Factores Políticos.

68

MODULE 3 SAMPLING THEORY

69

2.0 OBJECTIVES

At the end of this unit, you should be able to:

• know the meaning of sampling

• understand random samples

• understand random population parameters

3.0 MAIN CONTENT

3.1 Meaning of Sampling

If we draw an object from a pack of population, we have the choice of replacing or not replacing the object into the pack before we draw again. In this first case, a particular object can come up again and again, whereas in the second it can come up only once. Sampling where each member of the population may be chosen more than once is called sampling with replacement, while sampling where each member cannot be chosen more than once is called sampling without replacement.

But it should be noted that finite population that is sampled with replacement can theoretically be considered infinite since samples of any size can be drawn without exhausting the population. For most practical purposes, sampling from a finite population that is very large can be considered as sampling from an infinite population.

3.1.1 Populations

In statistics the term population has a slightly different meaning from the one given to it in ordinary speech. It need not refer only to people or to animate creatures - the population of Nigeria, for instance or the female population of Lagos. Statisticians also speak of a population of objects, or events, or procedures, or observations, including such things as the quantity of lead in urine, visits to the doctor, or surgical operations. A population is thus an aggregate of creatures, things, cases and so on.

Although a statistician should clearly define the population he or she is dealing with, they may not be able to enumerate it exactly. For instance, in ordinary usage the population of Nigeria denotes the number of people within Nigerian's boundaries, perhaps as enumerated at a census. But a physician might embark on a study to try to answer the question "What is the average systolic blood pressure of Nigerian men aged 30-69?" But who are the Nigerian men referred to here? Not all Nigerian men live in Nigeria, and the social and genetic background of those that do may vary. A surgeon may study the effects of two alternative operations for malaria. But one may ask a question that how old are the patients? What sex are they? How severe is their disease? Where do they live? And so on. The reader needs precise information on such matters to draw

70

valid inferences from the sample that was studied to the population being considered. Statistics such as averages and standard deviations, when taken from populations are referred to as population parameters.

3.1.2 Samples

A population commonly contains too many individuals to study conveniently, so an investigation is often restricted to one or more samples drawn from it. A well chosen sample will contain most of the information about a particular population parameter but the relation between the sample and the population must be such as to allow true inferences to be made about a population from that sample.

Consequently, the first important attribute of a sample is that every individual in the population from which it is drawn must have a known non-zero chance of being included in it; a natural suggestion is that these chances should be equal.

We would like the choices to be made independently; in other words, the choice of one subject will not affect the chance of other subjects being chosen

SELF ASSESSMENT EXERCISES

Discuss the use of sampling with replacement and without replacement

3.2 Random Samples and Random Numbers

Clearly, the reliability of conclusions drawn concerning a population depends on whether the sample is properly chosen so as to represent the population sufficiently well, and one of the important problems of statistical inference is just how to choose a sample.

However, one way to do this for finite populations is to make sure that each member of the population has the same chance of being in the sample, which invariably called a random sample. Random sampling can be accomplished for relatively small populations by drawing lots, or it equivalently, by using a standard table of random numbers. But it should be noted that it is normally constructed for such purposes.

Finally, because inferences from sample to population cannot be certain, we must use the language of probability in any statement of conclusion.

SELF ASSESSMENT EXERCISE

Differentiate between a Random samples and Random numbers.

71

4.0 CONCLUSION

In this unit, we have discussed about population and sample. However, we can conclude that population is the entire pool from which a statistical sample is drawn. The information obtained from the sample allows statisticians to develop hypotheses about the larger population. Researchers gather information from a sample because of the difficulty of studying the entire population. In statistical equations, population is usually denoted with a capital 'N', while the sample is usually denoted with a lowercase 'n'.

5.0 SUMMARY

This unit has really enabled us to do justice to population and sample. However, Population sampling is the process of taking a subset of subjects that is representative of the entire population. The sample must have sufficient size to warrant statistical analysis.

6.0 TUTOR MARKED ASSIGNMENT Differentiate between the following;

1. Population and a sample

2. Random Samples and Random Numbers 7.0 REFERENCES/FURTHER READINGS

Ademisan, T.Y. (2011) Introduction to Statistics, a contemporary issue, 1^st edition, Mill world Publication limited.

Adedayo, O. A (2000).Understanding Statistics, JAS publisher Akoka, Lagos

72

UNIT 2 POPULATION PARAMETERS