scholarly journals A Study on the X ¯ and S Control Charts with Unequal Sample Sizes

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 698
Author(s):  
Chanseok Park ◽  
Min Wang
Keyword(s):  
Sample Size ◽  
Control Charts ◽  
Weighted Average ◽  
Missing Observations ◽  
Population Parameters ◽  
Sample Sizes ◽  
Cost Constraints ◽  
The Mean ◽  
True Population ◽  
Average Sample

The control charts based on X ¯ and S are widely used to monitor the mean and variability of variables and can help quality engineers identify and investigate causes of the process variation. The usual requirement behind these control charts is that the sample sizes from the process are all equal, whereas this requirement may not be satisfied in practice due to missing observations, cost constraints, etc. To deal with this situation, several conventional methods were proposed. However, some methods based on weighted average approaches and an average sample size often result in degraded performance of the control charts because the adopted estimators are biased towards underestimating the true population parameters. These observations motivate us to investigate the existing methods with rigorous proofs and we provide a guideline to practitioners for the best selection to construct the X ¯ and S control charts when the sample sizes are not equal.

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 Methodological Reporting Behavior, Sample Sizes, and Statistical Power in Studies of Event- Related Potentials: Barriers to Reproducibility and Replicability

2019 ◽  
Author(s):  
Peter E Clayson ◽  
Kaylie Amanda Carbine ◽  
Scott Baldwin ◽  
Michael J. Larson
Keyword(s):  
Sample Size ◽  
Statistical Power ◽  
Event Related Potentials ◽  
Reporting Guidelines ◽  
Medium Effect ◽  
Sample Sizes ◽  
Reporting Behavior ◽  
Average Sample Size ◽  
Related Potentials ◽  
Average Sample

Methodological reporting guidelines for studies of event-related potentials (ERPs) were updated in Psychophysiology in 2014. These guidelines facilitate the communication of key methodological parameters (e.g., preprocessing steps). Failing to report key parameters represents a barrier to replication efforts, and difficultly with replicability increases in the presence of small sample sizes and low statistical power. We assessed whether guidelines are followed and estimated the average sample size and power in recent research. Reporting behavior, sample sizes, and statistical designs were coded for 150 randomly-sampled articles from five high-impact journals that frequently publish ERP research from 2011 to 2017. An average of 63% of guidelines were reported, and reporting behavior was similar across journals, suggesting that gaps in reporting is a shortcoming of the field rather than any specific journal. Publication of the guidelines paper had no impact on reporting behavior, suggesting that editors and peer reviewers are not enforcing these recommendations. The average sample size per group was 21. Statistical power was conservatively estimated as .72-.98 for a large effect size, .35-.73 for a medium effect, and .10-.18 for a small effect. These findings indicate that failing to report key guidelines is ubiquitous and that ERP studies are primarily powered to detect large effects. Such low power and insufficient following of reporting guidelines represent substantial barriers to replication efforts. The methodological transparency and replicability of studies can be improved by the open sharing of processing code and experimental tasks and by a priori sample size calculations to ensure adequately powered studies.

A Longitudinal Field Investigation of Auditor Risk Assessments and Sample Size Decisions

2003 ◽  
Vol 78 (4) ◽  
pp. 983-1002 ◽  
Author(s):  
Randal J. Elder ◽  
Robert D. Allen
Keyword(s):  
Sample Size ◽  
Field Investigation ◽  
Risk Assessments ◽  
Sample Sizes ◽  
Accounting Firms ◽  
Inherent Risk ◽  
Changes In Risk ◽  
Larger Sample ◽  
Average Sample ◽  
Do So

This study examines changes in auditor risk assessments and sample size decisions based on information gathered from three large accounting firms for audits during 1994 and 1999. The five-year interval between data collection periods allows us to measure changes in risk assessments and sample sizes between the two periods. Auditors relied on controls and assessed inherent risk below the maximum on most audits, and were more likely to do so in the later period, consistent with a trend of lower risk assessment levels. Average sample sizes declined between 1994 and 1999 for the firms that had larger sample sizes in the earlier period. Overall, we find a significant relationship between inherent risk assessments and sample sizes, but this relationship is stronger in the earlier period and is not significant for all firms, especially in the later period. We find limited evidence of a relationship between control risk and sample sizes.

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.

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.

scholarly journals Monitoring Aggregated Poisson Data for Processes with Time-Varying Sample Sizes

2017 ◽  
Vol 40 (2) ◽  
pp. 243-262 ◽  
Author(s):  
Victor Hugo Morales ◽  
José Alberto Vargas
Keyword(s):  
Sample Size ◽  
Data Aggregation ◽  
Control Charts ◽  
Average Run Length ◽  
Health Surveillance ◽  
Occurrence Rate ◽  
Time Varying ◽  
Sample Sizes ◽  
Time Period ◽  
Poisson Data

This article deals with the effect of data aggregation, when Poisson processes with varying sample sizes, are monitored. These aggregation procedures are necessary or convenient in many applications, and can simplify monitoring processes. In health surveillance applications it is a common practice to aggregate the observations during a certain time period and monitor the processes at the end of it. Also, in this type of applications it is very frequent that the sample size vary over time, which makes that instead of monitor the mean of the processes, as would be in the case of Poisson observations with constant sample size, the occurrence rate of an adverse event is monitored.Two control charts for monitoring the count Poisson data with time-varying sample sizes are proposed by Shen et al. (2013) and Dong et al. (2008). We use the average run length (ARL) to compare the performance of these control charts when different levels of aggregation, two scenarios of generating of sample size and different out-of-control states are considered. Simulation studies show the effect of data aggregation in some situations, as well as those in which their use may be appropriate without significantly compromising the prompt detection of out-of-control signals. We also show the effect of data aggregation with an example of application in health surveillance.

