Probability & Non Probability Sampling Methods Lecture 24

 Probability & Non-Probability Sampling

Lecture 24

Probability Sampling

In probability sampling, every unit of the population has a known, non-zero chance of being selected.

Following are methods of probability sampling.

Simple Random Sampling

Simple random sampling is the most basic technique, where each unit of the population has an equal probability of being selected and each selection is independent.

Let a population consist of “N” units, and a simple random sample of size “n” is selected with or without replacement. Then total possible samples will be:

Example 7.1: How many possible samples of size 2 can be selected from population size 5 by i) with replacement and ii) without replacement?

i. Total Possible Samples by With Replacement:

ii. Total Possible Samples without Replacement:

Advantages

i. It is free of errors.

ii. It is more representative of the population.

iii. It is simple to use.

iv. It is free from personal bias

v. It is simple to use

Disadvantages

i. Random selection is challenging.

ii. Heterogeneous populations fail this method.

iii. Lack of knowledge about population

iv. Applicable on small level

Stratified Random Sampling 

The stratified random sampling is a probability method of sampling in which the heterogeneous population of size N is distributed into homogeneous groups, i.e., N1, N2,..., Nk, known as strata, and each group is called a stratum. For every stratum, use the simple random sampling procedure to choose a sample of size n1 from N1, n2 from N2, and so forth. 

Advantages

i. Stratified sampling is an effective method of random sampling to collect information from a large population.

ii. It allows the investigator to manage a large population.

iii. It allows to collect the most accurate data.

iv. It allows to change sample size from stratum to stratum.

v. It helps to collect information from a more diverse range of data.

Disadvantages

i. It is difficult to use in non-statistical studies.

ii. All information about the structure of the population is required. It is extremely difficult in real-life studies.

Example 7.2: There are 2000 students studying in college. The students are split into four groups: male intermediate students make up 34%, female intermediate students make up 21%, male graduate students make up 28%, and female graduate students make up 17%.

Calculate the sizes of the strata.

Solution:

N = 2000

N1: Male intermediate students = 34 %

N2: Female intermediate students = 21%

N3: Malegraduate students = 28 %

N4: Female graduate students = 17%

N1 = N X 0.34 = 2000 X 0.34 = 680

N2 = N X 0.21 = 2000 X 0.21 = 420

N3 = N X 0.28 = 2000 X 0.28 = 560

N4 = N X 0.17 = 2000 X 0.17 = 340

Systematic Random Sampling

When the population is homogenous and a sampling frame is available, then we use simple random sampling. Now if the population is homogenous and a sampling frame is not available, another method of probability sampling known as systematic random sampling is used.

In the systematic random sampling method, a fixed interval k = N / n is first calculated, known as the sampling interval. The remaining units are chosen based on a pre-design pattern, while the first unit is chosen at random from this interval.

Assume that k = N / n is an integer and that the N population units are serially numbered from 1 to N. Let the ith unit be selected from the first k units. The following number of units will be included in the sample:

Example 7.3: A population consists of 100 units. How a sample size 4 is selected by systematic random sampling. demonstrated it with diagram.

Advantages

i. The sample can be selected quickly and easily.

ii. There is a low risk of the manupulation of data.

iii. The sample is evenly distributed and has the ability to cover a large population.

iv. A specialized sampling technique used in marketing assessments is the systematic random sample.

v. If propely is well-organized and controlled, the chance of sampling error is minimal.

Disadvantages

i. The assigning number to the observation / objects is a difficult task.

ii. The fixed interval can introduce bias.

Cluster Random Sampling

The population is some naturally separated into diverse groups, which are referred to as clusters. These situations include identifying the groups (cluster) and randomly selecting a cluster or a few clusters either by simple random sampling or systematic random sampling, in which a selected cluster is either subsampled or all of its units are included in the sample.

The cluster should be internally dissimilar, and different clusters should be very similar is the basic requirement of the cluster random sampling.

The Step-by-Step Guide to Cluster Sampling This is a condensed manual for performing cluster sampling: 

Step 1: Define the Population and Clusters:

Define the target population precisely first. Identify the natural clustering of the population.

Step 2: Choose Clusters at Random:

From the specified population, choose clusters using a random sampling technique or any other sampling technique. 

Step 3: Determine Cluster Size:

Choose how many elements (households, persons, etc.) will be included in the study for each chosen cluster.

