4 – Sampling Design

Introduction

Sampling is the process of picking units (e.g., people, organisations) from a population of interest so that we can fairly generalise our conclusions back to the population from which they were picked by examining the sample. Each observation quantifies one or more qualities (weight, position, etc.) of an observable entity enumerated to differentiate things or individuals. Survey weights are frequently applied to the data to account for the sample design. The outcomes of probability theory and statistics theory are used to influence practice.

4.1 Introduction to Sampling

A sample is a carefully chosen subset of a larger population that represents the entire population. The sampling frame is a list of components from which the sample is drawn. The sampling frame is nothing more than the correct population list.

For example, consider the telephone directory, the product finder, and the Yellow Pages. The sampling procedure is divided into various stages:

Identifying the population of interest
Defining a sampling frame, or a set of items or events that can be measured
Defining a sampling strategy for choosing objects or events from the frame
Choosing a sample size
Execution of the sample strategy
Data collection and sampling
Examining the sampling procedure

4.1.1 The Difference Between Census and Sampling

The term “census” refers to the comprehensive inclusion of all elements in a population. A sample is a subset of a population.

When Is a Census Necessary?

A census is necessary if the population is small.

For instance, a researcher may want to contact companies in the iron and steel or petroleum products industries. Because these industries are few, a census will suffice.

Sometimes, the researcher may be interested in acquiring information from every individual.

As an example, consider the quality of food offered at a shambles.

When Should You Use a Sample?

When there is a vast population.
When time and money are the most vital factors in research,
In the case of a homogeneous population.
In addition, there are times when a census is not practicable.

4.2 Steps of Sampling Design

Sampling design is a crucial aspect of research methodology, particularly in studies where collecting data from an entire population is impractical or impossible. Here’s a detailed explanation of the seven steps involved in sampling design:

1. Define the population:

The first step is clearly defining the target population, which is the group of individuals or elements the researcher intends to study. This definition should be specific and inclusive, ensuring it accurately represents the interest group. For example, if the research aims to study the opinions of college students on a particular topic, the population would be defined as all college students.

2. Identify the sampling frame:

Once the population is defined, the next step is to identify the sampling frame, a list or representation of all the units (individuals, households, organizations, etc.) within the defined population from which the sample will be drawn. The sampling frame must be comprehensive and accessible to ensure that all population elements have an equal chance of being included in the sample.

3. Specify the sampling unit:

The sampling unit refers to the individual elements or units included in the sample. This could be individuals, households, organizations, geographic areas, or any other defined unit within the population. The choice of sampling unit depends on the research objectives, the nature of the population, and practical considerations such as data collection methods and resources.

4. Selection of sampling method:

Various sampling methods are available, each with its advantages and disadvantages. The selection of the sampling method depends on factors such as the research objectives, the population’s characteristics, the desired precision level, and the available resources. Standard sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

5. Determination of sample size:

The sample size refers to the number of sampling units included. Determining the appropriate sample size is crucial for ensuring the reliability and validity of the study findings. Factors influencing sample size include the precision required, the variability of the population, the desired confidence level, and the chosen sampling method. Statistical formulas or software are often used to calculate the optimal sample size.

6. Specify sampling plan:

The sampling plan outlines how the sample will be selected from the sampling frame. It includes specific procedures for implementing the chosen sampling method, determining the sampling intervals (if applicable), and ensuring randomization (if applicable). The sampling plan should be carefully designed to minimize bias and maximize the sample’s representativeness.

7. Selection of sample:

Finally, the sample is selected according to the sampling plan. This involves randomly selecting sampling units from the sampling frame until the desired sample size is reached. The selection process should be conducted systematically and without bias to ensure that every population element has an equal chance of being included in the sample. Once the sample is selected, data collection can proceed according to the research plan.

4.2.1 Characteristics of a Good Sample Design

A successful sample design necessitates carefully considering four major criteria: goal direction, measurability, practicability, and economy.

1. Goal orientation: According to this definition, a sample design “should be oriented to the research aims, adapted to the survey design, and fitted to the survey conditions.” If this is done, it should impact the population selection, measurement, and sample selection procedures.

