This document describes a study that compares different methods for constructing confidence intervals for estimating a binomial proportion p. The study develops a modified interval estimator that imposes a continuity correction. Through numerical simulation and analysis, the study compares the standard interval, non-modified interval, and modified interval based on their coverage probabilities and expected widths for various sample sizes n and parameter values p. The results show that the modified interval has better coverage probability than the standard and non-modified intervals, and that all methods approach the nominal confidence level as n increases.
This document proposes a double acceptance sampling plan for truncated life tests where the lifetime of a product follows a Kumaraswamy-log-logistic distribution. The plan uses a zero-one failure scheme where the first sample size is n1, the second is n2, and the acceptance numbers are c1=0 and c2=1. The minimum sample sizes n1 and n2 are determined to ensure the median life is greater than or equal to the specified lifetime m0 at a given consumer confidence level P*. The operating characteristics and minimum median life ratios are analyzed to minimize producer and consumer risks at specified levels. Numerical examples are provided to illustrate the application of the sampling plan.
This document describes a new method called Likelihood-based Sufficient Dimension Reduction (LAD) for estimating the central subspace. LAD obtains the maximum likelihood estimator of the central subspace under the assumption of conditional normality of the predictors given the response. Analytically and in simulations, LAD is shown to often perform much better than existing methods like Sliced Inverse Regression, Sliced Average Variance Estimation, and Directional Regression. LAD also inherits useful properties from maximum likelihood theory, such as the ability to estimate the dimension of the central subspace and test conditional independence hypotheses.
This document discusses methods for estimating population parameters from sample data, including point estimates, confidence intervals, and determining sample size. It focuses on estimating the population proportion and mean. Key points covered include:
- Obtaining the point estimate of a population proportion or mean from sample data by calculating the sample proportion or mean.
- Constructing confidence intervals for a population proportion or mean based on the point estimate and margin of error, which depends on sample size, confidence level, and population variability.
- Determining the necessary sample size to estimate a population proportion or mean within a specified margin of error and confidence level, using formulas that involve the desired confidence level, margin of error, and an estimate of the population parameter
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document presents a chain sampling plan for truncated life tests when lifetimes follow a generalized exponential distribution. The plan determines the minimum sample size needed to satisfy producer and consumer risks at specified quality levels in terms of the distribution's median. Tables 1 and 2 show the minimum sample sizes and corresponding acceptance numbers for different confidence levels. They also provide the operating characteristic function values for various ratios of the true scale parameter to the specified scale parameter, given a shape parameter of 2. The plan allows accepting a lot if defects are below an acceptance number and no defects occurred in preceding samples, improving on single sampling plans.
An improvised similarity measure for generalized fuzzy numbersjournalBEEI
Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes.
Cointegration and Long-Horizon Forecastingمحمد إسماعيل
This document summarizes research on comparing the accuracy of long-horizon forecasts from multivariate cointegrated systems versus univariate models that ignore cointegration. The main findings are:
1) When accuracy is measured using standard trace mean squared error, imposing cointegration provides no benefit over univariate models at long horizons.
2) Both multivariate and univariate long-horizon forecasts satisfy the cointegrating relationships exactly.
3) The cointegrating combinations of forecast errors from both approaches have finite variance at long horizons.
- The document describes a study that uses a modified Kolmogorov-Smirnov (KS) test to test if the innovations of a GARCH model come from a mixture of normal distributions rather than a standard normal distribution.
- It establishes critical values for the KS test and modified KS (MKS) test through simulation under the null hypothesis. It then uses simulation to calculate the size and power of both tests when the innovations come from alternative distributions like the normal, Student's t, and generalized error distributions.
- The results show that the KS and MKS tests maintain the correct size when the innovations are actually from the mixture of normals. The power of both tests is greater than the nominal level when the innovations come
Parameter Optimisation for Automated Feature Point DetectionDario Panada
Parameter optimization for an automated feature point detection model was explored. Increasing the number of random displacements up to 20 improved performance but additional increases did not. Larger patch sizes consistently improved performance. Increasing the number of decision trees did not affect performance for this single-stage model, unlike previous findings for a two-stage model. Overall, some parameter tuning was found to enhance the model's accuracy but not all parameters significantly impacted results.
This document proposes a double acceptance sampling plan for truncated life tests where the lifetime of a product follows a Kumaraswamy-log-logistic distribution. The plan uses a zero-one failure scheme where the first sample size is n1, the second is n2, and the acceptance numbers are c1=0 and c2=1. The minimum sample sizes n1 and n2 are determined to ensure the median life is greater than or equal to the specified lifetime m0 at a given consumer confidence level P*. The operating characteristics and minimum median life ratios are analyzed to minimize producer and consumer risks at specified levels. Numerical examples are provided to illustrate the application of the sampling plan.
This document describes a new method called Likelihood-based Sufficient Dimension Reduction (LAD) for estimating the central subspace. LAD obtains the maximum likelihood estimator of the central subspace under the assumption of conditional normality of the predictors given the response. Analytically and in simulations, LAD is shown to often perform much better than existing methods like Sliced Inverse Regression, Sliced Average Variance Estimation, and Directional Regression. LAD also inherits useful properties from maximum likelihood theory, such as the ability to estimate the dimension of the central subspace and test conditional independence hypotheses.
This document discusses methods for estimating population parameters from sample data, including point estimates, confidence intervals, and determining sample size. It focuses on estimating the population proportion and mean. Key points covered include:
- Obtaining the point estimate of a population proportion or mean from sample data by calculating the sample proportion or mean.
- Constructing confidence intervals for a population proportion or mean based on the point estimate and margin of error, which depends on sample size, confidence level, and population variability.
- Determining the necessary sample size to estimate a population proportion or mean within a specified margin of error and confidence level, using formulas that involve the desired confidence level, margin of error, and an estimate of the population parameter
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document presents a chain sampling plan for truncated life tests when lifetimes follow a generalized exponential distribution. The plan determines the minimum sample size needed to satisfy producer and consumer risks at specified quality levels in terms of the distribution's median. Tables 1 and 2 show the minimum sample sizes and corresponding acceptance numbers for different confidence levels. They also provide the operating characteristic function values for various ratios of the true scale parameter to the specified scale parameter, given a shape parameter of 2. The plan allows accepting a lot if defects are below an acceptance number and no defects occurred in preceding samples, improving on single sampling plans.
