Improved strategy for computation of population mean under double stratified sampling framework

Abstract The article contains a new technique to estimate the mean of the variate of the interest of the finite population with the help of two auxiliary variates. The technique complies well with the stratified population in which each strata proportion is predicted by taking an initial sample called the first phase sample. When the first phase sample is taken, a second sample is taken from the first sample which is called the second phase sample which is used to estimate the mean of the variate of the interest. In our study, we have considered the population which has two correlated auxiliary variates that pass almost through the origin. In such a situation ratio estimation technique and product estimation technique that provides improved estimates of the mean of the variate of the interest. Our technique considers a ratio-product type exponential estimator of which we have established efficiency theoretically as well as empirically.

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Matrixplasty for the Treatment of Severe Incurved Toenail with Growth Plate Deformity

Journal of the American Podiatric Medical Association ◽

10.7547/1020198 ◽

2012 ◽

Vol 102 (3) ◽

pp. 198-204

Author(s):

J.-Young Kim

Keyword(s):

Growth Plate ◽

Clinical Results ◽

New Technique ◽

Partial Removal ◽

Edge Angle ◽

Results Of Treatment ◽

The Mean ◽

A New Technique ◽

Ingrown Toenails

Background: Severely incurved toenails are accompanied by deformity of the toenail growth plate. In such a condition, partial removal of the nail and nail bed and simple unfolding of the nail itself frequently result in the recurrence of symptoms. We sought to design and develop a new technique for the treatment of incurved toenail with growth plate deformity and to report the results of treating this disease entity. Methods: Forty consecutive patients (52 cases) underwent treatment of symptomatic incurved toenails with a new technique named matrixplasty. The mean ± SD patient age was 40.3 ± 18.9 years. Last follow-up was at a mean ± SD of 18.0 ± 1.3 months. An American Orthopedic Foot and Ankle Society (AOFAS) forefoot hallux score was assigned, and patients were evaluated before treatment and at last follow-up. Patient satisfaction and the recurrence rate of the deformity were evaluated. For evaluation of improvement in toenail shape, the center to edge angle of the toenail was measured before treatment and at last follow-up. The complication rate was also evaluated. Results: All of the ingrown toenails healed, and the nail deformities were corrected within 3 weeks after the procedure. None of the incurved toenails had recurred by last follow-up. The mean pretreatment AOFAS forefoot hallux score was 72.9, and it improved to 99.6 by last follow-up (P < .001). Every patient was very satisfied or satisfied with the results of treatment. The mean ± SD center to edge angle of the toenail improved from 53.3° ± 9.5° to 15.3° ± 5.2° by last follow-up (P < .001). Minor paronychia, which was managed with local wound dressing and oral antibiotics, was identified in four cases. No other complication was identified. Conclusions: Matrixplasty showed excellent clinical results in the treatment of severe incurved toenail, and this newly developed procedure showed improvement of the deformed toenail and its growth plate. (J Am Podiatr Med Assoc 102(3): 198–204, 2012)

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A Two-Phase Sample Design for Estimating the Finite Population Mean When There Is Nonresponse

Survey Sampling and Measurement ◽

10.1016/b978-0-12-513350-0.50014-4 ◽

1978 ◽

pp. 143-155

Author(s):

BAHADUR SINGH ◽

J. SEDRANSK

Keyword(s):

Finite Population ◽

Sample Design ◽

Two Phase ◽

Population Mean ◽

Phase Sample

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Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

Journal of Probability and Statistics ◽

10.1155/2015/248374 ◽

2015 ◽

Vol 2015 ◽

pp. 1-5 ◽

Cited By ~ 4

Author(s):

Mursala Khan ◽

Rajesh Singh

Keyword(s):

Finite Population ◽

Real Data ◽

Survey Sampling ◽

Systematic Sampling ◽

Auxiliary Variables ◽

Data Set ◽

Population Mean ◽

First Order ◽

The Mean ◽

A Chain

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

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Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

Mathematical Journal of Interdisciplinary Sciences ◽

10.15415/mjis.2020.82006 ◽

2020 ◽

Vol 8 (2) ◽

pp. 49-56

Author(s):

Akan Anieting

Keyword(s):

Mean Squared Error ◽

Auxiliary Variable ◽

Stratified Sampling ◽

Second Phase ◽

Two Phase ◽

Population Mean ◽

Squared Error ◽

Large Sample Approximation ◽

Sample Approximation ◽

Phase Sample

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

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Multi-phase sampling

Sampling Theory ◽

10.1093/oso/9780198815792.003.0010 ◽

2019 ◽

pp. 200-218

Author(s):

David G. Hankin ◽

Michael S. Mohr ◽

Ken B. Newman

Keyword(s):

Optimal Allocation ◽

Cost Effective ◽

Auxiliary Variable ◽

Sampling Effort ◽

Second Phase ◽

Two Phase ◽

Phase Errors ◽

The Mean ◽

Phase Sample ◽

Multi Phase

Attention is restricted to two-phase or double sampling. A large first-phase sample is used to generate a very good estimate of the mean or total of an auxiliary variable, x, which is relatively cheap to measure. Then, a second-phase sample is selected, usually from the first-phase sample, and both auxiliary and target variables are measured in selected second-phase population units. Two-phase ratio or regression estimators can be used effectively in this context. Errors of estimation reflect first-phase uncertainty in the mean or total of the auxiliary variable, and second-phase errors reflect the nature of the relation and correlation between auxiliary and target variables. Accuracy of the two-phase estimator of a proportion depends on sensitivity and specificity. Sensitivity is the probability that a unit possessing a trait (y = 1) will be correctly classified as such whenever the auxiliary variable, x, has value 1, whereas specificity is the probability that a unit not possessing a trait (y = 0) will be correctly classified as such whenever the auxiliary variable, x, has value 0. Optimal allocation results for estimation of means, totals, and proportions allow the most cost-effective allocation of total sampling effort to the first- and second-phases. In double sampling with stratification, a large first-phase sample estimates stratum weights, a second-phase sample estimates stratum means, and a stratified estimator gives an estimate of the overall population mean or total.

