Sample Size for a Specified Width Confidence Interval on the Ratio of Variances from Two Independent Normal Populations

Biometrics ◽  
1963 ◽  
Vol 19 (3) ◽  
pp. 465 ◽  
Author(s):  
Aaron Goldman
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Normal Populations ◽  
Ratio Of Variances ◽  
Width Confidence Interval

scholarly journals Multistage Estimation of the Rayleigh Distribution Variance

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2084
Author(s):  
Ali Yousef ◽  
Ayman A. Amin ◽  
Emad E. Hassan ◽  
Hosny I. Hamdy
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Interval Estimation ◽  
Sequential Estimation ◽  
Rayleigh Distribution ◽  
Point Estimation ◽  
Asymptotic Results ◽  
Squared Error Loss Function ◽  
Estimation Problems ◽  
Width Confidence Interval

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure attains asymptotic second-order efficiency and asymptotic consistency. A series of Monte Carlo simulations were conducted to study the procedure’s performance as the optimal sample size increases. We found that the simulation results agree with the asymptotic results.

scholarly journals The Probability That a Measurement Falls within a Range of Standard Deviations from an Estimate of the Mean

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Louis M. Houston
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
General Equation ◽  
Sample Sizes ◽  
The Mean ◽  
Standard Deviations ◽  
Intermediate Value ◽  
Theoretical Results

We derive a general equation for the probability that a measurement falls within a range of n standard deviations from an estimate of the mean. So, we provide a format that is compatible with a confidence interval centered about the mean that is naturally independent of the sample size. The equation is derived by interpolating theoretical results for extreme sample sizes. The intermediate value of the equation is confirmed with a computational test.

Statistical Principles for Clinical Trials

1998 ◽  
Vol 26 (2) ◽  
pp. 57-65 ◽  
Author(s):  
R Kay
Keyword(s):  
Clinical Trials ◽  
Confidence Interval ◽  
Sample Size ◽  
Sample Size Calculation ◽  
P Value ◽  
Clinical Value ◽  
Treatment Groups ◽  
Correct Calculation ◽  
Intent To Treat ◽  
Comparative Trials

If a trial is to be well designed, and the conclusions drawn from it valid, a thorough understanding of the benefits and pitfalls of basic statistical principles is required. When setting up a trial, appropriate sample-size calculation is vital. If initial calculations are inaccurate, trial results will be unreliable. The principle of intent-to-treat in comparative trials is examined. Randomization as a method of selecting patients to treatment is essential to ensure that the treatment groups are equalized in terms of avoiding biased allocation in the mix of patients within groups. Once trial results are available the correct calculation and interpretation of the P-value is important. Its limitations are examined, and the use of the confidence interval to help draw valid conclusions regarding the clinical value of treatments is explored.

scholarly journals From unloading to trimming: studying bruising in individual slaughter cattle

2020 ◽  
Vol 4 (3) ◽  
Author(s):  
Helen C Kline ◽  
Zachary D Weller ◽  
Temple Grandin ◽  
Ryan J Algino ◽  
Lily N Edwards-Callaway
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Animal Welfare ◽  
Economic Value ◽  
Traumatic Events ◽  
Visual Assessment ◽  
Slaughter Cattle ◽  
Number Of Factors ◽  
Trim Loss ◽  
Analyze Data

Abstract Livestock bruising is both an animal welfare concern and a detriment to the economic value of carcasses. Understanding the causes of bruising is challenging due to the numerous factors that have been shown to be related to bruise prevalence. While most cattle bruising studies collect and analyze data on truckload lots of cattle, this study followed a large number (n = 585) of individual animals from unloading through postmortem processing at five different slaughter plants. Both visual bruise presence and location was recorded postmortem prior to carcass trimming. By linking postmortem data to animal sex, breed, trailer compartment, and traumatic events at unloading, a rich analysis of a number of factors related to bruise prevalence was developed. Results showed varying levels of agreement with other published bruising studies, underscoring the complexity of assessing the factors that affect bruising. Bruising prevalence varied across different sex class types (P < 0.001); 36.5% of steers [95% confidence interval (CI): 31.7, 41.6; n = 378], 52.8% of cows (45.6, 60.0; 193), and 64.3% of bulls (no CI calculated due to sample size; 14) were bruised. There was a difference in bruise prevalence by trailer compartment (P = 0.035) in potbelly trailers, indicating that cattle transported in the top deck were less likely to be bruised (95% CI: 26.6, 40.4; n = 63) compared to cattle that were transported in the bottom deck (95% CI: 39.6, 54.2; n = 89). Results indicated that visual assessment of bruising underestimated carcass bruise trimming. While 42.6% of the carcasses were visibly bruised, 57.9% of carcasses were trimmed due to bruising, suggesting that visual assessment is not able to capture all of the carcass loss associated with bruising. Furthermore, bruises that appeared small visually were often indicators of larger, subsurface bruising, creating an “iceberg effect” of trim loss due to bruising.

Precision of sensitivity estimations in diagnostic test evaluations. Power functions for comparisons of sensitivities of two tests.

1985 ◽  
Vol 31 (4) ◽  
pp. 574-580 ◽  
Author(s):  
K Linnet
Keyword(s):  
Confidence Interval ◽  
Sample Size ◽  
Diagnostic Test ◽  
Diagnostic Tests ◽  
Sample Sizes ◽  
Power Functions ◽  
Gaussian Distributions ◽  
Sensitivity Estimate

Abstract The precision of estimates of the sensitivity of diagnostic tests is evaluated. "Sensitivity" is defined as the fraction of diseased subjects with test values exceeding the 0.975-fractile of the distribution of control values. An estimate of the sensitivity is subject to sample variation because of variation of both control observations and patient observations. If gaussian distributions are assumed, the 0.95-confidence interval for a sensitivity estimate is up to +/- 0.15 for a sample of 100 controls and 100 patients. For the same sample size, minimum differences of 0.08 to 0.32 of sensitivities of two tests are established as significant with a power of 0.90. For some published diagnostic test evaluations the median sample sizes for controls and patients were 63 and 33, respectively. I show that, to obtain a reasonable precision of sensitivity estimates and a reasonable power when two tests are being compared, the number of samples should in general be considerably larger.

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