2. Measurability: A sample design should allow for the calculation of accurate estimations of sampling variability. In surveys, this variability is typically reported as standard errors. However, this is only achievable with probability sampling. It is impossible to know the degree of precision of survey results in non-probability samples, such as quota samples.

3. Practicability: This suggests that the sample design can be implemented successfully in the survey, as previously planned. Complete, correct, practical, and unambiguous instructions must be given to the interviewer so that no errors in the selection of sampling units occur and the final selection in the field does not differ from the initial sample design. Practicality also refers to the design’s simplicity, meaning it should be understandable and followable in fieldwork operations.

4. Economy: Finally, the economy suggests that the survey’s objectives should be met with the least amount of money and effort. Generally, survey objectives are stated in terms of precision, which is defined as the inverse of the variation of survey estimates. The sample design should provide the lowest cost for a given degree of accuracy. Alternatively, the sample design should yield maximum precision for a given per-unit cost (minimum variance).

It should be noted that, in most circumstances, these four criteria contradict each other.

4.3 Types of Sample Design

There are two forms of sampling:

1. Probability sample: In a probability sample, every unit in the population has an equal chance of being chosen as a sample unit.

2. Non-probability sampling: In non-probability sampling, the population units have unequal or insignificant chances of being picked as a sample unit.

4.3.1 Techniques for Probability Sampling

Random sampling.
Systematic random sampling
Stratified Random Sampling
Cluster Sampling
Multistage Sampling

1. Random Sampling

Random sampling is a method in which each item in the population has an equal chance of being chosen.

In random sampling, two approaches are used:

The lottery method: Consider a town with four department stores: A, B, C, and D. Assume we need to select two retailers from a population using a basic random technique. We make a list of all possible samples of two. AB, AD, AC, BC, BD, and CD are six different combinations, each with two stores from the population. We can now write six sample combinations on six identical pieces of paper and fold them so they cannot be identified. Please place them in a container. Mix them up and choose one at random. The lottery method of random selection is used in this procedure.
Using a random number generator: A random number table comprises a collection of digits arranged in a random order; that is, each row, column, or diagonal in such a table contains numbers that are not in any systematic sequence.

Example: Using the store as an example. We begin by numbering the stores.

1 A, 2 B, 3 C, 4 D

The stores A, B, C, and D have been assigned the numbers 1, 2, 3, and 4.

We go as follows to choose two shops at random from a list of four:

Assume we begin with the second row in the first column of the table and read diagonally. The first digit is 8. The city has no department stores, with a population of 8 people. There are only four establishments. Proceed to the next diagonal digit, which is 0. Ignore it because it corresponds to none of the stores in the population. The diagonal’s next digit is 1, which corresponds to store A. Choose A and continue until we have two samples. The two department stores in this example are 1 and 4. Department stores A and D comprise the sample produced from this.

Random sampling has two possibilities: (a) the Probability is equal, or (b) the probability increases or decreases.

(i). Equal Probability: This method is also known as random sampling with replacement.

Example: Place 100 chits in a box labelled 1–100. Choose one number at random. The population now has 99 chits. When a second number is chosen, there will be 99 chits. The sample chosen will be replaced in the population to ensure equal probability.

(ii). Varying Probability: This is often called random sampling with no replacement. Once a number has been selected, it is not included again. As a result, the likelihood of picking one unit differs from that of the other. If we choose four samples from 100, the odds are 1/100, 1/99, 1/98, and 1/97.

2. Systematic Random Sampling

There are three steps to take:

a. The sampling interval K is calculated using the following formula:

K = No. of units in the population / No. of units desired in the sample

b. A random unit from the population list is chosen between the first and Kth units.

c. Add the Kth unit to the randomly selected number.

Example: Consider a sample of 1,000 households from which to select 50 units.

1000/50 = K

Calculate

To choose the first unit, we randomly pick a number from 1 to 20, say 17. So, our sample starts with 17, 37, 57… Please keep in mind that only the first item was chosen at random. The others are chosen systematically. This is a popular method because it only requires one random integer.

