Small-Sample Confidence Intervals for p 1 - p 2 and p 1 /p 2 in 2 × 2 Contingency Tables

1980 ◽  
Vol 75 (370) ◽  
pp. 386 ◽  
Author(s):  
Thomas J. Santner ◽  
Mark K. Snell
Keyword(s):  
Confidence Intervals ◽  
Contingency Tables ◽  
Small Sample

SMALL SAMPLE SIZE SCIENTIST

PEDIATRICS ◽  
1989 ◽  
Vol 83 (3) ◽  
pp. A72-A72
Author(s):  
Student
Keyword(s):  
Sample Size ◽  
Confidence Intervals ◽  
Causal Explanation ◽  
Small Sample Size ◽  
Small Sample ◽  
Small Samples ◽  
High Expectations ◽  
Sampling Variation ◽  
The Law ◽  
The Stability

The believer in the law of small numbers practices science as follows: 1. He gambles his research hypotheses on small samples without realizing that the odds against him are unreasonably high. He overestimates power. 2. He has undue confidence in early trends (e.g., the data of the first few subjects) and in the stability of observed patterns (e.g., the number and identity of significant results). He overestimates significance. 3. In evaluating replications, his or others', he has unreasonably high expectations about the replicability of significant results. He underestimates the breadth of confidence intervals. 4. He rarely attributes a deviation of results from expectations to sampling variability, because he finds a causal "explanation" for any discrepancy. Thus, he has little opportunity to recognize sampling variation in action. His belief in the law of small numbers, therefore, will forever remain intact.

Confidence intervals for a difference between lognormal means in cluster randomization trials

2014 ◽  
Vol 26 (2) ◽  
pp. 598-614 ◽  
Author(s):  
Julia Poirier ◽  
GY Zou ◽  
John Koval
Keyword(s):  
Confidence Intervals ◽  
Community Acquired Pneumonia ◽  
Small Sample ◽  
Cluster Randomization ◽  
Critical Pathway ◽  
Arithmetic Means ◽  
Multiple Parameters ◽  
The Difference ◽  
Using Data ◽  
Small Sample Sizes

Cluster randomization trials, in which intact social units are randomized to different interventions, have become popular in the last 25 years. Outcomes from these trials in many cases are positively skewed, following approximately lognormal distributions. When inference is focused on the difference between treatment arm arithmetic means, existent confidence interval procedures either make restricting assumptions or are complex to implement. We approach this problem by assuming log-transformed outcomes from each treatment arm follow a one-way random effects model. The treatment arm means are functions of multiple parameters for which separate confidence intervals are readily available, suggesting that the method of variance estimates recovery may be applied to obtain closed-form confidence intervals. A simulation study showed that this simple approach performs well in small sample sizes in terms of empirical coverage, relatively balanced tail errors, and interval widths as compared to existing methods. The methods are illustrated using data arising from a cluster randomization trial investigating a critical pathway for the treatment of community acquired pneumonia.

scholarly journals True and false positive rates for different criteria of evaluating statistical evidence from clinical trials

2019 ◽  
Vol 19 (1) ◽  
Author(s):  
Don van Ravenzwaaij ◽  
John P. A. Ioannidis
Keyword(s):  
Clinical Trials ◽  
Confidence Intervals ◽  
False Positive ◽  
Evaluation Criteria ◽  
Small Sample ◽  
Statistical Evidence ◽  
Bayes Factors ◽  
True Positive ◽  
Small Sample Sizes ◽  
Meta Analyses