An improvised similarity measure for generalized fuzzy numbersjournalBEEI
Similarity measure between two fuzzy sets is an important tool for comparing various characteristics of the fuzzy sets. It is a preferred approach as compared to distance methods as the defuzzification process in obtaining the distance between fuzzy sets will incur loss of information. Many similarity measures have been introduced but most of them are not capable to discriminate certain type of fuzzy numbers. In this paper, an improvised similarity measure for generalized fuzzy numbers that incorporate several essential features is proposed. The features under consideration are geometric mean averaging, Hausdorff distance, distance between elements, distance between center of gravity and the Jaccard index. The new similarity measure is validated using some benchmark sample sets. The proposed similarity measure is found to be consistent with other existing methods with an advantage of able to solve some discriminant problems that other methods cannot. Analysis of the advantages of the improvised similarity measure is presented and discussed. The proposed similarity measure can be incorporated in decision making procedure with fuzzy environment for ranking purposes.
Cointegration and Long-Horizon Forecastingمحمد إسماعيل
This document summarizes research on comparing the accuracy of long-horizon forecasts from multivariate cointegrated systems versus univariate models that ignore cointegration. The main findings are:
1) When accuracy is measured using standard trace mean squared error, imposing cointegration provides no benefit over univariate models at long horizons.
2) Both multivariate and univariate long-horizon forecasts satisfy the cointegrating relationships exactly.
3) The cointegrating combinations of forecast errors from both approaches have finite variance at long horizons.
- The document describes a study that uses a modified Kolmogorov-Smirnov (KS) test to test if the innovations of a GARCH model come from a mixture of normal distributions rather than a standard normal distribution.
- It establishes critical values for the KS test and modified KS (MKS) test through simulation under the null hypothesis. It then uses simulation to calculate the size and power of both tests when the innovations come from alternative distributions like the normal, Student's t, and generalized error distributions.
- The results show that the KS and MKS tests maintain the correct size when the innovations are actually from the mixture of normals. The power of both tests is greater than the nominal level when the innovations come
Parameter Optimisation for Automated Feature Point DetectionDario Panada
Parameter optimization for an automated feature point detection model was explored. Increasing the number of random displacements up to 20 improved performance but additional increases did not. Larger patch sizes consistently improved performance. Increasing the number of decision trees did not affect performance for this single-stage model, unlike previous findings for a two-stage model. Overall, some parameter tuning was found to enhance the model's accuracy but not all parameters significantly impacted results.
1) The standard 95% confidence interval formula for a single binomial proportion can have poor coverage, especially when the sample proportion is close to 0 or 1.
2) Brown et al. observed that the coverage can oscillate dramatically for different sample sizes even when the proportion is not close to the boundaries.
3) They recommend using the Wilson score interval, Agresti-Coull interval, or Jeffreys equal-tailed interval instead, as these have consistently good coverage near the nominal 95% level across a wide range of parameters.
The document discusses confidence intervals and hypothesis testing. It provides examples of constructing 95% confidence intervals for a population mean using a sample mean and standard deviation. It also demonstrates how to identify the null and alternative hypotheses, determine if a test is right-tailed, left-tailed, or two-tailed, and calculate p-values to conclude whether to reject or fail to reject the null hypothesis based on a significance level of 0.05. Examples include testing claims about population proportions and means.
The document discusses confidence intervals and hypothesis testing. It provides examples of constructing 95% confidence intervals for a population mean using a sample mean and standard deviation. It also demonstrates how to identify the null and alternative hypotheses, determine if a test is right-tailed, left-tailed, or two-tailed, and calculate p-values to conclude whether to reject or fail to reject the null hypothesis based on a significance level of 0.05. Examples include testing claims about population proportions and means.
The document discusses confidence intervals and hypothesis testing. It provides examples of constructing 95% confidence intervals for a population mean and proportion. It also demonstrates identifying the null and alternative hypotheses and interpreting the results of hypothesis tests, including calculating p-values.
This document provides an overview of Chapter 4: Statistics from the Analytical Chemistry I course. It discusses key topics from the chapter including the Gaussian distribution, confidence intervals, comparisons of means and standard deviations using t-tests and F-tests, identifying outliers, calibration curves, and the method of least squares for fitting data to lines. The chapter establishes the importance of statistics in analyzing experimental measurements and accounting for variability.
This document discusses methods for estimating population parameters from sample data, including point estimation, bias, confidence intervals, sample size determination, and hypothesis testing. Key points include defining point estimates as single values representing plausible population values based on sample data, describing how to calculate confidence intervals for population proportions and means using z-tests and t-tests, and outlining how to determine necessary sample sizes to achieve a desired level of accuracy and confidence.
Webinar slides- alternatives to the p-value and power nQuery
What are the alternatives to the p-value & power? What is the next step for sample size determination? We will explore these issues in this free webinar presented by nQuery
This study evaluated the performance of bootstrap confidence intervals for estimating slope coefficients in Model II regression with three or more variables. Simulation studies were conducted for different correlation structures between variables, sampling from both normal and lognormal distributions. The results showed that bootstrap intervals provided less than the nominal 95% coverage. Scenarios with strong relationships between variables produced better coverage, while scenarios with weaker relationships and bias produced poorer coverage, even with larger sample sizes. Future work could explore additional scenarios and alternative interval methods to improve accuracy of confidence intervals in Model II regression.
Monte Carlo Modelling of Confidence Intervals in Translation Quality Evaluati...Lifeng (Aaron) Han
This document discusses developing a statistical approach for measuring confidence intervals in translation quality evaluation and post-editing distance. It proposes modeling errors as independent binomial distributions and using Monte Carlo simulations to determine confidence intervals for different sample sizes. The simulations show that with samples of 100 sentences or less, the 95% confidence interval is too broad to reliably measure quality. A minimum sample of 30 pages is recommended to achieve a reasonable confidence level and narrower interval. Understanding confidence intervals provides a measure of reliability for translation quality scores.
