Statistics and Sampling Essay ⋆ Environment Essay Examples ⋆ EssayEmpire

This Statistics and Sampling Essay example is published for educational and informational purposes only. If you need a custom essay or research paper on this topic, please use our writing services. EssayEmpire.com offers reliable custom essay writing services that can help you to receive high grades and impress your professors with the quality of each essay or research paper you hand in.

The word st ati stic s is derived from the Latin term statisticum collegium, meaning “council of state,” and the Italian word statista, meaning “statesman” or “politician.” In 1749, Gottfried Achenwall introduced Statistik for the analysis of data to be used by government and administration, signifying the “science of state” (then called “political arithmetic” in English). It acquired the meaning of the collection and classification of data in the early 19th century. It was introduced into English by Sir John Sinclair. Statistics found its way into other areas like public health, economics, and social sciences during the 20th century.

The mathematical methods of statistics evolved from probability theory in 1654 as indicated in the correspondence of Pierre de Fermat and Blaise Pascal. In the early 1700s, Jakob Bernoulli (Ars Conjectandi) and Abraham de Moivre (Doctrine of Chances) treated the subject as a branch of mathematics. Adolphe Quetelet in the 19th century introduced the notion of the “average man” (l’homme moyen) as a means of understanding complex social phenomena such as crime, marriage, or suicide rates.

Statistics is a mathematical science related with collection, analysis, interpretation, and presentation of data. It helps to understand data and make informed decisions. It has applications in every field of arts, sciences, and humanities. Business, government, medicine, and academia use statistics to make informed decisions.

In order to apply statistics, a process or population to be studied is required. The data could be the demographics of a population of a city, deforestation, defoliation, or flocks of birds. It could also be a process observed at various times, for example sea levels at various times of day. Such data is referred to as time series data. There are four different kinds of measurement: nominal, ordinal, interval, and ratio.

Ordinal measurements consists of different categories, the order of which have a meaning, such as age groups. Nominal measurements also has categories that have no meaningful rank order among values, such as city names. Interval measurements have meaningful distances between measurements, but no meaningful zero value, such as height measurement. Ratio measurements, where both a zero value and distances between different measurements are defined, provide the greatest flexibility in statistical methods that can be used for analyzing data. The variables with ordinal and nominal measurements such as age groups or city names are referred to as categorical variables, and the variables with ratio and interval measurements are referred to as continuous variables.

Statistics can be divided into two groups-mathematical or theoretical statistics, and applied statistics. Applied statistics consists of descriptive and inferential statistics. Mathematical statistics is concerned with the theoretical basis of the subject. Descriptive statistics involves summarization or description of the data, for example the mean, standard deviation for continuous variables, count, and percent for categorical variables. It does not involve extrapolating the results to the population; it is a mere description of the study sample. Inferential statistics, on the other hand, involves modeling of the data that accounts for the randomness and uncertainty in observing data prior to drawing inferences (or conclusions) about the process or population under study. Some of the examples of inferential statistics are hypothesis testing, point or interval estimation, prediction, correlation, or regression. This involves drawing conclusions regarding the population based on the data collected on a sample.

Usually, it is not practical to collect data about the entire population or process; instead data is collected from a subset of population referred to as a sample. Data are collected on the sample in an experimental setting that is subjected to statistical analysis to describe the sample and draw inferences about the population. Sampling is concerned with the selection of individual observations intended to obtain knowledge about a population of concern, especially for the purposes of statistical inference. Pierre Simon Laplace was one of the first to use a sample to estimate the population of France in 1786. He also computed probabilistic estimates of the error. The sampling process consists of five stages:

Definition of the population of concern, such as the people of a city, birds, trees, or fish.
Specification of a sampling frame, representative of the population, a set of items or events that are possible to measure, such as the circumference of tree trunks.
Specification of sampling method for selecting items or events from the frame: simple random sampling, cluster sampling, two stage sampling, convenience sampling, systematic sampling, or quota sampling.
Sampling and data collecting: Following the defined sampling process, keeping data in time order, and recording comments and other contextual events as well as non-responses.
Review of sampling process: After sampling, the process followed in sampling should be reviewed for issues that might affect the final analysis.

Sampling methods can be classified as probability samples or nonprobability samples. In probability samples, each member of the population has a known nonzero probability of being selected. Probability methods include random sampling, systematic sampling, and stratified sampling. In nonprobability sampling, members are selected from the population in some nonrandom manner. These include convenience sampling, judgment sampling, quota sampling, and snowball sampling. It is possible to calculate sampling error only in probability sampling and inferences are often reported as plus or minus the sampling error.

The inferences and conclusions drawn from a sample can be extended to the population only if the sample is representative of the population. The biggest challenge usually lies in determining the extent to which the sample is representative of the population. As a result, much attention and research has taken place in the area of design of experiments that offers techniques to estimate and correct for randomness in the sample and in the data collection procedure. Another challenge in drawing the sample is determining the appropriate sample size that would be representative of the population and will help to draw conclusions controlling for type I as well as type II error rates. There are several tables available for determining the appropriate sample sizes for different tests (ttest, z-test, binomial test, ANOVA, regression) and criterion (one tailed, two tailed).

The statistical tests used to draw conclusions from data are categorized as parametric or nonparametric methods. Parametric methods involve assumption of the distribution of the data, most often data to be normally distributed. Some of the most common parametric tests used in statistics to draw conclusions are: Students t-test, Chi-square, ANOVA, and regression analysis. Non-parametric methods, on the other hand, do not make any such assumptions. Some of the non-parametric methods include the Mann-Whitney U test, Signed Ranked Test, Signed Tests, and Runs Tests.

Statistics collected and analyzed for understanding the environment and environmental change are numerous. Among many others, these include figures describing populations of animals and people, land cover areas, rates of expenditures on pollution controls, and estimates of carbon emissions, as well as basic environmental data, like sea surface temperature readings, tectonic movements, and water quality measures.

While the burgeoning growth of these statistical measures appears to bode well for increased understanding of environmental conditions and change, there are serious limits to, and problems within, socio-environmental statistics. At a global scale, most statistics are contributed to databases by individual nation states. In many cases, good data are simply not available for all environmental issues. In other cases, the methods of collecting or recording those data may vary dramatically between countries, making comparison or analysis questionable. In other cases, numbers are simply fabrications, stated for the protection and convenience of state interests. Many otherwise excellent databases, including those kept by the United Nations and the World Bank Group, are filled with data values that, even if reliable, must be treated with extreme caution in conducting any kind of comparison.

Many environmental problems, moreover, are not necessarily amenable to simple statistical analysis for explanation or management. While rates of pesticide use amongst consumers can be determined, and analyzed against housing values and incomes, truly explaining complex human environmental behaviors like these often requires more highly qualitative, interview-based exploration. Statistics are therefore essential to understanding environment and society problems but must be treated critically and will be most effective when coupled with other modes of analysis and forms of data.

Bibliography:

W.G. Cochran, Sampling Techniques (John Wiley & Sons, 1977);
Cohen, Statistical Power Analysis for Behavioral Sciences (Lawrence Erlbaum Associates, 1988);
V. Hogg, Allen Craig, and Joseph W. McKean, Introduction to Mathematical Statistics (Prentice Hall, 2004).