Topic
Population proportion
About: Population proportion is a research topic. Over the lifetime, 247 publications have been published within this topic receiving 4099 citations.
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TL;DR: In this paper, the problem of estimating a population proportion when only a subpopulation may be sampled is considered, and a Bayesian procedure is developed which may be used, however, if one is willing to make certain assumptions about the nuisance parameter.
Abstract: The problem of estimating a population proportion when only a subpopulation may be sampled is considered. This is a simplified version of a problem which arises when testing for the association between a risk factor and a disease by analyzing a contingency table constructed from, hospital data. The proportion for the subpopulation, is expressed in terms of the population proportion and a nuisance parameter in such a way that the model is unfortunately not identifiable. A Bayesian procedure is developed which may be used, however, if one is willing to make certain assumptions about the nuisance parameter. As an illustration the procedure is used with a particular prior to obtaina posterior confidence interval for the population proportion. The coverage probabilities of the interval for various fixed values of the parameters are then evaluated.
15 Dec 2010
TL;DR: In this paper, the consequences of making false decisions (type I and type II errors) are clarified and the difference between a one-and a two-tailed test is made clear.
Abstract: This article covers parametric tests of one and two samples. First, the implications of making decisions under uncertainty are discussed. Next, the concepts of hypothesis testing, probability values, and confidence intervals are introduced, and the steps of the hypothesis testing procedure are explicated. The consequences of making false decisions (type I and type II errors) are clarified and the difference between a one- and a two-tailed test is made clear. The following tests are covered: large sample test (i) of the mean and (ii) of the population proportion, and small sample test of (iii) mean and (iv) proportion. First, we show how to conduct the tests based on one sample where the empirical dataset is compared to a hypothesized value. Thereafter, we repeat the same four test conditions but now the focus is on the difference between two empirical samples. In separate sections, we describe how to carry out a matched sample test, a test for equality of two population variances, and a test of difference between means when variances are not equal.
Keywords:
hypothesis test;
confidence intervals;
type I and type II errors;
one- and two-tailed tests;
one and two samples;
test of difference between means and population proportions;
large and small independent samples;
matched samples;
differences between variances;
equal and unequal variances;
assumptions of normality
TL;DR: In this paper, the maximum likelihood estimate (MLE) of a population proportion when it differs from the same of a second population by a known value is derived, and the constrained MLE has a closed form.
Abstract: We derive the maximum likelihood estimate (MLE) of a population proportion when it differs from the same of a second population by a known value. This constrained MLE (CMLE) has a closed form in li...
TL;DR: In this paper, the authors explore the overlap between two associated confidence intervals and conclude that, among three methods, the overlapped method is under-estimated, and the difference of the population proportions method is overestimated on the basis of the proposed method.
Abstract: In order to examine whether the difference between two point estimates of population proportions is statistically significant, data analysts use two techniques. The first is to explore the overlap between two associated confidence intervals. Second method is to test the significance which is introduced at most statistical textbooks under the common assumptions of consistency, asymptotic normality, and asymptotic independence of the estimates. Under the null hypothesis which is two population proportions are equal, the pooled estimator (If population proportion is preferred as a point estimator since two independent random samples are considered to be collected from one population. Hence as an alternative method, we could obtain another confidence interval of the difference of the population proportions with using the pooled estimate. We conclude that, among three methods, the overlapped method is under-estimated, and the difference of the population proportions method is over-estimated on the basis of the proposed method.
TL;DR: In this paper, the authors use the idea of post-stratification based on the respondents' choice of a particular randomization device in order to estimate the population proportion of a sensitive characteristic.
Abstract: In this paper, we use the idea of post-stratification based on the respondents’ choice of a particular randomization device in order to estimate the population proportion of a sensitive characteristic. The proposed idea gives full freedom to the respondents and is expected to result in greater cooperation from them as well as to provide some increase in the relative efficiency of the newly proposed estimator.