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Modified chain regression type estimator for population mean in the presence of non- response

International Journal of Accounting and Economics Studies ◽

10.14419/ijaes.v3i2.5491 ◽

2015 ◽

Vol 3 (2) ◽

pp. 165

Author(s):

Brij Khare ◽

Habib Rehman

Keyword(s):

Sample Size ◽

Empirical Studies ◽

Fixed Cost ◽

Second Phase ◽

Population Mean ◽

Fixed Sample Size ◽

Fixed Sample ◽

Phase Sample ◽

Available Information

<p>A modified chain regression type estimator for population mean in the presence of non-response have been proposed replacing Hansen & Hurwitz (1946) estimator for population mean by Searls (1964) type improved estimator and using Hansen & Hurwitz (1946) estimator for based on available information comparing to the study character in the second phase sample. The expressions for MSE for fixed sample size and also fixed cost have been obtained. The empirical studies show that the proposed estimator is more efficient than the relevant estimators in the case of fixed sample size as well as for fixed cost.</p>

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A New Technique in Management of Pilonidal Sinus, a University Teaching Hospital Experience

International Surgery ◽

10.9738/intsurg-d-13-00064.1 ◽

2013 ◽

Vol 98 (4) ◽

pp. 304-306 ◽

Cited By ~ 7

Author(s):

Saleh M. Aldaqal ◽

Ahmed A. Kensarah ◽

Mostafa Alhabboubi ◽

Abdulrahman A. Ashy

Keyword(s):

Recurrence Rate ◽

Pilonidal Sinus ◽

Primary Closure ◽

Healing Time ◽

New Technique ◽

Controlled Study ◽

P Value ◽

Minimal Amount ◽

The Mean ◽

A New Technique

Abstract This paper evaluates a new technique that can lead to excision of pilonidal sinus with less healing time and low recurrence rate. A prospective randomized double-blind controlled study on 142 patients with pilonidal sinus conducted during the period from September 2008 to March 2012. The patients were prospectively randomized to be operated with one of four surgical techniques, excision and primary closure, or excision after using hydrogen peroxide (H202) and primary closure, or excision without closure, or excision after injection of H202 without closure. The main outcome measures were the healing time and the recurrence rate. Out of 142 patients, 118 patients were males (83%), and 24 were females (17%). The mean age was 24.5 years. The recurrence rate in patients treated with excision after injection of H202 without closure was the lowest (1.8%) with P-value < 0.005, and the mean duration of healing was 30.7 days with P-value < 0.005. We recommend using excision after injection of H202 without closure in management of PNS. Injection of H202 into the pilonidal tracts can give a precise delineation of the affected tracts, which can be excised with minimal amount of surrounding normal tissues and hence lead to a quicker recovery and low recurrence rate.

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New Technique for Quantitative SiO2 Determinations of Silicate Materials by X-Ray Diffraction Analysis of Glass

Advances in X-ray Analysis ◽

10.1154/s0376030800002548 ◽

1963 ◽

Vol 7 ◽

pp. 209-228 ◽

Cited By ~ 1

Author(s):

Douglas B. Nash

Keyword(s):

Diffraction Analysis ◽

Silicate Glasses ◽

New Technique ◽

Inverse Relation ◽

Diffraction Maximum ◽

X Ray Diffraction ◽

X Ray ◽

The Mean ◽

A New Technique ◽

Silicate Materials

AbstractResults of an experimental X-ray study on 96 synthetic glasses show that the 2θ positions of glass diffraction maxima have an inverse relation to SiO2 concentration in silicate glasses. This relationship is the basis of a new technique for semiquantitative determinations of SiOa in silicate materials by X-ray diffraction methods. Samples to be examined are fused and the resulting glass scanned from 12 to 40° 2θ using CiiKa radiation. The mean 2θ position of the diffraction maximum is a measure of the SiOs content of the glass. Calibration curves for both weight and molecular percent SiO2 vs. 2θ are presented in this report. The technique requires only small, unweighed amounts of sample for analysis ; it is simple, rapid, and utilizes standard diffraction equipment without modification. Its accuracy, at present, allows SiOa determinations to within ±1 to 4% of the actual concentration.

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A new technique for the measurement of low fluid velocities

Journal of Fluid Mechanics ◽

10.1017/s0022112064001136 ◽

1964 ◽

Vol 20 (2) ◽

pp. 183-192 ◽

Cited By ~ 40

Author(s):

M. Gaster

Keyword(s):

Free Convection ◽

Mean Value ◽

New Technique ◽

Mean Velocity ◽

Flowing Fluid ◽

Fluid Velocities ◽

New Instrument ◽

The Mean ◽

A New Technique

A new instrument for measuring the velocities of particles suspended in a flowing fluid is described. The instrument is linear and is therefore capable of measuring the mean velocity in a fluctuating stream, even when these fluctuations are greater than this mean value. This particular instrument was developed for free convection work where the velocities to be measured were in the range + k 0.2 in./sec to − 0.2 in./sec, but there seems to be no reason why this range could not be considerably extended.

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