Population proportion

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

Exact Distribution of Difference of Two Sample Proportions and Its Inferences

Abstract: Comparing two population proportions using confidence interval could be misleading in many cases, such as the sample size being small and the test being based on normal approximation. In this case, the only one option that we have is to collect a large sample. Unfortunately, the large sample might not be possible. One example is a person suffering from a rare disease. The main purpose of this journal is to derive a closed formula for the exact distribution of the difference between two independent sample proportions, and use it to perform related inferences such as a confidence interval, regardless of the sample sizes and compare with the existing Wald, Agresti-Caffo and Score. In this journal, we have derived a closed formula for the exact distribution of the difference between two independent sample proportions. This distribution doesn’t need any requirements, and can be used to perform inferences such as: a hypothesis test for two population proportions, regardless of the nature of the distribution and the sample sizes. We claim that exact distribution has the least confidence width among Wald, Agresti-Caffo and Score, so it is suitable for inferences of the difference between the population proportion regardless of sample size.

Optimum ratio estimators for the population proportion

Abstract: The problem of the estimation of a population proportion using auxiliary information has been recently studied by Rueda et al. (Estimators and confidence intervals for the proportion using binary auxiliary information with applications to pharmaceutical studies, J. Biopharmaceut. Statist. 21 (2011), pp. 526–554), which proposed several ratio estimators of the population proportion and studied some theoretical properties. In this paper, we define a new ratio estimator based on a linear combination of two ratio estimators defined by Rueda et al. (2011). The variance of the new estimator is calculated and it is used to obtain the optimum value into the linear combination in the sense of minimal variance. Theoretical and empirical studies show that the suggested ratio estimator performs better than alternative estimators.

Estimating a Finite Population Proportion Bearing a Sensitive Attribute from a Single Probability Sample by Item Count Technique

Abstract: Randomized Response Techniques (RRTs) initiated by Warner (1965) have some disadvantages. Some participants either do not understand the RRT procedure or suspect revelation of privacy. Sometimes they end up concluding the randomization procedure as a foul trick. To overcome these problems as well as to shape the whole procedure in the form of canvassing a survey questionnaire, Raghavarao and Federer (1979) , Miller (1984) , and Miller et al. (1986) introduced the Item Count Technique also known as the List Experiment or the Block Total Response or the Unmatched Count Technique which is user friendly. This method was revised by Chaudhuri and Christofides (2007) which was an improvement over the original Item Count Technique in terms of protection of privacy of the respondents drawn from the population using a general sampling design, whereas the original method was restricted to simple random sampling. But a serious disadvantage is that it requires the selection of two independent samples costing more time and money. Also it needs the knowledge of the population proportion of an innocuous characteristic unrelated to the sensitive characteristic whose proportion is to be estimated. This chapter avoids both the problems.

Comprensión del valor esperado y variabilidad de la proporción muestral por estudiantes de educación secundaria obligatoria

Abstract: We analyse secondary school students’ intuitive understanding of the relationships between the population proportion and the expected value of a sample proportion, as well as its variability in relation to the sample size. We propose to 302 students four items in each of which four probable values for the number of outcomes for a given event are requested and in which the proportion population and sample size are varied. The statistical analysis of the values provided by the students suggests a good understanding of the relationships between the population and sample proportions. The variability of the sample proportion is overestimated in big samples and depends on the problem context in small samples. We also observed the equiprobability, positive and negative recency biases.

New Randomized Response Procedures

Abstract: This article focuses on the estimation of population proportion when the study variable is sensitive in nature. Two implicit randomized response techniques are proposed where the unrelated trait can be chosen subjectively. In addition to unbiased estimation of population proportion and variance, an empirical study is conducted to inspect the relative efficiency facet of the proposed techniques. The cases of positive binomial and negative binomial sampling are also studied. The proposed techniques are exposed to be better at the job than the accustomed randomized response dealings in binomial sampling. Further, it is established that negative binomial sampling may result in more precise estimation of population proportion using the proposed techniques.