Systematic Random Sampling is a method of selecting a sample from a population in a structured and organized manner. It is a valuable technique in research and statistical analysis providing a systematic yet random approach to sample selection ensuring reliable and accurate results. In this article, we will discuss systematic random sampling in detail along with some solved examples and others in detail.
Table of Content
What is Systematic Sampling?
Systematic Sampling is a statistical technique where every nth member of a population is chosen for a sample after an initial random starting point.
Here’s how systematic sampling operates:
- Random Start: Initially, a starting point is randomly chosen from the first n elements of the population.
- Interval Selection: Every nth element from this randomly chosen starting point is included in the sample.
- Patterned Selection: This method establishes a structured pattern for selecting elements from the population.
Types of Systematic Sampling
Some of the types of Systematic Sampling are:
- Linear Systematic Sampling: In this method, individuals are chosen at regular intervals from a list. For instance, every 5th person is selected from a given population list after a random starting point.
- Circular Systematic Sampling: Particularly useful for circular or sequential data, this method involves selecting samples at regular intervals, looping back to the beginning when reaching the end of the sequence.
- Stratified Systematic Sampling: The population is divided into distinct strata or subgroups based on specific criteria. Then, systematic sampling is applied within each stratum independently to ensure representation from all groups.
- Cluster Systematic Sampling: Here, the population is divided into clusters, and a systematic sample of clusters is chosen. Then, within the selected clusters, all individuals are sampled systematically..
What is Systematic Random Sampling?
Systematic random sampling is a method that involves selecting elements from a population at regular intervals using a predetermined pattern. It’s a hybrid approach that combines randomness with a systematic method to ensure a representative sample.
Here’s a detailed breakdown of systematic random sampling:
- Random Start: Initially, a random starting point is chosen from the population. This starting point determines the first element to be included in the sample.
- Regular Intervals: After selecting the initial element randomly, subsequent elements are chosen at fixed intervals. For instance, if every 5th element is to be included in the sample, this pattern is followed consistently.
- Patterned Selection: The selection continues according to the specified interval until the desired sample size is achieved. This systematic approach ensures that each element in the population has an equal chance of being included in the sample.
Systematic random sampling helps avoid bias by ensuring randomness in the selection process while maintaining a systematic structure. This method is particularly useful when the population is large and ordered, providing a balanced representation of the entire population in the sample.
Systematic Random Sampling Definition
Systematic Random Sampling is a statistical technique used to select elements from a population at regular intervals through a systematic and structured approach.
Systematic Sampling involves choosing a starting point at random within the population and then selecting every nth element thereafter according to a predetermined pattern until the desired sample size is achieved.
This method combines systematicity with randomness to ensure that each member of the population has an equal probability of being included in the sample, making it a representative subset of the entire population
Check, Random Sampling
Systematic Random Sampling Examples
Example 1: Consider a university with 2000 students. To conduct a survey, a systematic random sample of 100 students is needed.
Solution:
Random Start: A random number between 1 and 10 is chosen as the starting point.
Sampling Interval: Every 20th student from the randomly selected starting point is chosen for the survey.
If the random start is student number 5, the selected students for the sample will be 5, 25, 45, 65, …, until 100 students are sampled.
Example 2: Suppose a company has a workforce of 500 employees and needs to gather feedback. They aim to survey 50 employees using systematic random sampling.
Solution:
Random Start: A random number between 1 and 10 is generated to select the starting point.
Sampling Interval: Every 10th employee from the randomly chosen starting point is included in the survey sample.
If the random start is employee number 3, the sample will include employees 3, 13, 23, 33, …, until 50 employees are surveyed.
Example 3: In a town with 1000 households, a government agency wants to survey 80 households for a census.
Solution:
Random Start: A random number between 1 and 10 is used as the starting point.
Sampling Interval: Every 12th household from the randomly chosen starting point is selected for the census.
If the random start is household number 8, the selected households will be 8, 20, 32, 44, …, until 80 households are surveyed.
