# Inferential statistics

Understanding Inferences

Inferential statistics is a set of methods used to draw conclusions or inferences about characteristics of populations based on data from a sample.The mean calculated for a population. The standard deviation calculated for a population. The objective of statistical inference is to draw conclusions about population characteristics based on the information contained in a sample.

Statistical inference in a practical situation contains two elements:

• The inference

• A measure of its validity

The steps involved in statistical inference are:

• Define the problem objective precisely.

• Decide if the problem will be evaluated by a one-tail or two-tail test.

• Formulate a null hypothesis and an alternate hypothesis.

• Select a test distribution and a critical value of the test statistic reflecting the degree of uncertainty that can be tolerated (the alpha, u, risk).

• Calculate a test statistic value from the sample information.

• Make an inference about the population by comparing the calculated value to the critical value. This step determines if the null hypothesis is to be rejected. If the null is rejected, the alternate must be accepted.

• Communicate the findings to interested parties.

Everyday, in our personal and professional lives, individuals are faced with decisions between choice A or choice B. In most situations, relevant information is available; but it may be presented in a form that is difficult to digest, quite often, the data seems inconsistent or contradictory, in these situations, an intuitive decision may be little more than an outright guess, while most people feel their intuitive powers are quite good, the fact is that decisions made on gut-feeling are often wrong.

SAMPLING TECHNIQUES AND USES

Sampling is the process of selecting a small number of elements from a larger defined target group of elements. Population is the total group of elements we want to study. Sample is the subgroup of the population we actually study. Sample would mean a group of ‘n’ employees chosen randomly from organization of population ‘N’

Sampling is done in situations :

• When the process involves destructive testing, e.g. taste tests, car crash tests, etc.

• When there are constraints of time and costs.

• When the populations cannot be easily captured.

Sampling is NOT done in situation:

When the events and products are unique and cannot be replicable.

Sampling Techniques can be classified into:

• Probability Sampling: Probability sampling is when there is a probability of an event to occur.

• No Probability Sampling: No probability sampling does not depend on the chance cause for an event to occur.

Probability Sampling includes:

1. Simple Random Sampling

2. Stratified Random Sampling

3. Systematic Sampling

4. Cluster Sampling

No Probability Sampling includes:

1. Convenience Sampling.

2. Judgment Sampling.

3. Quota Sampling.

4. Snowball Sampling.

Probability Sampling

Simple random sampling is a method of sampling in which every unit has equal chance of being selected. Stratified random sampling is a method of sampling in which stratum/groups are created and then units are picked randomly. Systematic sampling is a method of sampling in which every nth unit is selected from the population.

Cluster sampling is a method of sampling in which clusters are sampled every tth time.