The document discusses key concepts in statistical inference including estimation, confidence intervals, hypothesis testing, and types of errors. It provides examples and formulas for estimating population means from sample data, calculating confidence intervals, stating the null and alternative hypotheses, and making decisions to accept or reject the null hypothesis based on a significance level.
Interval Estimation & Estimation Of Proportionmathscontent
This document discusses interval estimation and estimation of proportions from sample data. It defines an interval estimate as a range of values (L1 to L2) that is likely to contain the true population parameter. A 100(1-α)% confidence interval is an interval where the probability of the parameter falling within the interval is 1-α. For large samples where the population variance is known, the confidence interval for the mean is calculated. For small samples or unknown variance, approximations are used. Estimation of a population proportion p is discussed, where the sample proportion p=X/n is an unbiased estimator of p. For large samples, a normal approximation can be used to construct a confidence interval for p. Sample size determination is
This document discusses interval estimation and estimation of proportions from sample data. It defines an interval estimate as a range of values (L1 to L2) that is likely to contain the true population parameter. A 100(1-α)% confidence interval is an interval where the probability of the parameter falling within the interval is 1-α. For large samples where the population variance is known, the confidence interval for the mean is calculated. For small samples or unknown variance, approximations are used. Estimation of a population proportion p is discussed, where the sample proportion p=X/n is an unbiased estimator of p. For large samples, a normal approximation can be used to construct a confidence interval for p. Sample size determination is
Running head COURSE PROJECT NCLEX Memorial Hospital .docxsusanschei
Running head: COURSE PROJECT: NCLEX Memorial Hospital 1
COURSE PROJECT: NCLEX Memorial Hospital 10
Introduction
This project aims to facilitate the improvement of the quality of healthcare services provided to individuals, families and communities at various age levels. Hence, this project used NCLEX Memorial Hospital, where over the past few days there has been a high level of infectious diseases. The dataset collected is from 60 patients whose age range is 35 to 76.
Classification of Variables
The quantitative variable is age. The qualitative variable is infectious diseases. Age is also a continuous variable as it can take on any value. A variable is any quantity that can be measured and whose value varies through the population and here the level of measurement is age, which we shall label a nominal measurement as numbers are used to classify the data.
The Measures of Center and the Measures of Variation
Themeasures of center are some of the most important descriptive statistics one might extrapolate. It helps give us an idea of what the "most" common, normal, or representative answers might be. Essentially, by getting an average, what you are really doing is calculating the "middle" of any group of observations. There are three measures of center that are most often used: Mean, Median and Mode. (NEDARC)
While measures of central tendency are used to estimate "normal" values of a dataset, measures of variation/dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa. A proper description of a set of data should include both of these characteristics. There are various methods that can be used to measure the dispersion of a dataset, each with its own set of advantages and disadvantages. (Climate Data Library)
The Measures of Center and the Measures of Variation Calculations
Column1
Mean
61.81667
Standard Error
1.152127
Median
61.5
Mode
69
Standard Deviation
8.924337
Sample Variance
79.64379
Midrange
58.5
Range
41
Conclusion
By looking at the dataset we find that patients after the age of 50 and most likely 60 to be the most affected by infection diseases. Hence, there should be a prevention plan in place to reduce the number of infected or most likely to be affected by various viruses.
Course Project Phase 2
Introduction
The data in the accompanying spreadsheet records the ages of sixty (60) patients at NCLEX Memorial Hospital who, upon admission, were found to be suffering from ...
This document discusses confidence intervals for estimating population parameters. It provides examples of constructing point and interval estimates for the population mean and proportion from sample data. Confidence intervals allow us to estimate a range of plausible values for the true population parameter based on the sample results and desired confidence level, rather than just a single point value. The width of the confidence interval depends on the sample size and confidence level, with larger samples and lower confidence levels producing narrower intervals.
This document discusses correlation, regression, and related statistical concepts. It begins by introducing correlation and describing how to test for a linear relationship between variables. It then discusses confidence intervals for correlation coefficients. The document explains regression, describing how to calculate a regression line using the least squares method and how to perform hypothesis tests and calculate confidence intervals for regression coefficients. It also discusses analyzing variance, the coefficient of determination, prediction, and correctly interpreting correlation vs assuming causation.
Estimating population values ppt @ bec domsBabasab Patil
This document discusses confidence intervals for estimating population parameters. It covers confidence intervals for the mean when the population standard deviation is known and unknown, as well as confidence intervals for the population proportion. Key points include:
- A confidence interval provides a range of plausible values for an unknown population parameter based on a sample statistic.
- The margin of error and confidence level affect the width of a confidence interval.
- The t-distribution is used instead of the normal when the population standard deviation is unknown.
- Sample size formulas allow determining the required sample size to estimate a population parameter within a specified margin of error and confidence level.
The document discusses various methods for constructing confidence intervals for estimating multinomial proportions. It aims to analyze the propensity for aberrations (i.e. unrealistic bounds like negative values) in the interval estimates across different classical and Bayesian methods. Specifically, it provides the mathematical conditions under which each method may produce aberrant interval limits, such as zero-width intervals or bounds exceeding 0 and 1, especially for small sample counts. The document also develops an R program to facilitate computational implementation of the various methods for applied analysis of multinomial data.
This document provides information on estimating population characteristics from sample data, including:
- Point estimates are single numbers based on sample data that represent plausible values of population characteristics.
- Confidence intervals provide a range of plausible values for population characteristics with a specified degree of confidence.
- Formulas are given for constructing confidence intervals for population proportions and means using large sample approximations or t-distributions.
- Guidelines for determining necessary sample sizes to estimate population values within a specified margin of error are also outlined.
