Random Sampling Case Study

Introduction

Researchers usually cannot make direct observations of every individual in the population they are studying.

Instead, they collect data from a subset of individuals a 'sample'and use those observations to make inferences about the entire Population.

Sampling helps to determine the corresponding value of the population and plays a vital role in marketing research, it is the backbone of marketing research.

Market research involves the collection of data to obtain insight and knowledge into the needs and wants of customers and the structure and dynamics of a market. In nearly all cases, it would be very costly and time-consuming to collect data from the entire population of a market. Accordingly, in market research, extensive use is made of sampling from which, through careful design and analysis, Marketers can draw information about the market.

History

Random sampling by using lots is an old idea, mentioned several times in the Bible. In 1786 Pierre Simon Laplace estimated the population of France by using a sample, along with ratio estimator. He also computed probabilistic estimates of the error. These were not expressed as modern confidence intervals but as the sample size that would be needed to achieve a particular upper bound on the sampling error with probability 1000/1001. His estimates used Bayes' theorem with a uniform prior probability and assumed that his sample was random. Alexander Ivanovich Chuprov introduced sample surveys to Imperial Russian in the 1870s.

In the USA the 1936 Literary Digest prediction of a Republican win in the presidental elections went badly awry, due to severe bias. More than two million people responded to the study with their names obtained through magazine subscription lists and telephone directories. It was not appreciated that these lists were heavily biased towards Republicans and the resulting sample, though very large, was deeply flawed.

On the birth of sampling theory

Sampling theory was not invented suddenly but in a continuum together with the development of other statistical methods. New methods are not born in isolation from other related methods, and not in isolation from the development of society, either. Usually methods are developed stepwise, by the same author or by other authors in the same field. Each new idea is based - in one way or another - on previous knowledge or ideas. However, every now and then there are remarkable points in time at which development takes a new direction, or development splits into two different paths. In Kuhn's (1975) terminology, these points are called "intellectually violent revolutions". A classical example of this is Darwin's Evolution Theory that replaced Christian theory. Another example is Einstein's Relativity Theory that came in the place of Newton's Theory of Gravity. However, most examples are not as remarkable. Science usually develops in smaller steps, but

the changes, according to Kuhn, are similar.

Although sampling theory has become a separate, grown-up branch in modern statistical science, this was certainly not the case at the beginning. The roots of survey sampling are more in official statistics and social statistics than in the probability theory and experimental design. Especially political arithmetic and later social calculus have been important activities in early stages that gave rise at a later stage to developments finally leading to modern sampling theory. However, only after the probability theory had become an inherent component of the sampling theory, it has been regarded as a genuine branch of statistical science. The history of survey sampling is longer, though.

To understand the history of sampling we should first ask where the history of

statistics begins. This also was the title of a paper by Kendall (1960). He claims that it is always difficult to trace the roots of specific themes back to the past, because developments usually have no clear-cut starting point. Only much later is it possible to see and understand what has influenced a discipline to be born. By looking back it is possible to assess the importance and impact of various factors, and trace crucial innovations. However, the reasons and motives usually remain uncertain because they are partly concluded by way of conjecture, and all affecting facts and factors may not be known at all. In addition, early scientific reports contained little reference to sources. This makes it difficult to follow paths to sources of ideas. All this applies to the history of survey sampling as well.

A general problem in understanding history development of ideas and science is that it is difficult to know what was known, and what was not known. There is always a risk that we project our present knowledge and ways of thinking to the past, and that may be wrong in many cases.

Yet, if a year must be chosen as a starting point for statistical sampling, 1895 would be a good candidate. There are many reasons to claim that this year marks the beginning of modern survey sampling. If there is one man that should be given credit for starting the development leading to the widespread use of sampling as a scientific method, it is Anders Kiaer, the director of the Norwegian Statistical Bureau. Many respected authors share this view, but different views also exist.

Sample and population

When we think of the term "population," we usually think of people in our town, region, state or country and their respective characteristics such as gender, age, marital status, ethnic membership, religion and so forth. In statistics the term "population" takes on a slightly different meaning. The "population" in statistics includes all members of a defined group that we are studying or collecting information on for data driven decisions.

A part of the population is called a sample. It is a proportion of the population, a slice of it, a part of it and all its characteristics. A sample is a scientifically drawn group that actually possesses the same characteristicsas the population - if it is drawn randomly.

Randomly drawn samples must have two characteristics:

- Every person has an equal opportunity to be selected for your sample; and,

- Selection of one person is independent of the selection of another person.

What is great about random samples is that you can generalize to the population that you are interested