3. Stratified Random Sampling

A probability sampling process in which simple random sub-samples are chosen from different strata that are more or less equal in some ways. There are two kinds of stratified sampling:

Proportionate stratified sampling: The number of sample units selected from each stratum is proportional to the stratum’s population size.
Disproportionate stratified sampling: The number of sample units selected from each stratum is determined by the analytical consideration but is not proportionate to that stratum’s population.

The sampling procedure is as follows:

The sampled population is separated into groups (stratified).
A simple random sample is selected.

Proportionate Stratified Sample Selection

Assume there are 60 students in a management school class, and 10 of them must be chosen to participate in a business quiz competition. Assume that the class comprises students specialising in marketing, finance, and human resources.

The first stage is to split the class into three homogeneous groups or stratify the student population based on the area of specialisation.

Marketing Streaming			Finance Stream		HR Stream
1	32	8	11	33	34
2	36	12	13	35	37
3	40	15	17	38	39
4	43	18	20	41	42
5	46	19	21	44	45
7	47	22	24	49	48
9	60	23	25	59	58
10	57	28	26	60	56
14	50	27	29	52	51
16	53	31	30	55	54

The second step is to calculate the sampling fraction f = n/N

n = Sample size required

N = Population size

Third step – Determine how many are to be selected from the marketing stream (say, n₁)

n₁ = 30 × 1/10 = 30 × 1/10

Sample to be selected from marketing strata n1 = 30 × 1/10 = 3

Now, we can randomly select 3 numbers from among 30, say 7, 60, and 22. Similarly, we can select n₂ n₃

n₂ = 20 × 1/10 = 2

The 2 numbers selected at random from the finance stream are 13, 59

N₃ = 10 × 1/10 = 1

Stratified sampling can be carried out with:

The same proportion across the strata proportionate stratified sample.
Varying proportions across the strata are disproportionate to the stratified sample.

Example:

Size of stores	No. of stores (Population)	Sample Proportionate	Sample Disproportionate
Large	2,000	20	25
Medium	3,000	30	35
Small	5,000	50	40
	10,000	100	100

Estimation of the mean of the universe using a stratified sample

Example:

Size of stores	Sample Mean Sales per store	No. of stores	Percent of stores
Large	200	2000	20
Medium	80	3000	30
Small	40	5000	50
		10,000	100

One can calculate the population mean of monthly sales by multiplying the sample mean by its relative weight.

200 × 0.2 + 80 × 0.3 + 40 × 0.5 = 84

Sample Proportionate

If N is the size of the population, and n is the size of the sample:

i represents the different strata (1, 2, 3, …, k) in the population.

Proportionate Sampling Formula:

P=N1/n1=N2/n2=N3/n3=⋯=Nk/nk=N/n

Where:

$, \dots$ represent the sample sizes from each stratum.
represent the population sizes of the corresponding strata.
n is the total sample size, and N is the total population size.

And so on for each stratum.

Example:

A survey is planned to examine people’s attitudes toward their religious activities. The population comprises individuals from five different religions: Hindus, Muslims, Christians, Sikhs, and Jains. The total population is 10,000. The distribution of people is as follows:

Hindus: 6,000
Muslims: 2,000
Christians: 1,000
Sikhs: 500
Jains: 500

The total required sample size is 200. Using proportionate stratified sampling, let’s calculate the sample size for each stratum.

Solution:

Total population $N = 10, 000$

Population of Hindus
Population of Muslims
Population of Christians
Population of Sikhs
Population of Jains

Using the proportionate sampling formula:

Let’s determine the sample size for each stratum.

For Hindus ():

For Muslims ():

For Christians ():

For Sikhs ():

For Jains ():

Finally, the total sample size:

Thus, the proportionate sample sizes for each stratum are as follows:

Hindus: 120
Muslims: 40
Christians: 20
Sikhs: 10
Jains: 10

4. Cluster Sampling

The following steps are taken:

The population has been divided into groups.
A random sample of a few clusters is chosen at random.
All of the units in the chosen cluster are investigated.

