes níveis populacionais nos Estados do Rio Grande do Sul, Santa Catarina, Paraná, São Paulo e Minas Gerais. O controle da população da vespa-da-madeira é feito principalmente pela utilização do nematoide Deladenus siricidicola Bedding (Nematoda: Neothylenchidae). A avaliação da eficiência dos inimigos naturais é dificultada por não haver um sistema de amostragem apropriado. Este estudo testou o sistema de amostragem hierárquica para definir o tamanho da amostra para monitorar a população de S. noctilio e também a eficiência dos inimigos naturais, a qual mostrou-se adequada.

Relationship between Extremal and Sum Processes Generated by the same Point Process

2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.

Characterizations of Exponential Distribution Based on Sample of Size Three

2010 Mathematics Subject Classification: 62G30, 62E10.

Family size, economics and child gender preference: A case study in the Nyeri district of Kenya

Kenyan women have more children, especially in rural areas, than in most developing nations. This is widely believed to be an impediment to Kenya’s economic development. Thus, factors influencing family size in the Kenyan context are important for its future. A brief review of economic theories of fertility leads to the conclusion that both economics and social/cultural factors must be considered simultaneously when examining factors that determine the number of children in a family. The need to do this is borne out in Kenya’s situation by utilising responses from a random sample of rural households in the Nyeri district of Kenya. Economic and social/cultural factors intertwine to influence family sizes in this district. After providing a summary of the main statistical results from the survey, we use multiple regression analysis to explore the influences of a woman’s age, level of education, whether she has outside employment, whether the family keeps livestock, whether she expresses a preference for more boys than girls, whether the family uses only family labour (including child labour) and the size of the farm, which is used as a proxy for family income. It was found that preference for male children has an important positive influence on family size in this district. Women were found to have greater preference for male children than their male counterparts possibly because of their fear of being disinherited if they do not produce an heir for their husbands. Preference for sons was also found in allocation of human capital resources at the household level in that the female respondents were found to have lower levels of education than their male counterparts. Various long-term policies are outlined that may help to reduce the number of offspring of women in Kenya.

Male dominance linked to size and age, but not to 'good genes' in brown trout (Salmo trutta).

BACKGROUND: Males that are successful in intra-sexual competition are often assumed to be of superior quality. In the mating system of most salmonid species, intensive dominance fights are common and the winners monopolise most mates and sire most offspring. We drew a random sample of mature male brown trout (Salmo trutta) from two wild populations and determined their dominance hierarchy or traits linked to dominance. The fish were then stripped and their sperm was used for in vitro fertilisations in two full-factorial breeding designs. We recorded embryo viability until hatching in both experiments, and juvenile survival during 20 months after release into a natural streamlet in the second experiment. Since offspring of brown trout get only genes from their fathers, we used offspring survival as a quality measure to test (i) whether males differ in their genetic quality, and if so, (ii) whether dominance or traits linked to dominance reveal 'good genes'. RESULTS: We found significant additive genetic variance on embryo survival, i.e. males differed in their genetic quality. Older, heavier and larger males were more successful in intra-sexual selection. However, neither dominance nor dominance indicators like body length, weight or age were significantly linked to genetic quality measured as embryo or juvenile survival. CONCLUSION: We found no evidence that females can improve their offspring's genetic viability by mating with large and dominant males. If there still were advantages of mating with dominant males, they may be linked to non-genetic benefits or to genetic advantages that are context dependent and therefore possibly not revealed under our experimental conditions - even if we found significant additive genetic variation for embryo viability under such conditions.

Random measurement error and regression dilution bias.

Summary points: - The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease) - Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null - Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant - Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable

Evaluation of a Bayesian MCMC Random Effects Inference Methodology for Capture-Mark-Recapture Data

Monte Carlo simulation was used to evaluate properties of a simple Bayesian MCMC analysis of the random effects model for single group Cormack-Jolly-Seber capture-recapture data. The MCMC method is applied to the model via a logit link, so parameters p, S are on a logit scale, where logit(S) is assumed to have, and is generated from, a normal distribution with mean μ and variance σ2 . Marginal prior distributions on logit(p) and μ were independent normal with mean zero and standard deviation 1.75 for logit(p) and 100 for μ ; hence minimally informative. Marginal prior distribution on σ2 was placed on τ2=1/σ2 as a gamma distribution with α=β=0.001 . The study design has 432 points spread over 5 factors: occasions (t) , new releases per occasion (u), p, μ , and σ . At each design point 100 independent trials were completed (hence 43,200 trials in total), each with sample size n=10,000 from the parameter posterior distribution. At 128 of these design points comparisons are made to previously reported results from a method of moments procedure. We looked at properties of point and interval inference on μ , and σ based on the posterior mean, median, and mode and equal-tailed 95% credibility interval. Bayesian inference did very well for the parameter μ , but under the conditions used here, MCMC inference performance for σ was mixed: poor for sparse data (i.e., only 7 occasions) or σ=0 , but good when there were sufficient data and not small σ .