Step 4: Sample Size:

Once clusters have been chosen, sample the components within each cluster based on the cluster size that has already been specified.

Step 5: Gather Information:

Gather information from each chosen cluster's sampled elements.

Advantages

i. Cluster random sampling saves money and time.

ii. It is a convenient method of sampling for geographically spread populations.

iii. The cluster sampling is more reliable if the population is properly clustered.

vi. The cluster random sampling allows for more manageable and focused studies.

Disadvantages

i. Compared to other probability sampling techniques, cluster sampling carries a larger risk of bias.

ii. The cluster sampling is considered to be more difficult and time-consuming than other sampling techniques.

Multistage Sampling

Multistage sampling is a sophisticated and flexible probability sampling technique that includes multistage sample selection. The sample progressively shrinks from a general population to more specified, smaller units at each stage. Simple random sampling is expensive and impractical in scenarios involving large samples and dispersed populations; in these cases, this sampling technique is helpful.

In multistage sampling, the population is divided into a number of units, called first stage units, which are subsampled. Each of the sleeted second stage units is further divided into third stage units, from which a subsampled is again selected, and so on. In a multistage sample, the sample size is the number of units included in the sample at the final stage in the sampling. 

The multisatage sampling is different from cluster sampling in that the cluster uses all the observations within a cluster, whereas multistage sampling selects samples within the clusters.

How Can Multistage Sampling Be Put Into Practice?

1. Define Population

2. Divided into Cluster

3. Randomly Select Clusters

4. Choose a Sampling Unit from Every Selected Cluster.

Advantages 

i. It is less costly.

ii. It requires less effort.

iii. It helps to analyze large populations.

iv. Deep intitution is developed about population.

Disadvantages

i. There is a risk of major bias.

ii. There is a risk of sampling error.

Non-Probability Sampling

Non-probability sampling is a sampling technique in which not all members of the population have a chance to be included in a sample. The selection of sampling units is based on investigator judgment or expertise. The non-probability sampling technique is most useful for exploratory studies like pilot survey, etc.

 Types of Non-Probability Sampling

1. Purposive Sampling

2. Quota Sampling

3. Snowball Sampling

Purposive Sampling

Purposive sampling is a non-probability sampling method in which the selection of sampling units is based on a researcher’s expertise about the population.

A purposive sample is liable to bias introduced by the deliberate subjective choice of the researcher who selects the sample.

Advantages

i. It is the most straightforward sampling technique.

ii. Less time-consuming and inexpensive.

iii. It is effectively used to conduct subjective studies.

iv. It contains a few small non-response units.

Disadvantages

i. A purpose sample is not used when there is a multipurpose objective.

ii. There is a risk of bias.

iii. Applicable on a small level.

Quota Sample

Quota sampling is a non-probability sampling technique in which the population is divided in groups on the basis of defined characteristics called quota, and select from sample from each group. e.g. quota of men and women, urban and rural etc. these factors are termed quota control.

Advantages

i. A quota sample is easy to administer.

ii. Less time-consuming and less expensive.

iii. Quota samples are extensively used in government organizations.

iv. It does need sampling frame.

Disadvantages

i. Selection is non-random, so there is a risk of bias.

ii. It only reflects in quota and has a chance to ignore some segments of the population.

Snowball Sampling

Snowball sampling is a type of non-probability sampling technique and use where the units of interest (participants) are difficult to locate in the target population. In the snowball method, the researcher locates a unit of interest in the target population and then collects information about the other units whom they know directly or indirectly.

The researcher recruits or use the reference of the previous selected units and this referral technique goes on and on, increasing the size of the respondent population like a snowball rolling down a hill until the researcher has sufficient data to analyze. Snowball sampling is also called chain referral sampling.

Snowball sampling consists of two steps:

1. Initially identify one or two units in the population.

2. Use chain referral technique and increase the sample size.

Advantages

i. It is very helpful in secret surveys.

ii. It is helpful to conduct studies which is not conducted due to lack of participants.

iii. It is helpful to conduct studies about medical diseases like HIV, etc. or social events like divorces, etc.

iv. Many hidden problems come to surface.

Disadvantages

i. Time consuming and costly

ii. Selection of initial units is hammering ice berg.

•  Read More: MCQ"S on Sampling
• Read More: Sampling Distribution