In the book titled Statistics, it explained a sample was a smaller group of members of a population selected to represent the population. In order to use statistics to learn things about the population, the sample must be random. A random sample is one in which every member of a population has an equal chance to be selected.

Random Sampling

Sampling can be a difficult job, especially if one does not organize its data to provide that every single individual in a group has an equal change of being chosen in the sample. A sample which has been chosen in this way is called a random sample. Getting random samples are not easy, because the expert must choose what he considers to be a representative selection.

In the book titled, Statistics it stated that there is only way to be absolutely sure of getting a true random sample. It is to assign a number to each individual in the parent group, and then select the requisite number of individuals to make up the sample group by using a Table of Random Numbers. A selection of random numbers is given opposite. These numbers have been found by a kind of electronic roulette wheel and have been checked in many different ways to ensure that they are as random as possible. They are chaotic, in that there is no rule connecting any digit with its neighbors, and yet there is a kind of overall regularity, in that each digit tends to occur with equal frequency when the Table is viewed as a whole.

Sample Size

The reason for having a particular size is so that sample can give an accurate estimate of the topic, for example you don’t want to just sample two women and expect to give an accurate estimate of the average weight of women.

With random samples, the larger the sample the more accurate it will reflect the characteristics of the population. In the book titled, Practical Statitistics, it stated that this accuracy increases with the square root of the sample size, so that a sample must be increased 100-fold to get a 10-fold increase in accuracy.

So one must remember that the reliability of infomation provided by a sample depends, on the care one takes to ensure its randomness, and on the size of the sample. The reliability is a function of the sample size itself, not of the proportion that the sample bears to its parent group (unless the sample consits of 20% or more of the parent group). This means that a random sample of 1,000 people taken from a town of 6,000 people will not prove appreciably more accurate than a similar sample of 1,000 people taken from a city of 2,000 people. It is the sample size itself which counts.

Other Sampling Methods

There are a few different sampling methods. The first one is called systematic sampling and the second is a presenting sample and there are still other methods with special applications, but today I want to focus on these two methods.

The systematic sampling is used in moving production lines in a factory. The process is decribed in great detail in the book titled, Practical Statistics, it entails selecting individual items at regular specified intervals along the line. Suppose that the degree of precision required has dictated that 10% of the parent group should be inspected, this would be done by examining every 10th individual along the line. A Table of Random Numbers is used to choose the 1st item out of the the initial 10 in the line. Suppose that the degree of precision required has dicated that 10% of the parent group should be inspected, this would be one by examining every 10th individual along the line. A Table of Random Numbers is used to chose the 1st itme out of th initial 10 in the line; suppose this turns out to be 3, you would then sample the 3rd , 13th, 23rd, 33rd, and so on, item along the line. If for any reason it is suspected tha the parent group may vary in some regular cyclical way, it would be necessary to select individuals at irregular intervals, for example at random intervals out of each group of 10 (or whatever proportion is being sampled).

A presenting sample, consists of consecutive patients who present themselves for treatment of a certain complaint. An example used in Practical Statistics explained that a doctor may report on the last 50 cases of appendictites that he has seen. Such a sample can often be accepted as being equivalent to a truly random sample, such as might be drawn from a parent group consisting of all possbile cases for the disease in question. But this is not always the case. For one thing, the patients must be genuinely consecutive; the exclusion of any cases from the series would certainly destroy the randomness, and it would obvioulsy be unwise to draw any general conclusion from a hand-picked sample.

So when deciding to do a sample, one must carefully select individuals, according to a definite plane and use the Table of Radom Numbers. Whatever method you choose, remember that a badly chosen sample is worse than useless - it is positively misleading!