Abnormalities of hormones and inflammatory cytokines in women affected with p...Alexander Decker
Women with polycystic ovary syndrome (PCOS) have elevated levels of hormones like luteinizing hormone and testosterone, as well as higher levels of insulin and insulin resistance compared to healthy women. They also have increased levels of inflammatory markers like C-reactive protein, interleukin-6, and leptin. This study found these abnormalities in the hormones and inflammatory cytokines of women with PCOS ages 23-40, indicating that hormone imbalances associated with insulin resistance and elevated inflammatory markers may worsen infertility in women with PCOS.
1) The standard 95% confidence interval formula for a single binomial proportion can have poor coverage, especially when the sample proportion is close to 0 or 1.
2) Brown et al. observed that the coverage can oscillate dramatically for different sample sizes even when the proportion is not close to the boundaries.
3) They recommend using the Wilson score interval, Agresti-Coull interval, or Jeffreys equal-tailed interval instead, as these have consistently good coverage near the nominal 95% level across a wide range of parameters.
The document discusses confidence intervals and hypothesis testing. It provides examples of constructing 95% confidence intervals for a population mean using a sample mean and standard deviation. It also demonstrates how to identify the null and alternative hypotheses, determine if a test is right-tailed, left-tailed, or two-tailed, and calculate p-values to conclude whether to reject or fail to reject the null hypothesis based on a significance level of 0.05. Examples include testing claims about population proportions and means.
The document discusses confidence intervals and hypothesis testing. It provides examples of constructing 95% confidence intervals for a population mean using a sample mean and standard deviation. It also demonstrates how to identify the null and alternative hypotheses, determine if a test is right-tailed, left-tailed, or two-tailed, and calculate p-values to conclude whether to reject or fail to reject the null hypothesis based on a significance level of 0.05. Examples include testing claims about population proportions and means.
The document discusses confidence intervals and hypothesis testing. It provides examples of constructing 95% confidence intervals for a population mean and proportion. It also demonstrates identifying the null and alternative hypotheses and interpreting the results of hypothesis tests, including calculating p-values.
This document provides an overview of Chapter 4: Statistics from the Analytical Chemistry I course. It discusses key topics from the chapter including the Gaussian distribution, confidence intervals, comparisons of means and standard deviations using t-tests and F-tests, identifying outliers, calibration curves, and the method of least squares for fitting data to lines. The chapter establishes the importance of statistics in analyzing experimental measurements and accounting for variability.
This document discusses methods for estimating population parameters from sample data, including point estimation, bias, confidence intervals, sample size determination, and hypothesis testing. Key points include defining point estimates as single values representing plausible population values based on sample data, describing how to calculate confidence intervals for population proportions and means using z-tests and t-tests, and outlining how to determine necessary sample sizes to achieve a desired level of accuracy and confidence.
Webinar slides- alternatives to the p-value and power nQuery
What are the alternatives to the p-value & power? What is the next step for sample size determination? We will explore these issues in this free webinar presented by nQuery
This study evaluated the performance of bootstrap confidence intervals for estimating slope coefficients in Model II regression with three or more variables. Simulation studies were conducted for different correlation structures between variables, sampling from both normal and lognormal distributions. The results showed that bootstrap intervals provided less than the nominal 95% coverage. Scenarios with strong relationships between variables produced better coverage, while scenarios with weaker relationships and bias produced poorer coverage, even with larger sample sizes. Future work could explore additional scenarios and alternative interval methods to improve accuracy of confidence intervals in Model II regression.
Monte Carlo Modelling of Confidence Intervals in Translation Quality Evaluati...Lifeng (Aaron) Han
This document discusses developing a statistical approach for measuring confidence intervals in translation quality evaluation and post-editing distance. It proposes modeling errors as independent binomial distributions and using Monte Carlo simulations to determine confidence intervals for different sample sizes. The simulations show that with samples of 100 sentences or less, the 95% confidence interval is too broad to reliably measure quality. A minimum sample of 30 pages is recommended to achieve a reasonable confidence level and narrower interval. Understanding confidence intervals provides a measure of reliability for translation quality scores.
The document discusses key concepts in statistical inference including estimation, confidence intervals, hypothesis testing, and types of errors. It provides examples and formulas for estimating population means from sample data, calculating confidence intervals, stating the null and alternative hypotheses, and making decisions to accept or reject the null hypothesis based on a significance level.
Interval Estimation & Estimation Of Proportionmathscontent
This document discusses interval estimation and estimation of proportions from sample data. It defines an interval estimate as a range of values (L1 to L2) that is likely to contain the true population parameter. A 100(1-α)% confidence interval is an interval where the probability of the parameter falling within the interval is 1-α. For large samples where the population variance is known, the confidence interval for the mean is calculated. For small samples or unknown variance, approximations are used. Estimation of a population proportion p is discussed, where the sample proportion p=X/n is an unbiased estimator of p. For large samples, a normal approximation can be used to construct a confidence interval for p. Sample size determination is
This document discusses interval estimation and estimation of proportions from sample data. It defines an interval estimate as a range of values (L1 to L2) that is likely to contain the true population parameter. A 100(1-α)% confidence interval is an interval where the probability of the parameter falling within the interval is 1-α. For large samples where the population variance is known, the confidence interval for the mean is calculated. For small samples or unknown variance, approximations are used. Estimation of a population proportion p is discussed, where the sample proportion p=X/n is an unbiased estimator of p. For large samples, a normal approximation can be used to construct a confidence interval for p. Sample size determination is
Running head COURSE PROJECT NCLEX Memorial Hospital .docxsusanschei
Running head: COURSE PROJECT: NCLEX Memorial Hospital 1
COURSE PROJECT: NCLEX Memorial Hospital 10
Introduction
This project aims to facilitate the improvement of the quality of healthcare services provided to individuals, families and communities at various age levels. Hence, this project used NCLEX Memorial Hospital, where over the past few days there has been a high level of infectious diseases. The dataset collected is from 60 patients whose age range is 35 to 76.
Classification of Variables
The quantitative variable is age. The qualitative variable is infectious diseases. Age is also a continuous variable as it can take on any value. A variable is any quantity that can be measured and whose value varies through the population and here the level of measurement is age, which we shall label a nominal measurement as numbers are used to classify the data.
