Population proportion

About: Population proportion is a research topic. Over the lifetime, 247 publications have been published within this topic receiving 4099 citations.

Dynamic Research on China's Gini Coefficient

Abstract: Based on the grouped data of resident income in Statistical Yearbook, the paper calculates the China’s Gini coefficients of urban, rural and national residents in the ten years from 2002 to 2011 according to the characteristics of income data of urban residents and rural residents, and finally analyzes the Gini coefficients of urban, rural and national residents calculated, to come to the conclusion that the Gini coefficient of resident income breaks through the warning line and keeps highly stable, which reflects the wealth gap of China’s residents in the current stage is still in the process of developing from a rational gap to an excessive gap, but there is no polarization. Introduction China has gradually entered the stage of a wealthy and strong country since the reform and opening up, but there is no doubt that the gap of resident income also becomes larger. Gini coefficient gives the quantity line reflecting the economic difference among residents, and based on that, the wealth gap among residents can be reflected intuitively and objectively, to provide early warning and prevent the appearance of wealth polarization, and it is an internationally accepted authoritative index measuring the level of a country’s wealth gap and income distribution gap. The paper studies the dynamic trajectory of Gini coefficient through calculating the Gini coefficients of China in recent ten years, so as to grasp the distribution situation and variation trend of China’s resident income. The Empirical Analysis on Gini Coefficient The Computing Method of Gini Coefficient As a common conception measuring income gap, Gini coefficient descries the comparative deviation degree of average income gap caused by population distribution to the expected value of total income. Its computing method is based on the data which evenly distribute population into several groups N, namely the proportion of each group’s population to the total population is the same, and meanwhile, the mean value μ of corresponding evenly divided group can be obtained, so the computing formula of Gini Coefficient is 2 1 1 1 2 N N i j i j G y y N       . i j y y  represents the absolute value of the income mean difference of any two evenly divided groups. μ represents the expected value of various evenly divided groups’ total income. According to the formula, it can be found that G is the average deviation of total income.The average deviation value will be divided by the expected value of total income μ to obtain the comparative deviation degree of average income deviation to the expected value of total income μ, which is Gini coefficient G. International Conference on Humanities and Social Science (HSS 2016) © 2016. The authors Published by Atlantis Press 579 The Calculation of Urban Gini Coefficient The mean values of urban resident income in different groups are determined according to the distribution of population, but due to the unequal grouping proportion of population as well as the difference in the number of members in each household in corresponding groups, the income mean values of several groups are determined not based on the grouping of equal population proportion. Therefore, the problem needing to be solved is to regroup based on the existing information and work out the corresponding income mean values of those groups according to the several evenly divided groups of population. For the specific computing process, it can be carried in accordance with the following two steps. Firstly, according to the characteristics of 7 groups of values given in the Statistical Yearbook, they can be preliminary divided into 5 groups which are based on approximately even division; and then according to the proportions of household groups and their corresponding population data of each household, the corresponding proportion values of those 7 groups can be calculated. Secondly, implementing even distribution for the population in the groups whose population proportion closing to 20%, to realize that the population proportions of all five groups equal to 20%, and work out the corresponding income mean value in various groups. Based the first assumption, the corresponding values of point 10, 30, 50, 70, 90 and other points can be calculated to regard them as the income mean values of those five evenly divided groups, see Table 1. Table 1: The Mean of the Five Evenly Divided Groups’ Corresponding Income Group One Two Three Four Five Evenly Divided Population Distribution 20 20 20 20 20 Corresponding Income Mean Value 3510.9 5736.55 7868.7 10532.08 19225.77 According to the corresponding income mean value of those evenly divided groups, we can work out that 1 1 N N i j i j y y     =72443.86, and the overall mean value of income in those five groups μ=9373.86. Based on N=5, various values are brought into the formula to obtain the urban resident coefficient in G2004=0.309131. The Calculation of Rural Gini Coefficient The calculation method of rural Gini coefficient is completely the same as that of urban Gini coefficient, and the difference between them is the data of urban resident data are evenly divided into 5 groups, see the following Table 3. In a similar way, according to the data, we can work out that 1 1 N N i j i j y y     =25424.60, and the mean value μ=2996.7. Based on N=5, various values are brought into the formula to obtain the urban rural coefficient in G2004=0.339368.

Chapter 25 – Power and Sample Size Calculations

Abstract: This chapter introduces several fundamental concepts related to power and sample size calculations. We first review some key questions that should be considered when developing research studies. We then introduce the concept of statistical power and explain why having adequate power is essential for designing successful studies. Next, we present some basic sample size formulas for when we plan to collect a sample of either continuous or binary data and then wish to construct a confidence interval for the population mean or the population proportion with a certain degree of precision. Subsequently, we present some basic sample size formulas for when we plan to collect one sample, a paired sample, or two independent samples of either continuous or binary data and then wish to test hypotheses about specific characteristics of the populations from which the data came. Finally, we discuss several advanced topics related to sample size calculation and the collaborative process of study design.

Consistency for the tree bootstrap in respondent-driven sampling.

Abstract: Respondent-driven sampling is an approach for estimating features of populations that are difficult to access using standard survey tools, e.g., the fraction of injection drug users who are HIV positive. Baraff et al. (2016) introduced an approach to estimating uncertainty in population proportion estimates from respondent-driven sampling using the tree bootstrap method. In this paper we establish the consistency of this tree bootstrap approach in the case of [Formula: see text]-trees.

Bayesian Inference for the Difference of Two Proportion Parameters in Over-Reported Two-Sample Binomial Data Using the Doubly Sample

Abstract: We construct a point and interval estimation using a Bayesian approach for the difference of two population proportion parameters based on two independent samples of binomial data subject to one type of misclassification. Specifically, we derive an easy-to-implement closed-form algorithm for drawing from the posterior distributions. For illustration, we applied our algorithm to a real data example. Finally, we conduct simulation studies to demonstrate the efficiency of our algorithm for Bayesian inference.

Confidence Intervals I

Abstract: In the last unit you explored how sample statistics (in particular, sample proportions) vary from sample to sample. The Central Limit Theorem has allowed you to make probability statements about a sample proportion falling in a certain interval, provided that one knows the value of the population proportion. The much more common problem is to estimate or to make a decision about an unknown population parameter based on an observed sample statistic. These are goals of statistical inference.