1st step: The preceding cluster sampling is analogous to the first step of stratified random sampling. However, the two sample procedures are not the same. The key to cluster sampling is whether the clusters are homogeneous or heterogeneous.

The scenario of sample selection is a significant advantage of simple cluster sampling. Assume we have a population of 20,000 units from which to choose 500. If we utilise the Random Numbers table, selecting a sample of that size takes a long time. Assuming the total population is organised into 80 clusters of 250 units each, we can easily choose two sample clusters (2 250 = 500) using cluster sampling. The most challenging task is forming clusters. In marketing, the researcher divides the market into clusters so that he can approach each one differently.

Assume there are 20 households in a neighbourhood.

Cross	Houses
1	X₁	X₂	X₃	X₄
2	X₅	X₆	X₇	X₈
3	X₉	X₁₀	X₁₁	X₁₂
4	X₁₃	X₁₄	X₁₅	X₁₆

We must choose eight houses. We have the option of selecting eight houses at random. Alternatively, two clusters of four dwellings each might be selected. In this strategy, each feasible sample of eight dwellings has a known likelihood of being chosen – i.e., a one-in-two chance. We must remember that each house in the cluster has the same qualities. It is impossible to select a specific random sample using cluster sampling. For example, in the cluster mentioned above sampling method, the following housing combinations could not occur: X₁, X₂, X₅, X₆, X₉, X₁₀, X₁₃, X₁₄. This is because the original cosmos of 16 dwellings has been reimagined as a universe of four clusters. As a result, only clusters can be chosen as samples.

Example: Assume we want 7500 households from throughout the country. In such circumstances, 30 districts out of 600 are chosen from around the country from the first stage.

I Stage – Cities: Assume 5 cities are chosen from each of the 30 districts, and

II Stage – Wards/Localities: Assume 10 wards/localities are chosen from each city. Households: 50 households are selected from each ward/locality.

We can use stratified sampling in stage I.

We can employ cluster sampling in stage II.

We can use basic random sampling in stage III.

5. Multistage Sampling

The name implies that sampling occurs in stages. This is employed in stratified/cluster designs.

The following is an example of double sampling.

A recently opened club’s management is looking for new members. All corporations were supplied with information during the initial rounds so those interested could enrol. After enrolling, the second phase focuses on how many people are interested in joining the club’s numerous leisure activities such as billiards, indoor sports, swimming, gym, etc. After gathering this information, you may want to categorise the interested respondents. This will also inform you how new members react to particular activities,. This technique is deemed scientific because there is no way to ignore the universe’s properties.

Sampling by Area

This is a probability sample, which is a subset of cluster sampling.

For example, if you wish to measure toffee sales in retail stores, you may select a city neighbourhood and audit toffee sales in retail outlets.

The biggest issue with area sampling is the lack of lists of establishments offering toffee in a specific area. As a result, selecting a probability sample directly from these outlets would be impossible. Thus, the initial task is to select a geographical area and list toffee-selling outlets. Then, the probability sample for shops from the prepared list comes.

For example, you might look for stores selling Cadbury dairy milk. The drawback of area sampling is that it is costly and time-consuming.

4.3.2 Non-probability Sampling Techniques

1. Deliberate sampling
2. Shopping mall intercept sampling
3. Sequential sampling
4. Quota sampling
5. Snowball sampling
6. Panel samples

1. Purposive or Deliberate Sampling

This is sometimes referred to as judgment sampling. The investigator chooses sample observations from the cosmos at his discretion, which results in some bias in the selection process. According to the scientist, the sample thus picked may accurately represent the universe. However, not all units in the universe have an equal chance of being included in the sample, so it cannot be classified as probability sampling.

For example, test market towns are chosen based on judgment sampling because they are seen as typical cities matching particular demographic criteria. A judgement sample is also regularly used to select stores to introduce a new display.

2. Shopping mall intercept sampling

This is a method of non-probability sampling. Using this strategy, respondents are recruited for individual interviews at predetermined sites in shopping malls.

Sunday through Monday: Shopper’s Shoppe, Food World.