The Measures of Center and the Measures of Variation
Themeasures of center are some of the most important descriptive statistics one might extrapolate. It helps give us an idea of what the "most" common, normal, or representative answers might be. Essentially, by getting an average, what you are really doing is calculating the "middle" of any group of observations. There are three measures of center that are most often used: Mean, Median and Mode. (NEDARC)
While measures of central tendency are used to estimate "normal" values of a dataset, measures of variation/dispersion are important for describing the spread of the data, or its variation around a central value. Two distinct samples may have the same mean or median, but completely different levels of variability, or vice versa. A proper description of a set of data should include both of these characteristics. There are various methods that can be used to measure the dispersion of a dataset, each with its own set of advantages and disadvantages. (Climate Data Library)
The Measures of Center and the Measures of Variation Calculations
Column1
Mean
61.81667
Standard Error
1.152127
Median
61.5
Mode
69
Standard Deviation
8.924337
Sample Variance
79.64379
Midrange
58.5
Range
41
Conclusion
By looking at the dataset we find that patients after the age of 50 and most likely 60 to be the most affected by infection diseases. Hence, there should be a prevention plan in place to reduce the number of infected or most likely to be affected by various viruses.
Course Project Phase 2
Introduction
The data in the accompanying spreadsheet records the ages of sixty (60) patients at NCLEX Memorial Hospital who, upon admission, were found to be suffering from ...
This document discusses confidence intervals for estimating population parameters. It provides examples of constructing point and interval estimates for the population mean and proportion from sample data. Confidence intervals allow us to estimate a range of plausible values for the true population parameter based on the sample results and desired confidence level, rather than just a single point value. The width of the confidence interval depends on the sample size and confidence level, with larger samples and lower confidence levels producing narrower intervals.
This document discusses correlation, regression, and related statistical concepts. It begins by introducing correlation and describing how to test for a linear relationship between variables. It then discusses confidence intervals for correlation coefficients. The document explains regression, describing how to calculate a regression line using the least squares method and how to perform hypothesis tests and calculate confidence intervals for regression coefficients. It also discusses analyzing variance, the coefficient of determination, prediction, and correctly interpreting correlation vs assuming causation.
Estimating population values ppt @ bec domsBabasab Patil
This document discusses confidence intervals for estimating population parameters. It covers confidence intervals for the mean when the population standard deviation is known and unknown, as well as confidence intervals for the population proportion. Key points include:
- A confidence interval provides a range of plausible values for an unknown population parameter based on a sample statistic.
- The margin of error and confidence level affect the width of a confidence interval.
- The t-distribution is used instead of the normal when the population standard deviation is unknown.
- Sample size formulas allow determining the required sample size to estimate a population parameter within a specified margin of error and confidence level.
The document discusses various methods for constructing confidence intervals for estimating multinomial proportions. It aims to analyze the propensity for aberrations (i.e. unrealistic bounds like negative values) in the interval estimates across different classical and Bayesian methods. Specifically, it provides the mathematical conditions under which each method may produce aberrant interval limits, such as zero-width intervals or bounds exceeding 0 and 1, especially for small sample counts. The document also develops an R program to facilitate computational implementation of the various methods for applied analysis of multinomial data.
This document provides information on estimating population characteristics from sample data, including:
- Point estimates are single numbers based on sample data that represent plausible values of population characteristics.
- Confidence intervals provide a range of plausible values for population characteristics with a specified degree of confidence.
- Formulas are given for constructing confidence intervals for population proportions and means using large sample approximations or t-distributions.
- Guidelines for determining necessary sample sizes to estimate population values within a specified margin of error are also outlined.
Abnormalities of hormones and inflammatory cytokines in women affected with p...Alexander Decker
Women with polycystic ovary syndrome (PCOS) have elevated levels of hormones like luteinizing hormone and testosterone, as well as higher levels of insulin and insulin resistance compared to healthy women. They also have increased levels of inflammatory markers like C-reactive protein, interleukin-6, and leptin. This study found these abnormalities in the hormones and inflammatory cytokines of women with PCOS ages 23-40, indicating that hormone imbalances associated with insulin resistance and elevated inflammatory markers may worsen infertility in women with PCOS.
A usability evaluation framework for b2 c e commerce websitesAlexander Decker
This document presents a framework for evaluating the usability of B2C e-commerce websites. It involves user testing methods like usability testing and interviews to identify usability problems in areas like navigation, design, purchasing processes, and customer service. The framework specifies goals for the evaluation, determines which website aspects to evaluate, and identifies target users. It then describes collecting data through user testing and analyzing the results to identify usability problems and suggest improvements.
A universal model for managing the marketing executives in nigerian banksAlexander Decker
This document discusses a study that aimed to synthesize motivation theories into a universal model for managing marketing executives in Nigerian banks. The study was guided by Maslow and McGregor's theories. A sample of 303 marketing executives was used. The results showed that managers will be most effective at motivating marketing executives if they consider individual needs and create challenging but attainable goals. The emerged model suggests managers should provide job satisfaction by tailoring assignments to abilities and monitoring performance with feedback. This addresses confusion faced by Nigerian bank managers in determining effective motivation strategies.
A unique common fixed point theorems in generalized dAlexander Decker
This document presents definitions and properties related to generalized D*-metric spaces and establishes some common fixed point theorems for contractive type mappings in these spaces. It begins by introducing D*-metric spaces and generalized D*-metric spaces, defines concepts like convergence and Cauchy sequences. It presents lemmas showing the uniqueness of limits in these spaces and the equivalence of different definitions of convergence. The goal of the paper is then stated as obtaining a unique common fixed point theorem for generalized D*-metric spaces.
A trends of salmonella and antibiotic resistanceAlexander Decker
This document provides a review of trends in Salmonella and antibiotic resistance. It begins with an introduction to Salmonella as a facultative anaerobe that causes nontyphoidal salmonellosis. The emergence of antimicrobial-resistant Salmonella is then discussed. The document proceeds to cover the historical perspective and classification of Salmonella, definitions of antimicrobials and antibiotic resistance, and mechanisms of antibiotic resistance in Salmonella including modification or destruction of antimicrobial agents, efflux pumps, modification of antibiotic targets, and decreased membrane permeability. Specific resistance mechanisms are discussed for several classes of antimicrobials.
