Elementary Statistics

I.  Introduction

Statistical thinking will one day be as necessary as the ability to read and write.

- H. G. Wells

We have come into the age of computerization and are becoming rich in information at a very fast rate. However, data gathered will not make sense unless we know how to use the available information to make good decisions. This problem can be aided by Statistics because Statistics deals with the collection, presentation, analysis and interpretation of a set of data in order to yield meaningful information.

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Some uses of Statistics:

To know how to properly present and describe information.

To know how to draw conclusions about large populations based only on information obtained from samples.

Population  –  refers to the totality of the observations of which the study is concerned

Sample –  refers to a part or subset of a population

To know how to improve processes like strategies on how to improve sales or quality of a product or services delivered by an organization.

To know how to obtain reliable forecasts.

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Two Major Areas of Statistics:

Descriptive Statistics – defined as those statistical methods concerned with the collection, presentation and characterization of a set of data in order to describe the various features of that set of data properly.

Inferential Statistics – defined as those statistical methods that make possible the estimation of a characteristic of a population or the making of a decision concerning a population based only on sample results.

Illustration. Suppose a study will be conducted in order to learn about student perceptions concerning the imposition of a tuition fee increase in MSU.

Population of the study: All currently enrolled students of MSU.

Main objective of the study: To estimate the various attitudes or characteristics of interest of the entire population.

Application of Inferential Statistics: Select a sample from the population and use the statistics computed from the sample to draw conclusions about the population parameters or characteristics.

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Remark:  Inferential Statistics has been developed due to the benefits of studying only a sample instead of a whole population.

Advantages of sampling:

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In sampling, only a relatively small number of respondents or experimental units will be involved; thus, it is better because:

it entails lesser cost;

it is less time consuming;

it is less cumbersome and more practical to administer; and

some experiments are destructive so it is not possible to involve the whole population. For example, in the quality sampling of products, if you test or taste the product, usually it cannot be sold anymore.

Sampling also has disadvantages, the biggest of which is that the sample may not truly reflect the characteristic of the population and this would lead to wrong conclusions. Hence, care must be taken in choosing a sample.

II.  Sampling Procedures

A. Non-probability Sampling – is one in which individuals or items are chosen without regard to their probability of occurrence. This is usually used when the size of the population is unknown.

Examples: 

Purposive Sampling - making a sample which agrees with the profile of the population based on some pre-selected characteristics.

Quota Sampling - selecting a specified number (quota) of units possessing certain characteristics.

Convenience Sampling - using results that are readily available.

Judgment Sampling - selecting a sample in accordance with an expert’s judgment.

B. Probability Sampling – is one in which the elements of the sample are chosen on the basis of known probabilities. Each element in the population has an equal and independent chance