Abstract Background Until recently a typical rule that has often been used for the endorsement of new medications by the Food and Drug Administration has been the existence of at least two statistically significant clinical trials favoring the new medication. This rule has consequences for the true positive (endorsement of an effective treatment) and false positive rates (endorsement of an ineffective treatment). Methods In this paper, we compare true positive and false positive rates for different evaluation criteria through simulations that rely on (1) conventional p-values; (2) confidence intervals based on meta-analyses assuming fixed or random effects; and (3) Bayes factors. We varied threshold levels for statistical evidence, thresholds for what constitutes a clinically meaningful treatment effect, and number of trials conducted. Results Our results show that Bayes factors, meta-analytic confidence intervals, and p-values often have similar performance. Bayes factors may perform better when the number of trials conducted is high and when trials have small sample sizes and clinically meaningful effects are not small, particularly in fields where the number of non-zero effects is relatively large. Conclusions Thinking about realistic effect sizes in conjunction with desirable levels of statistical evidence, as well as quantifying statistical evidence with Bayes factors may help improve decision-making in some circumstances.

scholarly journals Confidence and coverage for Bland–Altman limits of agreement and their approximate confidence intervals

2016 ◽  
Vol 27 (5) ◽  
pp. 1559-1574 ◽  
Author(s):  
Andrew Carkeet ◽  
Yee Teng Goh
Keyword(s):  
Confidence Intervals ◽  
Small Sample ◽  
Interval Methods ◽  
Tolerance Interval ◽  
Confidence Limits ◽  
Sample Sizes ◽  
Limits Of Agreement ◽  
Approximate Methods ◽  
Exact Confidence Intervals ◽  
Tolerance Factors

Bland and Altman described approximate methods in 1986 and 1999 for calculating confidence limits for their 95% limits of agreement, approximations which assume large subject numbers. In this paper, these approximations are compared with exact confidence intervals calculated using two-sided tolerance intervals for a normal distribution. The approximations are compared in terms of the tolerance factors themselves but also in terms of the exact confidence limits and the exact limits of agreement coverage corresponding to the approximate confidence interval methods. Using similar methods the 50th percentile of the tolerance interval are compared with the k values of 1.96 and 2, which Bland and Altman used to define limits of agreements (i.e. [Formula: see text]+/− 1.96Sd and [Formula: see text]+/− 2Sd). For limits of agreement outer confidence intervals, Bland and Altman’s approximations are too permissive for sample sizes <40 (1999 approximation) and <76 (1986 approximation). For inner confidence limits the approximations are poorer, being permissive for sample sizes of <490 (1986 approximation) and all practical sample sizes (1999 approximation). Exact confidence intervals for 95% limits of agreements, based on two-sided tolerance factors, can be calculated easily based on tables and should be used in preference to the approximate methods, especially for small sample sizes.

Bootstrap confidence limits for groundfish trawl survey estimates of mean abundance

1997 ◽  
Vol 54 (3) ◽  
pp. 616-630 ◽  
Author(s):  
S J Smith
Keyword(s):  
Confidence Intervals ◽  
Probability Model ◽  
Small Sample ◽  
Trawl Survey ◽  
Confidence Limits ◽  
Complex Sampling ◽  
Survey Estimates ◽  
Small Sample Sizes ◽  
Complex Sampling Designs ◽  
Trawl Surveys

Trawl surveys using stratified random designs are widely used on the east coast of North America to monitor groundfish populations. Statistical quantities estimated from these surveys are derived via a randomization basis and do not require that a probability model be postulated for the data. However, the large sample properties of these estimates may not be appropriate for the small sample sizes and skewed data characteristic of bottom trawl surveys. In this paper, three bootstrap resampling strategies that incorporate complex sampling designs are used to explore the properties of estimates for small sample situations. A new form for the bias-corrected and accelerated confidence intervals is introduced for stratified random surveys. Simulation results indicate that the bias-corrected and accelerated confidence limits may overcorrect for the trawl survey data and that percentile limits were closer to the expected values. Nonparametric density estimates were used to investigate the effects of unusually large catches of fish on the bootstrap estimates and confidence intervals. Bootstrap variance estimates decreased as increasingly smoother distributions were assumed for the observations in the stratum with the large catch. Lower confidence limits generally increased with increasing smoothness but the upper bound depended upon assumptions about the shape of the distribution.

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