A transformational generative approach towards understanding al-istifhamAlexander Decker
This document discusses a transformational-generative approach to understanding Al-Istifham, which refers to interrogative sentences in Arabic. It begins with an introduction to the origin and development of Arabic grammar. The paper then explains the theoretical framework of transformational-generative grammar that is used. Basic linguistic concepts and terms related to Arabic grammar are defined. The document analyzes how interrogative sentences in Arabic can be derived and transformed via tools from transformational-generative grammar, categorizing Al-Istifham into linguistic and literary questions.
A time series analysis of the determinants of savings in namibiaAlexander Decker
This document summarizes a study on the determinants of savings in Namibia from 1991 to 2012. It reviews previous literature on savings determinants in developing countries. The study uses time series analysis including unit root tests, cointegration, and error correction models to analyze the relationship between savings and variables like income, inflation, population growth, deposit rates, and financial deepening in Namibia. The results found inflation and income have a positive impact on savings, while population growth negatively impacts savings. Deposit rates and financial deepening were found to have no significant impact. The study reinforces previous work and emphasizes the importance of improving income levels to achieve higher savings rates in Namibia.
A therapy for physical and mental fitness of school childrenAlexander Decker
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A simulated data analysis on the interval estimation for the
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A Simulated Data Analysis on the Interval Estimation for the
Binomial Proportion P
Junge B. Guillena
Adventist Medical Center College, Iligan City, Philippines
jun20guillena@yahoo.com
Abstract
This study constructed a quadratic-based interval estimator for binomial proportion p. The modified
method imposed a continuity correction over the confidence interval. This modified quadratic-based
interval was compared to the different existing alternative intervals through numerical analysis using the
following criteria: coverage probability, and expected width for various values of n, p and α = 0.05.
Simulated data results generated the following observations: (1) the coverage probability of modified
interval is larger compared to that of the standard and non-modified intervals, for any p and n; (2) the
coverage probability of all the alternative methods approaches to the nominal 95% confidence level as n
increases for any p;(3) the modified and non-modified intervals have indistinguishable width differences
for any p as n gets larger; (4) the expected width of the modified and alternative intervals decreases as n
increases for 05.0 and any p. Based on these observations one can say that the modified method is
an improvement of the standard method. It is therefore recommended to modify other existing alternative
methods in such a way that there’s an increase in performance in terms of coverage properties, expected
width, and other measures.
Keywords: Confidence Interval, Binomial Distribution, Standard Interval, Coverage Probability,
Expected Width
Introduction
Inferential problem like interval estimation arising from binomial experiments is one of the classical problems in
statistics offering many arguments and disputes. When constructing a confidence interval, one usually wishes the
actual coverage probability to be close to the nominal confidence level, that is, it closely approximates to 1 .
The unexpected difficulties inherent to the choice of a confidence interval estimate of the binomial parameter p, and
the relative inefficiency (Marchand, E., Perron, F., and Rokhaya, G., 2004) f the “standard” Wald confidence
interval, has resurfaced recently with the work of Brown, L. D., Cai, T.T., and DasGupta, A. (1999a and 199b) and
Agresti and Coull (1998). Along with this, several alternative interval estimates have been suggested. Some
alternative intervals make use of a continuity correction while others guarantee a minimum 1 coverage
probability for all values of the parameter p. In line with this, this study aims to develop an alternative method with
slight modifications of the method first developed by Casella, et al., 1990. As suggested, this modification imposes a
continuity correction factor.
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Purpose of the Study
The objective of this study is to construct a non-randomized confidence interval XC for p, such that the coverage
probability 1xCpPp , where is some pre-specified value between 0 and 1 (Casella and Berger,
1990) Specifically, the objective of this study is to compare numerically the performance of the standard, non-
modified and modified intervals and some alternative interval estimators based on coverage probability and
expected width.
BASIC CONCEPTS:
Confidence Interval
Definition 1: Let nXXX ,..., 21 be a random sample from the density xf . Let nxxxlxl ,...,)( 21 and
nxxxuxu ,...,)( 21 be two statistics satisfying xuxl for which 1)()( xuxlP . Then
the random interval )(),( xuxl is called a )%1(100 confidence interval for ; 1 is called the
confidence coefficient; and )(xl and )(xu are called the lower and upper confidence limits, respectively, for .
Expected Width and Coverage Probability: Some criteria for evaluating interval estimators are the interval width
and coverage probability. Ideally, an interval must have narrow width with large coverage probability, but such sets
are usually difficult to construct.
Definition 2: The coverage probability of the confidence set xC is defined as
xdFxCIXCP
where: is the sample space of X and )(xCI is an indicator function for a nonrandomized set equal to 1 if
xC , otherwise it is 0.
Definition 3: The expected width is defined as:
xfXLXUXCofwidthE
n
x
n
0
, , where
XU and XL are the upper and lower limits respectively of the confidence set xC
Standard Interval Estimator: A standard confidence interval for p based on normal approximation has gained
universal recommendation in the introductory statistics textbooks and in statistical practice. The interval is known to
guarantee that for any fixed p, the coverage probability nasxCpP 1 .
To show this interval estimator, let zandz be the standard normal density function and cumulative
distribution, respectively. Let 211
2
zz ,
n
x
p ˆ and pq ˆ1ˆ , where 1ˆˆ qp .The normal
theory approximation of a confidence interval for binomial proportion is defined as:
n
pp
zpXC s
ˆ1ˆ
ˆ
,
where z is the 2/1 th quantile of the standard normal distribution.
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The Proposed Modified Interval: Due to the discreteness of the binomial distribution and as suggested by Casella,
et al., 1990, this proposed modified interval imposes a continuity correction,
n
c
4
1
, over the modified interval.
The factor is arbitrarily chosen.