Advantages and Disadvantages of Systematic Random Sampling
The advantages and disadvantages of Systematic Random Sampling is tabulated below:
|
Advantages of Systematic Random Sampling |
Disadvantages of Systematic Random Sampling |
|---|---|
|
Provides a structured and systematic approach to sampling, ensuring representative results. |
Prone to periodic patterns in the population that may align with the sampling interval, leading to bias. |
|
Simpler and more practical to execute compared to simple random sampling in large populations. |
Requires an accurately ordered or randomly ordered list of the population elements. |
|
Helps avoid human bias in selection due to its predetermined selection process. |
Susceptible to errors if there are any flaws or inaccuracies in the ordering of the population list. |
|
Offers a balance between random selection and systematic organization, providing efficiency. |
If a periodic pattern exists, it can lead to a skewed or unrepresentative sample. |
|
Provides ease in understanding and implementing the sampling process. |
Can be time-consuming if the population list is extensive or complex. |
Why to Use Systematic Random Sampling Technique?
Systematic random sampling is employed for several reasons due to its unique advantages in statistical analysis. Here are the key points explaining why this technique is used:
- Representative Sampling: Systematic random sampling ensures a representative subset of the population, reducing the risk of bias and providing reliable insights into the entire population.
- Efficiency: It offers greater efficiency compared to simple random sampling, especially in large populations, as it maintains randomness while structuring the selection process.
- Systematic Approach: It combines randomness with a systematic approach, making it easier to implement and understand compared to some other sampling methods.
- Reduced Bias: By eliminating personal bias in selecting samples, it provides an impartial method of obtaining a diverse representation from the population.
- Balanced Method: Offers a balanced compromise between systematic selection and randomization, ensuring fairness in the selection process.
- Minimizes Error: It reduces the chances of error due to subjective judgment in selecting samples, enhancing the reliability of the obtained results.
- Saves Time: It can be quicker than other methods, especially when a structured and systematic sampling technique is required for analysis.
Systematic Random Sampling vs Simple Random Sampling
The comparison between Systematic Random Sampling and Simple Random Sampling is tabulated below:
|
Difference Between Systematic Random Sampling and Simple Random Sampling |
|
|---|---|
|
Systematic Random Sampling |
Simple Random Sampling |
|
Selects samples at regular intervals using a systematic pattern. |
Selects samples purely at random without any pattern or structure. |
|
Requires an ordered list of the population, and the sampling interval is predetermined. |
Doesn’t require an ordered list; samples are chosen entirely by chance. |
|
Combines systematic structure with randomness, offering efficiency and representative results. |
Provides equal chances of selection for each element, ensuring unbiased representation. |
|
Can be more practical and time-efficient for larger populations. |
Equally applicable to any population size but might be more labor-intensive for large populations. |
|
More susceptible to periodic patterns in the population, leading to bias if present. |
Less prone to systematic bias, but variations in random selection might result in occasional bias. |
How is Sampling Interval Calculated in Systematic Random Sampling
To conduct systematic random sampling, determine the sampling interval (k), randomly select a starting point, and then choose every kth element thereafter until the desired sample size is achieved. The sampling interval (k) is determined by dividing the population size (N) by the desired sample size (n). Mathematically,
k = N/n
Systematic Sampling Method
To calculate systematic random sampling, follow these steps:
- Determine Population Size: Identify the total number of elements in the population you want to sample from.
- Decide Sample Size: Determine the size of the sample required for your study or survey.
- Calculate Sampling Interval: Divide the population size by the desired sample size. This gives the sampling interval (k).
- Sampling Interval (k) = Population Size / Sample Size
- Select a Random Start: Choose a random number between 1 and the sampling interval (k). This number determines the starting point.
- Systematic Selection: Begin from the randomly selected starting point and select every kth element until you reach the desired sample size.
- Ensure Randomness in Selection: It’s crucial to ensure the randomness of the starting point. We can use random number generators or tables to determine the starting point.
- Verify Coverage: Confirm that the systematic selection covers the entire population and that each element has an equal chance of being selected.
This method ensures that each element in the population has an equal chance of being included in the sample, promoting statistical validity.
Why is it Important to Randomly Select the Starting Point in Systematic Random Sampling
Randomly selecting the starting point ensures that the systematic sampling maintains its randomness and avoids introducing bias into the sample selection process.
Benefits of Systematic Random Sampling
The advantages of Systematic Random Sampling are mentioned below:
- Ease of Implementation: It’s relatively straightforward compared to other sampling methods, making it user-friendly.
- Representative Samples: When properly executed, this method can yield samples that accurately represent the larger population.
- Reduced Bias: By following a systematic pattern, it minimizes potential biases introduced by subjective selections.
- Efficiency: It can be more efficient, particularly when dealing with extensive populations, saving time and resources.
- Equal Probability: Every element in the population has an equal chance of selection, ensuring fairness and impartiality.
