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Inferential Statistics

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Inferential Statistics

The Objectives are:

  • What is meant by a sample and a population?

  • What is meant by inferential statistics?

  • Identification of biased samples.

  • How is simple random sampling different from stratified sampling?

  • How is random sampling different from random assignment?

Inferential Statistics Definition

What is meant by a Population and a sample?

In a statistical investigation the interest lies in some characteristics relating to a group of individuals and such a group under study is referred to as thepopulation. Quite often, it may not be practicable to study the whole population due to limited time, money, and man power, or due to the population being infinite, and as such, we are to depend on the study of a part of the population for determination of the population characteristics. A few examples are given below:

  1. Example 1: A politician calls you on the phone .He asks you to find out the percentage of the voters in the country who are registered voters, will vote for him. Now, to do so, there are two ways of doing so.

  2. The first option will be to call the voters and ask them about their voting preference, i.e., who they will vote for. Although this process of asking yields accurate results yet it is quite time-consuming and tedious. So the better option will be to take a sample, rather than considering the whole population. The second option will be to take a reasonable sample which will give accurate results.

  3. Example 2: If one wants to know the average height of women who belongs to the age group of 15-30.It becomes impossible to know the heights of every person belonging to this age group. So it is reasonable to consider a sample in such case.

  4. Example 3: To study the health of all children who were born in the year 2002. Here, also it will be meaningless to consider the whole population. Instead, you should take a sample of babies born in that year.

  5. Example4: To know about the Americans who played volleyball in the last two years. Here also you should consider a sample.

Types of Inferential Statistics

Simple Random Sampling

If a sample is drawn from a given population in such a manner that each member of the population has a definite pre-assigned probability of being included in the sample, the sampling is called random sampling. In simple random sampling all the members have the same or equal probability or chance of being selected The sample obtained, is called a simple random sample. Simple random sampling may be with or without replacement.

  1. Example 1: Let us consider a sample of 60 numbers. Call out the 60 random numbers like 129, 265, 698, 1099, etc. and after which those numbers are searched in the phone book. Make a call to those people by asking them your questions related to your research. Also, you can dial the numbers randomly.

Thus, this is an example of simple random sampling.

  1. Example 2: In selecting a random sample of 2 boys from a group of 6 boys by tossing a fair coin. Here the population size is 6 and so we consider 3 tosses of a fair coin for constructing the miniature population. Let the outcomes HHH, HHT, HTH, HTT, THH and THT correspond to boys having serial numbers 1, 2, 3,4,5,6 respectively. Suppose the coin is tossed three times and the outcome THH is obtained. Then the first member of the sample will be the boy with number 5. Let in the next 3 tosses, the result is TTH. In this case, it is rejected, since it does not correspond to any boy. In this way the sampling is performed and the desired sample is obtained.

Sample size:

We know that, when each member of the population has an equal chance of being selected, then the sampling is called simple random sampling. It is not the result of the sampling, the sampling procedure involved is random. In random sampling, if the sample size is small then it is not necessary that the sample will represent the whole population. In such cases the sample drawn is random, but this sample would not be a reprehensive of the whole population. If the sample size is large then it becomes likely that the sample is a close representative of the population. This is the reason why inferential statistics considers sample size when results are generated from the samples to populations. Mathematical techniques are there to ensure the sensitivity to sample size. The sample size thus matters.

More complex sampling

There are some cases it is not meaningful to build a simple random sampling. Let us consider an example where the people are sampled starting from poor area and ending at an expensive district. In such case, if a simple random sampling is done, then too many samples from high end and too few from low end or vice versa may occur. So, here the idea of performing simple random sampling is not good. Thus, sometimes more complex sampling is required.

What is Random Assignment?

The experimental technique of assigning the subjects to different treatments so no treatment is known as random assignment or random placement. In random assignment, the treatments are randomly assigned, the groups under consideration are roughly equivalent, as a result of it the observed effect between the treatment groups is linked to the treatment effect, and the individual doesn’t possess this characteristics. In experimental design, at the outset of the experiment, the random assignment of individuals in experimental group and control group ensures the difference that occurs between group and within group is not systematic. Random assignment tells us that the differences are due to chance, but it does not guarantee that whether the groups are matched or equivalent.

The Steps of Random assignment are:

  • Start with a collection of subjects.

  • A method is devised for randomization which should be mechanical.

  • After which subjects are assigned to the two groups viz - Control Group and Experimental Group.

Example: In our example we consider a treatment and a control group. Let from a population of 40, the experimenter finds that 20 people possess brown eyes and 20 have blue eyes. The result becomes biased if the experimenter assigns all of the brown eyed individuals to the treatment group and all the brown-eyed individuals to the control group. In analyzing the result a question may arise that whether the effect which is observed, was due to applied experiment or was due to the color of the eye.

In random assignment, the individuals are randomly assigned to either the treatment group or the control group, and so a better chance can be made in detecting that the change is due to experimental treatment or due to chance.

What is Stratified Sampling?

Another method of sampling is the stratified sampling. In this method, before drawing the random sample, one divides the population into several strata or sub populations, which are relatively homogeneous within themselves and the means of which are as widely different as possible. Stratified random sampling is preferable to simple random sampling on the following cases:

  1. In many situations stratified sampling will be administratively more convenient.

  2. Stratified sampling will be more representative in the sense that here it can be ensured that some individuals from each of the strata will be included in thesesample.

  3. Stratified sampling, moreover, has the merit of supplying not only an estimate for the population as a whole, but also separate estimates for the individual strata.

  4. Since a portion of the variability identifiable as between strata variance is eliminated in stratified random sampling, it is more efficient than simple random sampling.

Example 1: For example a student studying in a school determines the registration tuition class as strata and, then the students are randomly selected from each of these classes.

Example 2: Let us consider the number of men is greater than that of women in a company. However, we are required to have equal representation of each group. Thus, two strata having equal number of men and women are created.

Variance is controlled through stratification, as a result of which standard error can be reduced.

Statistical help and online statistics help provided by us will thus help you to learn the proper use and various aspects of statistics.

Inferential Statistics Examples

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