Theorem 1: The approximate 1 confidence interval for p with
n
c
4
1
is given by
n
z
n
z
n
p
n
z
n
p
n
z
n
p
XC 2
2
2
1
2
22
2
2
2
2
12
1
4
1
ˆ4
2
1
ˆ2
2
1
ˆ2
where the lower limit is given by,
n
z
n
z
n
p
n
z
n
p
n
z
n
p
nxL 2
2
2
1
2
22
2
2
2
2
12
1
4
1
ˆ4
2
1
ˆ2
2
1
ˆ2
,
and upper limit is given by
n
z
n
z
n
p
n
z
n
p
n
z
n
p
nxU 2
2
2
1
2
22
2
2
2
2
12
1
4
1
ˆ4
2
1
ˆ2
2
1
ˆ2
,
Simulated Results and Discussions: This section presents the comparative graphical and numerical results and
comparisons of the different alternative interval estimators, in terms of its coverage probability behavior, and
expected width. In investigating the performance of the standard interval and the alternative intervals, the usual =
0.05 is utilized. Simulation of data values was done through Maple program.
Comparison for Standard, Non-Modified and Modified Intervals in terms of Coverage Probability:
Figures 1 presents the result of the coverage graphs of the standard, the non-modified and the modified intervals for
n = 20, 40, 70 and 100 with nominal 95%. It shows that both the non-modified and the standard intervals have
significantly downward spikes near p close to 0 or 1, while the modified interval has a good coverage probability
behavior for any p. The above aforementioned results give evidences and supports to the following claim: the
coverage probability of the modified interval has much better behavior over the standard and the non-modified
intervals for any p and n.
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Comparison for Modified and Alternative Intervals
Figures 2 shows the result of the coverage probability graphs of the Wilson, the Agresti – Coull, the arcsine, the
Wilson*, the Logit**, and the modified intervals for n = 70, 150, 300 and 500 with variable p for nominal 95%
confidence level. It reveals that the Agresti-Coull interval has conservative coverage probability near p = 0, which
means that most of the coverage probability is above the nominal level. On the other hand, the Wilson interval has a
fairly downward spike near 0 or 1, but has a good coverage probability away from the boundaries. The arcsine
interval has an erratic pattern near the boundaries, since the coverage probability cuts off quickly at some values of
054.0,034.0p or 966.0,946.0p with values below 0.95. The modified interval has some downward
spike near the boundaries but gradually disappear as p approaches to 0.5 or away from 0 or 1. This interval is
comparable to other alternative intervals like the logit**, the Wilson, the arcsine but less comparable to the Agresti-
Coull and Wilson* intervals in terms of coverage probability behavior. When 086.0,01.0p or
99.0,914.0p the Agresti-Coull interval aside from the Wilson* have coverage probabilities greater than
0.95. For larger values of n, which in this case n = 300 and 500, the Wilson* has a consistent coverage probability
behavior that is greater than or equal to 0.95 for all values of p. The Wilson, arcsine, logit** and modified intervals
have some downward spike near p = 0.01, but still the coverage probability of these intervals perform well in the
middle parameter space region. These numerical findings show that the modified interval has a comparable coverage
probability behavior both in n = 70, 150, 300 and 500 for nominal 95% confidence level. These results give support
to the following suggestion that the coverage probability behavior of all the methods approaches to the nominal 95%
confidence level as n increases for any p.
n = 20, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
coverageprobability
standard
nonmodified
modified
n = 40, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
coverageprobability
standard
non-modified
modified
n = 70, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.4
0.5
0.6
0.7
0.8
0.9
1.0
coverageprobability
standard
non-modified
modified
Figure 1 Comparison of coverage probability of the standard, the non-modified and
the modified intervals for n = 20, 40, 70 and 100 with 95.01
n = 100, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
coverageprobability
standard
non-modified
modified
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Comparison for Standard, Non-Modified and Modified Intervals in terms of Expected Width
Figure 3 shows the comparison of expected width of the standard, the non-modified and the modified intervals for n
= 20, 40, 70 and 100 with nominal 95% level. Results show that at smaller ( 40n ), the modified interval has
larger width near the boundaries 0 or 1, but as p approaches to 0.5, it has similar width with the non-modified
interval. The standard interval has wider width near p close to 0.5. But as n increases, they have comparable width
performance. The preceding results give validity to the conjecture that the non-modified and the modified intervals
have comparable expected width when n gets larger for any p.
n = 70, v ariable p
nominal 95% lev el
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
coverageprobability
w ils on
agres ti-c oull
arc s ine
w ils on*
logit**
modified
Figure 2 Comparison of coverage probability of the Wilson, the Agresti-Coull, the arcsine, the
Wilson*, the logit** and the modified intervals for n = 70, 150, 300 and 500 with 95.01 .
n = 150, v ariable p
nominal 95% lev el
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
coverageprobability
w ils on
agres ti-c oull
arc s ine
w ils on*
logit**
modified
n = 300, v ariable p
nominal 95% lev el
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
coverageprobability
w ils on
agres ti-c oull
arc s ine
w ils on*
logit**
modified
n = 500, v ariable p
nominal 95% lev el
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
coverageprobability
w ils on
agres ti-c oull
arc s ine
w ils on*
logit**
modified
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Comparison for Modified and Alternative Intervals in terms of Expected Width
Figure 4 displays the result for the graphs of the expected width of the Wilson interval, the Agresti-Coull interval,
the arcsine interval, the Wilson*, the logit** interval and the modified interval for n = 40, 80, 150 and 300 with
nominal 95% confidence level, respectively. Result shows that the modified interval has the shortest width
when 861.0139.0 p , the Wilson interval and Agresti-Coull interval have a comparable width with the
modified interval when p approaches 0.5, the Wilson* interval is consistent for having the largest width when
104.0p or 896.0p , and the logit** interval is the largest at near the boundaries or when 103.0p .