This type of research would involve multiple malls, each servicing a different socioeconomic population.

For example, the researcher might want to compare the reactions to two or more TV advertisements for two or more items. Mall samples can be helpful in these kinds of studies. Mall samples should not be employed if the difference in efficiency of two ads fluctuates with the frequency of mall shopping, a change in the demographic characteristics of mall shoppers, or any other variable. This method’s success is determined by “how well the sample is picked.”

3. Sequential sampling

This is a way of forming a sample based on subsequent judgments. They seek to answer the research question using the evidence that has accumulated. Sometimes, a researcher may want to examine the outcomes of a small sample. Then, s(he) will determine whether more information is required, in which case larger samples will be evaluated. More samples are needed if the evidence is inconclusive after a small sample size. If the results are still equivocal, larger samples are collected. At each level, a choice is made as to whether further information should be gathered or whether the evidence is now sufficient to allow a conclusion.

Example: Assume you need to evaluate a product.

A tiny probability sample is drawn from the existing user base. Assume that the average annual usage is between 200 and 300 units. The product is only economically viable if the average consumption is 400 units. This information is adequate to decide whether or not to discontinue the product. If, on the other hand, the initial sample reveals a consumption level of 450 to 600 units, additional samples will be required for future research.

4. Quota sampling

Quota sampling is commonly employed in marketing research. It entails establishing precise quotas that interviewers must meet.

Assume 200,000 students are taking a competitive examination. We need to select 1% of them using quota sampling. The following quota classifications are possible:

Sample Classification as an Example

Category	Quota
General merit	1,000
Sport	600
NRI	100
SC/ST	300
Total	2,000

5. Snowball Sampling:

Snowball sampling is a type of non-probability sampling method. Initially, a random group of respondents is selected. Then, subsequent respondents are chosen based on referrals or recommendations provided by the initial respondents. As the process continues, each new respondent may refer more individuals, creating a “snowball effect” where the sample size grows. Typically, the referrals share demographic and psychographic characteristics similar to those of the referring individuals. For instance, college students might introduce more students to a study on Pepsi consumption. The primary advantage of snowball sampling is its ability to capture specific characteristics within the population.

6. Panel Samples:

Panel samples are commonly used in marketing research. For instance, imagine a study aiming to track changes in household consumption patterns. Initially, a sample of households is selected. These households are then contacted to collect data on their consumption patterns. After a certain period, such as six months, the same households are approached again for updated information. Panel samples provide valuable insights into trends within a consistent group, allowing researchers to observe changes and patterns within specific demographics or consumer behaviours.

4.3.3 Distinction between Probability Sample and Non-probability Sample

Aspect	Probability Sample	Non-probability Sample
Method of Selection	Every member of the population has a known chance of selection	Members of the population are selected based on criteria such as convenience, judgment, or referral
Representative Sample	It is likely to be representative of the population if properly executed	Not guaranteed to be representative of the population due to selection bias
Sampling Error	Can be quantified and reduced through statistical techniques	Cannot be quantified or reduced through statistical methods
Types of Sampling	Simple random sampling, stratified sampling, cluster sampling	Convenience sampling, purposive sampling, snowball sampling, quota sampling
Generalizability	Results can be generalized to the population with confidence	Results may have limited generalizability to the broader population
Statistical Analysis	Allows for inferential statistics and hypothesis testing	Limitations on the use of inferential statistics and hypothesis testing
Bias	Less susceptible to bias if properly executed	More vulnerable to bias due to non-random selection methods

4.4 Fieldwork

The fieldwork includes informal discussions and formal structured interviews, which may include projections or questionnaires. Initially, the research was carried out by a single person. Changes in society have changed study, for the most part, into a collaborative effort. However, compelling research can still be conducted by a single individual. Traditionally, educational researchers started their research with hypotheses, whereas the fieldworker’s hypothesis arises through the fieldwork.

Fieldwork may appear unorganised in its early stages. The notes are disorganised, and information is arriving from everywhere. The hypothesis has not yet emerged, although it may quickly become evident. Once the hypothesis is established, the fieldworker keeps an open mind, allowing additional hypotheses to arise.

