Basic Statistical Concepts: Data Collection by Sampling Method

The aim of Statistics is to provide insights by way of numbers. In pursuit of this aim, Statistics divides the study of data into three parts; collecting data, describing and presenting data, and drawing conclusions from data. Statistics gives designs or patterns or outlines used to arrange observations and experiments. Such designs are called sampling method for collecting data by observations and experimental method for collecting data by experimentation.

Sampling

The essential idea of sampling is to gain information about the whole by examining only a part. Here is the basic terminology used by statisticians to discuss sampling. Population, the entire group of objects about which information is desired. Unit, defined as any individual member of the population. Sample, a part or subset of the population to gain information about the whole. Sampling frame, the list of units from which the sample is chosen. Variable, a characteristic of a unit, to be measured for those units in the sample.

Examples of sampling method.

1.Public opinion polls are designed to determine public opinion on a variety of issues. The specific variables measured are responses to questions about public issues. Though most noticed at election time, these polls are conducted on a regular basis throughout the year. A typical poll has a sample population, say, 18 years of age and over and about 2,000 persons interviewed personally.

2.Market research is designed to discover consumer preferences and usage of products. Among the better-known examples of market research are the television rating services, which typically have has a sample population, say, all households with at least one TV set and about 1,200 households that agree to keep a TV diary.

3.The decennial census is required by the constitution. An attempt is made to collect basic information (ex. number of occupants, age, sex, income, etc.) from each household in the country. Much other information is collected, but only from a sample of households. A typical decennial census consist of all households in the country and has the entire population for basic information, and 20% of the population for other information

4.Acceptance sampling is the selection and careful inspection of a sample from a large lot of a product shipped by a supplier. On the basis of this, a decision is made whether to accept or reject the entire lot. The exact acceptance sampling procedure to be followed is usually stated in the contract between the purchaser and the supplier. A typical acceptance sampling method requires a lot of items shipped by the supplier and a portion of the lot that the purchaser chooses for inspection.

A census is a sample consisting of the entire population. If information is desired about the population, why not take a census? The following are some reasons why a sample is preferable to a census. First, if the population is large, it is too expensive and time consuming to take a census. Second, in some cases, such as acceptance sampling of fuses or ammunition, the units are destroyed during testing. And lastly, a relatively small sample yields accurate data than a census.

Selection of whichever units of the population are easily accessible is called convenience sampling. Samples obtained in this way are often not representative of the population and lead to misleading conclusions about the population. Convenience samples are often biased (often called favoritism); the results consistently and repeatedly differ from the truth about the population in the same direction. A remedy caused by the “favoritism” usually caused by a convenience sampling is to take a simple random sample. A simple random sample (SRS) of size n is a sample of n units chosen in such a way that every collection of n units from the sampling frame has the same chance of being chosen. A SRS is fair or unbiased: No part of the sampling frame is under-represented or over-represented.

In summary, despite the sampling variability of statistics from an SRS, the values of those SRS have a known distribution in repeated sampling. When the sampling frame lists the entire population, simple random sampling produces unbiased estimates, the values of a statistic from an SRS neither consistently over estimate nor consistently underestimate the population parameter. And the precision of a statistic from an SRS depends on the size of the sample and can be made as high as desired by taking a large enough sample.