These numerical evaluations show that the modified interval has a better performance in terms of expected width,
the Wilson* has a larger width of what is expected since this interval is partly conservative in terms of coverage
properties especially near the boundaries. For n = 150, the standard interval shows the shortest when
114.0p or 886.0p ; the modified interval is the shortest when 115.0p or 885.0p , and still the
Wilson (0.5) is the largest for most values of n, and the logit** interval is the largest when p nearer the boundaries.
For n = 300, the results show that the standard interval is the shortest when 102.0p or 898.0p , the Wilson,
Agresti-Coull, arcsine, logit** and modified intervals have almost indistinguishable width difference when
103.0p or 887.0p , while the Wilson* is significantly larger. This suggests that the Wilson, Agresti-Coull,
arcsine, Logit (-0.87) and the modified intervals are all preferable methods for larger values of n in terms of
expected width. But if the precision of the estimate is preferred for an increased width, Wilson (0.5) interval is
preferable especially for larger values of n. The aforementioned results build up the following evidence that the
interval that has a coverage probability closely approximate to the nominal 95% confidence level, yields a narrower
expected width.
Figure 3 Comparison of Expected Width of the standard, the non-modified and the
modified intervals for n = 20, 40, 70 and 100 with 95.01
n = 20, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
expectedwidth
standard
non-modified
modified
n = 40, variable p
nominal 95%
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
expectedwidth
standard
non-modified
modified
n = 70, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
0.24
0.26
expectedwidth
standard
non-modified
modified
n = 100, variable p
nominal 95% level
0.0 0.2 0.4 0.6 0.8 1.0
probability
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
0.22
expectedwidth
standard
non-modified
modified
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Conclusion and Recommendation
The existing and additional results would suggest rejection of the conditions made by several authors regarding the
use of the standard interval, but instead utilize the alternative methods found in the literature which perform better in
terms of coverage properties and other criteria. The performance of the alternative methods and the proposed
method modified by the researcher and the results show that some of these intervals have very good coverage
probability behavior and smaller expected width.
Given the varied options, the best solution will no doubt be influenced by the user’s personal preferences. A wise
choice could be either one of the Wilson, Agresti-Coull, Wilson*, logit**, arcsine and modified intervals which
show decisive improvement over the standard interval. Based on the analysis and results obtained, the researcher’s
recommendations to compare and investigate the performance (like coverage properties) of the most probable
classical and Bayesian intervals and examine the RMSE property of the modified interval discussed in the current
study.
References
Agresti, A., and Caffo, B. (2000). Simple and Effective Confidence Intervals for Proportions and Differences of
Proportions Result from Adding Two Success and Two Failures. The American Statistician, 54, 280 – 288.
Boomsma, A. (2005). Confidence Intervals for a Binomial Proportion. University of Groningen. Department of
Statistics & Measurement Theory.
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agresti-coull
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0.0 0.2 0.4 0.6 0.8 1.0
probability
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agresti-coull
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0.0 0.2 0.4 0.6 0.8 1.0
probability
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0.06
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0.10
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expectedwidth
wilson
agresti-coull
arcsine
wilson*
logit**
modified
Figure 4 Comparison of expected width of the Wilson, the Agresti-Coull, the arcsine, the Wilson*, the logit**
and the modified intervals for n = 40, 80, 150 and 300 with 95.01 .
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Chemical and Process Engineering Research CPER@iiste.org
Engineering, Technology and Systems Journals PAPER SUBMISSION EMAIL
Computer Engineering and Intelligent Systems CEIS@iiste.org
Innovative Systems Design and Engineering ISDE@iiste.org
Journal of Energy Technologies and Policy JETP@iiste.org
Information and Knowledge Management IKM@iiste.org
Journal of Control Theory and Informatics CTI@iiste.org
Journal of Information Engineering and Applications JIEA@iiste.org
Industrial Engineering Letters IEL@iiste.org
Journal of Network and Complex Systems NCS@iiste.org
Environment, Civil, Materials Sciences Journals PAPER SUBMISSION EMAIL
Journal of Environment and Earth Science JEES@iiste.org
Journal of Civil and Environmental Research CER@iiste.org
Journal of Natural Sciences Research JNSR@iiste.org
Life Science, Food and Medical Sciences PAPER SUBMISSION EMAIL
Advances in Life Science and Technology ALST@iiste.org
Journal of Natural Sciences Research JNSR@iiste.org
Journal of Biology, Agriculture and Healthcare JBAH@iiste.org
Journal of Food Science and Quality Management FSQM@iiste.org
Journal of Chemistry and Materials Research CMR@iiste.org
Education, and other Social Sciences PAPER SUBMISSION EMAIL
Journal of Education and Practice JEP@iiste.org
Journal of Law, Policy and Globalization JLPG@iiste.org
Journal of New Media and Mass Communication NMMC@iiste.org
Journal of Energy Technologies and Policy JETP@iiste.org
Historical Research Letter HRL@iiste.org
Public Policy and Administration Research PPAR@iiste.org
International Affairs and Global Strategy IAGS@iiste.org
Research on Humanities and Social Sciences RHSS@iiste.org
Journal of Developing Country Studies DCS@iiste.org
Journal of Arts and Design Studies ADS@iiste.org
10. The IISTE is a pioneer in the Open-Access hosting service and academic event management.
The aim of the firm is Accelerating Global Knowledge Sharing.
More information about the firm can be found on the homepage:
http://www.iiste.org
CALL FOR JOURNAL PAPERS
There are more than 30 peer-reviewed academic journals hosted under the hosting platform.
Prospective authors of journals can find the submission instruction on the following
page: http://www.iiste.org/journals/ All the journals articles are available online to the
readers all over the world without financial, legal, or technical barriers other than those
inseparable from gaining access to the internet itself. Paper version of the journals is also
available upon request of readers and authors.
MORE RESOURCES
Book publication information: http://www.iiste.org/book/
IISTE Knowledge Sharing Partners
EBSCO, Index Copernicus, Ulrich's Periodicals Directory, JournalTOCS, PKP Open
Archives Harvester, Bielefeld Academic Search Engine, Elektronische Zeitschriftenbibliothek
EZB, Open J-Gate, OCLC WorldCat, Universe Digtial Library , NewJour, Google Scholar