Another significant distinction between study kinds is the “nature of the proposition sought: his propositions are rarely of the A causes B type, the normal incidental interrelationships between two or more variables dealt with in an experimental investigation.”

Much naturalistic data is gathered using raw materials: notes stating the delivered answer. Recorders are frequently used to ensure accuracy. Experienced researchers develop their approaches and the capacity to remember the material that must be recorded.

The fieldworker determines when the investigation should be completed by examining the data as it is collected. The fieldworker’s job is done when he or she notices trends but no new substantial changes.

The following are three critical points that must be included:

The data can be subjective when subjected to quantitative analysis.
Most practitioners of the approach undoubtedly believe its products to be full-fledged studies.
Irrespective of abstraction, it is plausible.

4.5 Errors in Sampling

4.5.1 Sampling Error

The only method to minimise sampling error is to select the appropriate sample size. The sampling error is the difference between the sample and the population mean.

For example, if a survey is conducted among Maruti car owners in a city to determine the average monthly expenditure on auto maintenance, all Maruti car owners can be included. The survey can also be conducted by selecting a sample rather than the full population. There will be a difference between the two techniques in terms of monthly expenses.

4.5.2 Non-sampling Error

One distinction between sampling and non-sampling error is that, whilst sampling error refers to random changes that may be found in the form of standard error, non-sampling error occurs in some systematic manner that is difficult to assess.

4.5.3 Sampling Frame Error

A sampling frame is a predetermined list of population units from which the sample for a study is drawn.

Example:

1. A multinational bank wishes to collect a sample of credit card holders. They may quickly obtain a complete list of credit card holders, which serves as the foundation of their data bank. The desired individuals can be chosen from this frame. In this case, the sample frame is the same as the ideal population: all credit card holders. In this scenario, there is no sampling error.

2. Assume a bank wishes to promote a home loan product to persons in a specific profession (doctors, attorneys) over the phone. The telephone directory serves as the sample frame in this example. This sample frame may cause several issues:

(1) It is possible that people have migrated.

(2) The numbers have shifted.

(3) Many numbers have yet to be listed. The question is, “Are the residents who are listed in the directory likely to be different from those who are not?” The answer is yes. As a result, there will be a sampling error in this scenario.

4.5.4 Non-response Error

This happens because the anticipated sample and the final sample differ significantly.

Marketers, for example, want to know about television viewing habits nationwide. They select 500 households and mail the questionnaire to them. Assume that only 200 people respond. This does not indicate a non-response error dependent on the difference. There is no non-response error if the 200 responses did not differ from the 500 picked.

Consider another option. Those who responded had a lot of free time. As a result, it is assumed that non-respondents do not have enough leisure time. In this scenario, the final sample and the planned sample are not the same. If it were assumed that all 500 picked have leisure time, but in the end, only 200 have leisure time, and the others do not, a sampling based on leisure time results in response error.

Guidelines to Increase the Response Rate

Every researcher wants to acquire as many responses as possible from their respondents and would be overjoyed if every single one of them responded. Unfortunately, this does not always happen. By raising the response rate, the non-response error can be lowered. The higher the response rate, the more accurate and dependable the data. Some helpful tips for accomplishing this could be as follows:

Inform the respondents in advance by letter. This will boost preparation.
A cover letter should be sent with the personalised questionnaire.
Ensure the confidentiality of the information.
The questionnaire length will be limited.
Personal interviews are becoming more common, and I.D. cards are required to confirm one’s identity.
Financial incentives and presents will serve as motivators.
Reminders or revisions would be beneficial.
Return the completed questionnaire in a self-addressed, stamped envelope.

4.5.5 Data Error

This happens during data gathering, data analysis, or data interpretation. Respondents may give distorted replies unintentionally while answering challenging questions or when the question is unusually long, and the respondent does not have an answer. Data inaccuracies can also emerge due to the interviewer’s and respondent’s physical and social traits. Tone and voice are two examples of factors that can affect responses. As a result, we can conclude that the interviewer’s traits can also result in data mistakes. In addition, dishonesty on the part of the interviewer results in data errors. When answers to open-ended questions are incorrectly recorded, data problems can arise.

