Post-stratified estimation: within-strata and total sample size recommendations

2011 ◽  
Vol 41 (5) ◽  
pp. 1130-1139 ◽  
Author(s):  
James A. Westfall ◽  
Paul L. Patterson ◽  
John W. Coulston
Keyword(s):  
Sample Size ◽  
Forest Inventory ◽  
Total Sample ◽  
Standard Errors ◽  
Sample Sizes ◽  
Total Sample Size ◽  
Survey Statistics ◽  
Population Structures ◽  
The Mean ◽  
Volume Estimates

Post-stratification is used to reduce the variance of estimates of the mean. Because the stratification is not fixed in advance, within-strata sample sizes can be quite small. The survey statistics literature provides some guidance on minimum within-strata sample sizes; however, the recommendations and justifications are inconsistent and apply broadly for many different population structures. The impacts of minimum within-strata and total sample sizes on estimates of means and standard errors were examined for two forest inventory variables: proportion forestland and cubic net volume. Estimates of the means seem unbiased across a range of minimum within-strata sample sizes. A ratio that described the decrease in variability with increasing sample size allowed for assessment of minimum within-strata sample requirements to obtain stable estimates of means. This metric indicated that the minimum within-strata sample size should be at least 10. Estimates of standard errors were found to be biased at small total sample sizes. To obtain a bias of less than 3%, the required minimum total sample size was 25 for proportion forestland and 75 for cubic net volume. The results presented allow analysts to determine within-stratum and total sample size requirements corresponding to their criteria for acceptable levels of bias and variability.

Proportion of Returns in Survey Research

1981 ◽  
Vol 41 (4) ◽  
pp. 1033-1038 ◽  
Author(s):  
Lewis R. Aiken
Keyword(s):  
Sample Size ◽  
Survey Research ◽  
Total Sample ◽  
Standard Errors ◽  
Mean Values ◽  
Survey Item ◽  
The Mean ◽  
The Difference

Formulas are given for computing, from the responses of returnees alone, the maximum and minimum values between which the mean response to a survey item must fall in the total sample. Expressions for the standard errors of these maximum and minimum mean values are provided. The difference between the maximum and minimum means, in addition to the magnitudes of their standard errors, vary inversely with the proportion of returns. It is also shown that the extent to which the responses of returnees to a survey item are representative of the responses of the total sample is a function of sample size, proportion of returns, and proportion of returnees responding to the item in a specified direction. Formulas are derived for computing (1) the probability that the difference between the proportion of returnees who respond in a specified direction and the proportion of the total sample responding in that direction will be equal to or greater than an acceptable value, and (2) the minimum proportion of returns required to be fairly confident that the responses of returnees are representative of the responses of the total sample.

Farmers Sustainability and Social Justice: Evidences of Land Inequalities in Uttar Pradesh

2020 ◽  
pp. 232-238
Keyword(s):  
Social Justice ◽  
Sample Size ◽  
Field Survey ◽  
Uttar Pradesh ◽  
Total Sample ◽  
Small Farmers ◽  
Land Fragmentation ◽  
Total Sample Size ◽  
Fragmentation Index ◽  
State Economy

The present study is an attempt to inspect the aspect of social justice among the farmers in terms of fragmented land and farmers’ distress in Uttar Pradesh. The data were obtained through field survey via interview scheduled. A sample of 80 respondents from each targeted village namely, Jansar, Sithauli, Charsoni, and Jonai were selected from each region of Uttar Pradesh state economy. Thus, the study used a total sample size of 320 samples. Simmons index (1968) for canvassing the land fragmentation index (LFI) was applied in the Uttar Pradesh context. Further distress was measured via the help of ratios. It flaunted causes and degrees of distress were relatively high among marginal and small farmers. The result of LFI confirms that high fragmentation was a cause of subsistence income among marginal and small farms compared to semi-medium, and medium farms.

Growth in Self-Actualization (Personal Orientation Inventory) in Adult Encounter Groups

1981 ◽  
Vol 1 (1) ◽  
pp. 5-8
Author(s):  
Les Beach
Keyword(s):  
Sample Size ◽  
Personal Growth ◽  
Total Sample ◽  
Small Samples ◽  
Total Sample Size ◽  
Personal Orientation Inventory ◽  
Self Actualization ◽  
Personal Orientation

To test the efficacy of the Personal Orientation Inventory in assessing growth in self-actualization in relation to encounter groups and to provide a more powerful measure of such changes, pre- and posttest data from 3 highly comparable encounter groups (N = 43) were combined for analysis. Results indicated that the Personal Orientation Inventory is a sensitive instrument for assessing personal growth in encounter groups and that a larger total sample size provides more significant results than those reported for small samples (e. g., fewer than 15 participants).

