Showing papers on "Population proportion published in 2010"

Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute

Abstract: Some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute, are proposed. Under simple random sampling without replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to the first order of approximation are derived. The results obtained have been illustrated numerically by taking some empirical population considered in the literature.

Bayesian penalized spline model-based inference for finite population proportion in unequal probability sampling.

Abstract: We propose a Bayesian Penalized Spline Predictive (BPSP) estimator for a finite population proportion in an unequal probability sampling setting. This new method allows the probabilities of inclusion to be directly incorporated into the estimation of a population proportion, using a probit regression of the binary outcome on the penalized spline of the inclusion probabilities. The posterior predictive distribution of the population proportion is obtained using Gibbs sampling. The advantages of the BPSP estimator over the Hajek (HK), Generalized Regression (GR), and parametric model-based prediction estimators are demonstrated by simulation studies and a real example in tax auditing. Simulation studies show that the BPSP estimator is more efficient, and its 95% credible interval provides better confidence coverage with shorter average width than the HK and GR estimators, especially when the population proportion is close to zero or one or when the sample is small. Compared to linear model-based predictive estimators, the BPSP estimators are robust to model misspecification and influential observations in the sample.

Ratio-Product Type Exponential Estimator For Estimating Finite Population Mean Using Information On Auxiliary Attribute

Abstract: In practice, the information regarding the population proportion possessing certain attribute is easily available see Jhajj et.al. (2006). For estimating the population mean Y of the study variable y, following Bahl and Tuteja (1991), a ratio-product type exponential estimator has been proposed by using the known information of population proportion possessing an attribute (highly correlated with y) in simple random sampling. The expressions for the bias and the mean-squared error (MSE) of the estimator and its minimum value have been obtained. The proposed estimator has an improvement over mean per unit estimator, ratio and product type exponential estimators as well as Naik and Gupta (1996) estimators. The results have also been extended to the case of two phase sampling. The results obtained have been illustrated numerically by taking some empirical populations considered in the literature.

Bayesian estimation of proportion and sensitivity level in randomized response procedures

Abstract: A Bayesian approach to the joint estimation of population proportion and sensitivity level of a stigmatizing attribute is proposed by adopting a two-stage randomized response procedure. In the first stage the direct question method is carried out for each respondent, while in the second stage the randomization is exclusively carried out for those individuals declaring their membership in the non-sensitive group. The randomization is implemented on the basis of Franklin’s procedure. The proposed Bayesian method avoids the drawbacks usually connected with the use of maximum-likelihood or moment estimation.

The Effect of Differential Recruitment, Non-response and Non-recruitment on Estimators for Respondent-Driven Sampling

Abstract: Respondent-driven sampling is a widely-used network sampling technique, designed to sample from hard-to-reach populations. Estimation from the resulting samples is an area of active research, with software available to compute at least four estimators of a population proportion. Each estimator is claimed to address deficiencies in previous estimators, however those claims are often unsubstantiated. In this study we provide a simulation-based comparison of five existing estimators, focussing on sampling conditions which a recent estimator is designed to address. We find no estimator consistently out-performs all others, and highlight sampling conditions in which each is to be preferred.

Chapter 8 – Estimation

Abstract: We learn how to use sample data to estimate a population mean, a population variance, and a population proportion. We discuss point estimates, which are single-value estimates of the parameter. The standard error of these estimates is considered. We also consider interval estimates that contain the parameter with specified degrees of confidence.

Applied Statistics for Business and Economics

Abstract: Introduction to Statistics What Is Statistics Good for? Some Further Applications of Statistics Some Basic Statistical Ideas On Studying Statistics Describing Data: Tables and Graphs Looking at a Single Variable Looking for Relationships Looking at Variables over Time Describing Data: Summary Statistics When Pictures Will Not Do Measures of a Single Numeric Variable Measures of a Single Categorical Variable Measures of a Relationship Basic Probability Why Probability? The Basics Computing Probabilities Some Tools That May Help Revising Probabilities with Bayes' Theorem Probability Distributions Discrete Random Variables The Binomial Probability Distribution Continuous Random Variables The Normal Distribution: The Bell-Shaped Curve The Normal Approximation to the Binomial Sampling and Sampling Distributions Sampling What Are Sampling Distributions and Why Are They Interesting? The Sampling Distribution of a Proportion The Sampling Distribution of a Mean: sigmaX Known The Sampling Distribution of a Mean: sigmaX Unknown Other Sampling Distributions Estimation and Confidence Intervals Point and Interval Estimators of Unknown Population Parameters Estimates of the Population Proportion Estimates of the Population Mean A Final Word on Confidence Intervals Tests of Hypotheses: One-Sample Tests Testing a Claim: Type I and Type II Errors A Two-Tailed Test for the Population Proportion A One-Tailed Alternative for the Population Proportion Tests for the Population Mean A Two-Tailed Test for the Population Mean A One-Tailed Alternative for the Population Mean A Final Word on One-Sample Tests Tests of Hypotheses: Two-Sample Tests Looking for Relationships Again A Difference in Population Proportions A Difference in Population Means A Difference in Means: sigmas Known A Difference in Means: sigmas Unknown but Equal A Difference in Means: sigmas Unknown and Unequal A Difference in Means: Using Paired Data A Final Word on Two-Sample Tests Tests of Hypotheses: Contingency and Goodness-of-Fit A Difference in Proportions: An Alternate Approach Contingency Tables with Several Rows and/or Columns A Final Word on Contingency Tables Testing for Goodness-of-Fit A Final Example on Testing for Goodness-of-Fit Tests of Hypotheses: ANOVA and Tests of Variances A Difference in Means: An Alternate Approach ANOVA with Several Categories A Final Word on ANOVA A Difference in Population Variances Simple Regression and Correlation The Population Regression Line The Sample Regression Line Evaluating the Sample Regression Line Evaluating the Sample Regression Slope The Relationship of F and t: Here and Beyond Predictions Using the Regression Line Regression and Correlation Another Example Dummy Explanatory Variables The Need for Multiple Regression Multiple Regression Extensions of Regression Analysis The Population Regression Line The Sample Regression Line Evaluating the Sample Regression Line Evaluating the Sample Regression Slopes Predictions Using the Regression Line Categorical Variables Estimating Curved Lines Additional Examples Time-Series Analysis Exploiting Patterns over Time The Basic Components of a Time Series Moving Averages Seasonal Variation The Long-Term Trend The Business Cycle Putting It All Together: Forecasting Another Example Appendix A Appendix B: Answers to Odd-Numbered Exercises Appendix C Index

Hypothesis Testing Related to Differences Parametric Tests

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