Failure of the Interviewer to Follow Instructions

Before the interview, the respondent must be briefed on “what is expected.” “To what extent should he respond?” In addition, the interviewer must ensure that the respondent is knowledgeable about the issue. Errors will occur if the interviewer does not make things obvious.

Other causes include editing errors editors commit while transferring data from questionnaires to computers.

The respondent may withdraw from the data collection process if he or she believes the questionnaire is excessively long and tiresome.

4.6 Sample Size Decision

The first factor to consider when estimating sample size is the allowable error.
The larger the sample size, the greater the needed precision.
The larger the sample, the higher the confidence level in the estimate. With a fixed-size sample, there is a trade-off between the degree of confidence and precision.
The sample’s size must be proportional to the number of sub-groups of interest inside it.
Cost determines the sample size.

Sixth, there is the question of response rate: The number of surveys that must be sent out must be considered when determining the required sample size. We may send out questionnaires to the necessary amount of people, but we may not obtain a response. For example, we might want to get the family income level via a postal survey, but the researcher might not get a response from everyone. If the researcher believes the response rate is 40%, he must send out that many more surveys. A poor response rate can generate significant issues for the researcher. This is referred to as a non-response error.

Non-response error can occur due to (1) failure to locate or (2) flat refusal.

Failure to locate: People relocate to new locations. This difficulty, however, can be avoided if the sample frames used are of recent provenance.

Refusal outright: We don’t know if individuals who didn’t react have different perspectives or attitudes than those who did.

This suggests that individuals who do not reply should be encouraged to do so. It can be accomplished in any of the following ways:

A letter informing respondents that they will receive a questionnaire and soliciting their cooperation will generally boost the reaction rate.
Respondents will answer more enthusiastically if given a monetary incentive or a present.
After the potential respondent receives the questionnaire, proper follow-up is required.

4.7 Sampling Distribution

The probability distribution of a particular statistic based on a random sample of size n is known as a sampling distribution. It can be considered the statistic’s distribution for all feasible sample sizes. The underlying population distribution, the figures under analysis, and the sample size all play a role in determining the sampling distribution. The asymptotic distribution corresponds to the limit situation and is commonly contrasted to the sampling distribution.

Consider an average population with a mean and a variance. Assume we regularly take samples of a given size from this population and calculate the arithmetic mean for each sample—this statistic is known as the sample mean. Each sample has its average value, and the distribution of these averages is called the “sampling distribution of the sample mean.” Because the underlying population is normal, this distribution will be normal N(m, s²/n).

The standard deviation of the statistic’s sampling distribution is the standard error of that quantity. The standard error for the case where the statistic is the sample mean is:

SAMPLING

Where σ is the standard deviation of the population distribution of that quantity and n is the sample’s size (number of items).

REVIEW QUESTIONS:

What are the advantages and disadvantages of probability sampling in your analysis?
In studies where the level of accuracy may deviate from prescribed norms, which sampling method would you employ and why?
Why is Shopping Mall Intercept Sampling not considered a scientific approach?
Is the lack of prior knowledge about the cell to which each population unit belongs an advantage or disadvantage for Quota Sampling?
What recommendations would you propose to mitigate non-sampling error?
When one mobile phone user is asked to recruit another, what sampling method is this referred to as, and why?
Is sampling considered a part of the population? True or False? Why or why not?
What would be the determined sample size if the population’s standard deviation is 20 and the standard error is 4.1?
Why is purposive sampling often referred to as judgment sampling?

Curriculum

Research Methodology

4 – Sampling Design

Introduction

4.1 Introduction to Sampling

4.2 Steps of Sampling Design

4.3 Types of Sample Design

Proportionate Sampling Formula:

Example:

Solution:

4.4 Fieldwork

4.5 Errors in Sampling

4.6 Sample Size Decision

4.7 Sampling Distribution

REVIEW QUESTIONS: