Statistics review 2: samples and populations

Journal of Family Planning and Reproductive Health Care, 2002

Introductory Notes on a first course on Statistics

Statistics represents that body of methods by which characteristics of a population are inferred through observations made in a representative sample from that population. Since scientists rarely observe entire populations, sampling and statistical inference are essential. This article first discusses some general principles for the planning of experiments and data visualization. Then, a strong emphasis is put on the choice of appropriate standard statistical models and methods of statistical inference. (1) Standard models (binomial, Poisson, normal) are described. Application of these models to confidence interval estimation and parametric hypothesis testing are also described, including two-sample situations when the purpose is to compare two (or more) populations with respect to their means or variances. (2) Non-parametric inference tests are also described in cases where the data sample distribution is not compatible with standard parametric distributions. (3) Resampling methods using many randomly computer-generated samples are finally introduced for estimating characteristics of a distribution and for statistical inference. The following section deals with methods for processing multivariate data. Methods for dealing with clinical trials are also briefly reviewed. Finally, a last section discusses statistical computer software and guides the reader through a collection of bibliographic references adapted to different levels of expertise and topics.

2010

E stimation is the process of determining a likely value for a population parameter (eg, the true population mean or proportion) based on a random sample. In practice, a sample is drawn from the target population, and sample statistics (eg, the sample mean or sample proportion) are used to generate estimates of the unknown parameter. The sample should be representative of the population, ideally with participants selected at random from the population. Because different samples can produce different results, it is necessary to quantify the sampling error or variation that exists among estimates from different samples.

Journal of the Royal Statistical Society. Series …, 1971

Tracy et al.[8] have introduced a family of estimators using Srivenkataramana and Tracy ([6],[7]) transformation in simple random sampling. In this article, we have proposed a dual to ratio-cum-product estimator in stratified random sampling. The expressions of the mean square error of the proposed estimators are derived. Also, the theoretical findings are supported by a numerical example. Abstract Singh et al. (20009) introduced a family of exponential ratio and product type estimators in stratified random sampling. Under stratified random sampling without replacement scheme, the expressions of bias and mean square error (MSE) of Singh et al. (2009) and some other estimators, up to the first-and second-order approximations are derived. Also, the theoretical findings are supported by a numerical example.

Statistical techniques can be employed in almost all areas of life to draw inference about populations. In the context of market research the researcher samples customers from populations of consumers in order to establish what they think of particular products and services, or to identify purchasing behaviour so as to predict future preferences or buying habits. The information gathered in these surveys can then be used to draw inference about the wider population with a certain level of statistical confidence that the results are accurate. A necessary prerequisite to conducting a survey, and subsequently to drawing inference about a population, is to decide upon the best method of data collection. Data collection encompasses the fundamental areas of survey design and sampling. These are key elements in the statistical process, a poorly designed survey and an inadequate sample may lead to biased or misleading results which in turn will lead the researcher to draw incorrect inference. Analysing the collected data is another fundamental aspect and can include any number of statistical techniques. For the newcomer a broad understanding of numerical data and an ability to interpret graphical and numerical descriptive measures is an important starting point for becoming proficient at data collection, analysis and interpretation of results. The aim of this document is to provide a broad overview of survey design, sampling and statistical techniques commonly used in a market research environment to draw inference from survey data.

Methods of Demographic Analysis, 2013

The purpose of this chapter is to introduce some basic statistical measures that are commonly used in demographic analysis. The concepts are defined in general terms without going into theoretical details. Methods of calculation of various measures are described. The statistical measures discussed in this chapter consist of counts, frequencies, proportions, rates, various measures of central tendency, dispersion, comparison, correlation and regression. 3.2 Demographic Data and Analysis Demographic data can be classified according to their level of measurement. This is useful because the level of measurement helps the selection of what statistical analysis is most appropriate. Several classifications can be used. This book uses the four-fold classification system proposed by Stevens (1946) that classifies data as being (1) nominal, (2) ordinal, (3) interval and (4) ratio. There are other systems such as the twofold classification of (1) discrete and (2) continuous. In the classification system proposed by Stevens, the nominal level is known as the lowest level of measurement. Here, the values just name the attribute uniquely and do not imply an ordering of cases. For example, the variable marital is inherently nominal. In a study it might be useful to have attributes such as never married, married, separated, divorced and widowed. These attributes are mutually exclusive and exhaustive. They could be coded N, M, S, D and W respectively, or coded as 1, 2, 3, 4 and 5. In the latter, the numbers are not numbers in a real sense since they cannot be added or subtracted. Thus, numbers assigned to serve as values for nominal level variables such as marital status cannot be added, subtracted, multiplied or divided in a meaningful way. An exception is the dummy coding of F. Yusuf et al., Methods of Demographic Analysis,