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.

scholarly journals Small Area Estimation of Postfire Tree Density Using Continuous Forest Inventory Data

2021 ◽  
Vol 4 ◽  
Author(s):  
George C. Gaines ◽  
David L. R. Affleck
Keyword(s):  
Forest Inventory ◽  
Mean Squared Error ◽  
Tree Density ◽  
Standard Errors ◽  
Sample Sizes ◽  
Management Planning ◽  
Forest Management Planning ◽  
Continuous Forest ◽  
Sample Data ◽  
Regional Forest

Wildfire activity in the western United States is expanding and many western forests are struggling to regenerate postfire. Accurate estimates of forest regeneration following wildfire are critical for postfire forest management planning and monitoring forest dynamics. National or regional forest inventory programs can provide vegetation data for direct spatiotemporal domain estimation of postfire tree density, but samples within domains of administrative utility may be small (or empty). Indirect domain expansion estimators, which borrow extra-domain sample data to increase precision of domain estimates, offer a possible alternative. This research evaluates domain sample sizes and direct estimates in domains spanning large geographic extents and ranging from 1 to 10 years in temporal scope. In aggregate, domain sample sizes prove too small and standard errors of direct estimates too high. We subsequently compare two indirect estimators—one generated by averaging over observations that are proximate in space, the other by averaging over observations that are proximate in time—on the basis of estimated standard error. We also present a new estimator of the mean squared error (MSE) of indirect domain estimators which accounts for covariance between direct and indirect domain estimates. Borrowing sample data from within the geographic extents of our domains, but from an expanded set of measurement years, proves to be the superior strategy for augmenting domain sample sizes to reduce domain standard errors in this application. However, MSE estimates prove too frequently negative and highly variable for operational utility in this context, even when averaged over multiple proximate domains.

Unequal Randomisation Can Improve the Economic Efficiency of Clinical Trials

1997 ◽  
Vol 2 (2) ◽  
pp. 81-85 ◽  
Author(s):  
David Torgerson ◽  
Marion Campbell
Keyword(s):  
Clinical Trials ◽  
Sample Size ◽  
Statistical Power ◽  
Cost Effective ◽  
Total Sample ◽  
Cost Ratio ◽  
Treatment Groups ◽  
Total Sample Size ◽  
Effectiveness Analysis ◽  
Research Resources

Objectives: In the majority of clinical trials patients are randomised equally between treatment groups. This approach maximises statistical power for a given total sample size. The objectives of this paper were to determine if, when research costs between treatments differ, it is more economically efficient to randomise additional patients to the cheaper treatment, and how the optimum randomisation ratio can be estimated. Methods: Estimation of the most economically efficient randomisation ratio for four hypothetical clinical trials using cost-effectiveness analysis. Results: When research costs differ between treatments, and there is no constraint on total sample size, it is always more cost-effective to randomise more patients to the cheaper treatment. For example, a cost ratio between the lesser and more expensive treatment of ten, results in a randomisation ratio of 3.2:1. Conclusions: Unequal randomisation ratios should be more widely used as this will achieve optimum statistical power for the lowest expenditure of research resources.

scholarly journals Sample Size to Estimate the Mean and Median of Traits in Canola

2018 ◽  
Vol 10 (11) ◽  
pp. 123
Author(s):  
Alberto Cargnelutti Filho ◽  
Cleiton Antonio Wartha ◽  
Jéssica Andiara Kleinpaul ◽  
Ismael Mario Marcio Neu ◽  
Daniela Lixinski Silveira
Keyword(s):  
Sample Size ◽  
Aerial Part ◽  
Dry Matter ◽  
Central Tendency ◽  
Sample Sizes ◽  
Brassica Napus L ◽  
Fresh Matter ◽  
The Mean ◽  
Productive Traits ◽  
Larger Sample

The aim of this study was to determine the sample size (i.e., number of plants) required to estimate the mean and median of canola (Brassica napus L.) traits of the Hyola 61, Hyola 76, and Hyola 433 hybrids with precision levels. At 124 days after sowing, 225 plants of each hybrid were randomly collected. In each plant, morphological (plant height) and productive traits (number of siliques, fresh matter of siliques, fresh matter of aerial part without siliques, fresh matter of aerial part, dry matter of siliques, dry matter of aerial part without siliques, and dry matter of aerial part) were measured. For each trait, measures of central tendency, variability, skewness, and kurtosis were calculated. Sample size was determined by resampling with replacement of 10,000 resamples. The sample size required for the estimation of measures of central tendency (mean and median) varies between traits and hybrids. Productive traits required larger sample sizes in relation to the morphological traits. Larger sample sizes are required for the hybrids Hyola 433, Hyola 61, and Hyola 76, in this sequence. In order to estimate the mean of canola traits of the Hyola 61, Hyola 76 e Hyola 433 hybrids with the amplitude of the confidence interval of 95% equal to 30% of the estimated mean, 208 plants are required. Whereas 661 plants are necessary to estimate the median with the same precision.

scholarly journals Evaluation of the Skin Infections and Conditions among Students of Gomal Medical College Pakistan

2021 ◽  
pp. 218-222
Author(s):  
Shumaila Parveen ◽  
Yaser M. Alahmadi ◽  
Faryal Adnan ◽  
Eshawa Darr ◽  
Ali Alalawi ◽  
...  
Keyword(s):  
Medical Students ◽  
Observational Study ◽  
Sample Size ◽  
Total Sample ◽  
Skin Infections ◽  
Age Group ◽  
Cross Sectional ◽  
Total Sample Size ◽  
Medical College ◽  
Dermatological Disorders

Objective: The objective of the current study is to determine the pattern of dermatological disorders and to find out their connection with different socioeconomically factors among students of the Medical College. Methodology: The Cross sectional observational study was carried out for the period of three months .The research instrument used was the well developed questionnaire. Results: The questionnaire was administered among total 350 students and the most participant age group was the > 22 and that was about 47.4% of the total sample size the more skin complication seen was the acne that was about 59.7%, in addition to this dandruff contributed very heavily to the hair complexities which makes about 35.7% of the sample. Conclusion: Skin infections especially the cosmetic are very common among the Medical students.

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