scholarly journals Sampling of cashew nuts from cashew tree clones

2020 ◽  
Vol 42 (1) ◽  
Author(s):  
Adroaldo Guimarães Rossetti ◽  
Francisco das Chagas Vidal Neto ◽  
Levi de Moura Barros
Keyword(s):  
Sample Size ◽  
Genetic Improvement ◽  
Morphological Study ◽  
Stratified Sampling ◽  
Anacardium Occidentale ◽  
Sample Sizes ◽  
Margin Of Error ◽  
The Mean ◽  
Cashew Tree

Abstract The aim of this work was to estimate sample sizes to assist the genetic improvement of the cashew tree (Anacardium occidentale L.). Stratified sampling, comprising five strata (S5, S4, S3, S2, and S1) of five cashew clones (BRS 274, BRS 275, BRS 226, BRS 189 and CCP 76), was effective for estimating the different sample sizes of the nut. Sample size for each clone depends on the weight-nut variance, the margin of error B permitted in the estimates and the desired precision of the results. The increases in sample size with clone variance, lowered the permitted margin of error B, and increased the desired precision of the results. These clones required different sample sizes for a morphological study of the nuts. Larger nuts require larger samples for the same margin of error B. For an error B of 0.2g, the sample size for clones S5, S4 and S3 were n5 = 84, n4 = 49 and n3 = 37 nuts. For clones BRS 274 (S5) and BRS 275 (S4), with better nut classification, the mean weights were respectively 16.79 and 12.78g. Clones BRS 189 (S2) and CCP 76 (S1), with smaller nuts, have a smaller variances, s22 = 0.7638 and s12 = 1.0712, where the mean weight was 8.29 and 7.81g respectively.

scholarly journals Tools for Ergonomic Intervention: The Development and Analysis of a Cost Calculator

2020 ◽  
Vol 64 (1) ◽  
pp. 465-469
Author(s):  
Derek Stephens ◽  
Diana J. Schwerha
Keyword(s):  
Decision Making ◽  
Sample Size ◽  
Small Sample Size ◽  
Small Sample ◽  
Quality Data ◽  
Sample Sizes ◽  
System Usability ◽  
The Mean ◽  
Larger Sample ◽  
Ergonomic Intervention

The purpose of this study was to determine if safety professionals can use an ergonomic intervention costing calculator, which integrates performance and quality data into the costing matrix, to increase communication and better of decision making for the company. The sample size included 9 participants, which included four safety managers, four EHS managers, and one HR generalist. Results showed that all participants found the calculator very useful, well integrated, and it increased communication across the company. The mean System Usability Score (SUS) score was 82, which is rated as a perfectly acceptable software for use. Recommendations from this study include adding some additional features to the calculator, increasing awareness and availability of the calculator, and conducting further analysis using larger sample sizes. Limitations in this study include small sample size and limited interventions that were tested.

Comparaison de différentes approches, modèles et tailles d'échantillons pour l'établissement de relations hauteur-diamètre locales

1995 ◽  
Vol 25 (8) ◽  
pp. 1303-1312 ◽  
Author(s):  
Jean Bégin ◽  
Frédéric Raulier
Keyword(s):  
Sample Size ◽  
Residual Variance ◽  
Sample Plot ◽  
Sample Sizes ◽  
Total Height ◽  
Breast Height ◽  
Mean Diameter ◽  
The Mean ◽  
The Individual ◽  
Model Approach

This study compares the predictability of 3 approaches, 4 models, and 10 different sample sizes to determine local relationships between total height and diameter at breast height in balsam fir stands less than 50 years old. The results show that a system of height–diameter curves based on the mean diameter and mean height of the sampled trees (approach 3) gives the most precise estimations in comparison with curves resulting from pooling all sampled trees in a single height–diameter model (approach 1) and with those resulting from the application of a height–diameter model for each of the combinations of sample plot–measurement periods (approach 2). Depending on the sample size, the residual variance of the total height or the total volume is reduced 2 to 2.5 times for the individual stems and 2 to 15 times for the mean stem, when using approach 3 instead of approach 1. Approach 3 is more precise than approach 2 for sample sizes that vary between three and five sampled trees per plot. However, this gain in precision becomes negligible when the sample size approaches 10 sampled trees per plot.

SAMPLE SIZES REQUIRED FOR PREDICTING ALBUMEN QUALITY IN STORED EGGS FROM EIGHT COMMERCIAL STOCKS

1980 ◽  
Vol 60 (4) ◽  
pp. 979-989 ◽  
Author(s):  
A. T. HILL ◽  
R. C. EISSINGER ◽  
D. M. HAMILTON ◽  
J. PATKO
Keyword(s):  
Sample Size ◽  
Sample Sizes ◽  
Unit Value ◽  
Evaluation Test ◽  
The Mean ◽  
Grading Standards ◽  
Haugh Unit

Over a period of 48 wk, eggs were sampled from the eight commercial strains in a layer evaluation test. Half the eggs were oiled as laid. All eggs, except those broken on day 1, were washed and graded 4 days after lay. Samples of eggs were broken at 1, 5, 12, 19 and 26 days after lay for Haugh unit determination. The number of eggs required to assure the mean Haugh unit value in the sample, within ±2.5 Haugh units of the mean of the population, 90% of the time, was computed. This sample size varied with age of the layer, from 19 to 52 for eggs of layers of brown-shelled eggs and from 16 to 32 for eggs from layers of white-shelled eggs. Days in storage and oiling had comparatively little effect on these sample sizes. The Haugh unit losses varied with length of storage, age of birds and oiling from 1.8 to 22.1. The implications of these losses upon the maintenance of Canada’s egg-grading standards are discussed.

Sign in / Sign up

Export Citation Format

Share Document