Population proportion

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

Visualizing and Understanding Confidence Intervals Using Dynamic Software

Abstract: One of the standard topics in any introductory statistics course is confidence intervals for estimating the value of some population parameter. In particular, consider the notion of estimating the unknown mean p for a population based on the data obtained from a random sample drawn from that population. The confidence interval so constructed is centered at the sample mean x and extends sufficiently far in each direction so as to have a pre-determined probability of containing p. To construct a 95% confidence interval for the mean, the interval should have a 95% chance of containing p. Equivalently, in 95% of the confidence intervals so constructed, the resulting interval should contain the true mean p.For most students in introductory statistics, the above statements represent little more than acts of faith. They do not fully appreciate the fact that the confidence interval constructed will correctly contain p with probability 0.95. There is simply no effective way to construct, in class, a large variety of different confidence intervals based on different sample data to see whether or not the theoretical considerations actually make sense. Instead, the students just perform the appropriate manipulations to calculate the correct answer to such problems in a purely mechanical fashion or have the calculations done for them with either a calculator routine or some statistical software package.Unfortunately, this is a topic that all too often reduces to rote memorization of formulas and procedures, in large measure because there are so many variations considered. For instance, there are:* confidence intervals for the population mean p when you have a large sample, and when you have a small sample;* confidence intervals for the population proportion n when you have a large sample, and when you have a small sample;* confidence intervals for the difference in population means when you have two samples drawn from similar populations, and* confidence intervals for the difference in population proportions.It is not in the least surprising that many students find their heads reeling and so come out of the course with little understanding of what confidence intervals are all about.Technology has much to offer to reduce the tendency for the topic to be treated as a variety of exercises in rote memorization. Most graphing calculators contain a full menu of statistical functions that include most variations on constructing confidence intervals, as do statistical software packages and spreadsheets such as Excel. Some older calculator models only operated on a set of data entered in one or more lists to calculate the summary statistical measures and the corresponding confidence interval. Newer calculators give the option to work either with the raw data or the statistical measures, which more closely mirrors the typical kind of problems found in most textbooks in which students are asked to construct the confidence interval based on a sample of size n = 36 where the sample mean is 24 and the sample standard deviation is 9, say.Even when students utilize technology to construct confidence intervals, the majority still tend to come away with very little in the way of basic understanding of the underlying fundamental concepts. In particular, they don't understand the significance of:* the variation in the results due to the variations between different samples;* the effects of sample size on the results;* the effects of changes in the sample data or the sample statistics on the results;* the effects of the choice of confidence level on the length of the confidence interval.Gaining a solid understanding of all of these ideas requires the use of dynamic software to bring the concepts to life and so make a far stronger impact on the students.DYNAMIC PROGRAMS IN EXCELThe authors have developed a collection of dynamic modules in Excel that are intended to enhance student understanding of the fundamental concepts related to confidence intervals (as well as virtually every other topic in introductory statistics). …

New Evidence on Linear Regression and Treatment Effect Heterogeneity

Abstract: In this paper I provide new evidence on the implications of treatment effect heterogeneity for least squares estimation when the effects are inappropriately assumed to be homogenous. I prove that under a set of benchmark assumptions linear regression provides a consistent estimator of the population average treatment effect on the treated times the population proportion of the nontreated individuals plus the population average treatment effect on the nontreated times the population proportion of the treated individuals. Consequently, in many empirical applications the linear regression estimates might not be close to any of the standard average treatment effects of interest.

Estimation and Hypotheses Testing

Abstract: In this chapter, we shall discuss statistical inference where data collected will be viewed as a random sample from some population. The information so gathered from such a sample will then be used to conduct a Statistical estimation which basically comprises of determining an estimate of some parameter of the population as well as assessing the precision of such an estimate. We present an example relating to contamination counts of a sample of 20 vaccines preserved with phenol.

Estimating sensitive population proportion using a combination of binomial and hypergeometric randomized responses by direct and inverse mechanism

Abstract: For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to...