Where is Systematic Random Sampling Commonly Used
Systematic Random Sampling is commonly used in following situations
- Surveys and Market Research: When conducting surveys it’s often used to select participants systematically from a larger pool ensuring diverse representation.
- Quality Control: In manufacturing, it helps inspect a systematic subset of products to ensure consistent quality.
- Ecological Studies: Sampling trees in a forest or species in an ecosystem can employ this method to study biodiversity patterns.
- Education Research: To gather student feedback or test scores from a large educational institution, this method helps in systematic data collection.
- Clinical Trials: In medical research, it’s utilized to select patients systematically from a pool for drug testing or treatment studies.
Also, Check
Systematic Random Sampling – Solved Examples
Example 1: Given Population size (N): 100, Desired sample size (n): 10. Calculate Systematic Random Sampling.
Solution:
Sampling interval (k) = N/n
= 100/10 = 10
Randomly select a starting point: 7
Selected Sample:
7, 17, 27, 37, 47, 57, 67, 77, 87, 97
Example 2: Given Population size (N): 150, Desired sample size (n): 15. Calculate Systematic Random Sampling.
Solution:
Sampling interval (k) = N/n
= 150/15
= 10
Randomly select a starting point: 4
Selected Sample:
4, 14, 24, 34, 44, 54, 64, 74, 84, 94, 104, 114, 124, 134, 144
Example 3: Given Population size (N): 90, Desired sample size (n): 9. Calculate Systematic Random Sampling.
Solution:
Sampling interval (k) = N/n
= 90/9
= 10
Randomly select a starting point: 6
Selected Sample:
6, 16, 26, 36, 46, 56, 66, 76, 86
Example 4: Given Population size (N): 160, Desired sample size (n): 16. Calculate Systematic Random Sampling.
Solution:
Sampling interval (k) = N/n
= 160/16
= 10
Randomly select a starting point: 3
Selected Sample:
3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, 123, 133, 143, 153
Example 5: Given Population size (N): 80, Desired sample size (n): 8. Calculate Systematic Random Sampling.
Solution:
Sampling interval (k) = N/n
= 80/8
= 10
Randomly select a starting point: 2
Selected Sample:
2, 12, 22, 32, 42, 52, 62, 72
Systematic Random Sampling Practice Problems
Problem 1: Given Population size (N): 120, Desired sample size (n): 10. Calculate Systematic Random Sampling.
Problem 2: Given Population size (N): 80, Desired sample size (n): 4. Calculate Systematic Random Sampling.
Problem 3: Given Population size (N): 60, Desired sample size (n): 8. Calculate Systematic Random Sampling.
Problem 4: Given Population size (N): 40, Desired sample size (n): 6. Calculate Systematic Random Sampling.
Problem 5: Given Population size (N): 20, Desired sample size (n): 4. Calculate Systematic Random Sampling.
Systematic Random Sampling: FAQs
Is Systemic Random Sampling Qualitative or Quantitative?
Systematic Random Sampling is a Quantitative Sampling Technique
What Challenges Associated with Systematic Random Sampling?
One challenge is that if there is an unseen periodicity or pattern in the population, it may coincide with the sampling interval, potentially leading to biased results. Additionally, it may be impractical if the population is not easily ordered.
Can Systematic Random Sampling be used with Large Populations?
Yes, systematic random sampling is suitable for large populations. Its efficiency makes it feasible for selecting representative samples even when dealing with extensive datasets.
How does Systematic Random Sampling compare to other Sampling Methods?
Systematic random sampling strikes a balance between simplicity and representativeness. It may be more efficient than simple random sampling and less prone to bias than some non-random methods.
What Steps can be Taken to Enhance the Reliability of Systematic Random Sampling Results?
Ensuring a truly random starting point, using a suitable sampling interval, and being mindful of potential biases or patterns in the population are key steps to enhance the reliability of systematic random sampling results.
Is there a Risk of Introducing Bias in Systematic Random Sampling?
While systematic random sampling aims to be unbiased, there’s a risk if there is an unnoticed pattern in the population that aligns with the sampling interval potentially leading to biased results.
Can Systematic Random Sampling be Applied to Qualitative Research?
Yes, systematic random sampling can be adapted for qualitative research such as selecting interviews or cases systematically from a larger pool providing a structured yet unbiased approach.
How is Systematic Sampling different from Random Sampling?
Systematic sampling involves selecting every nth element from a population after an initial random start, whereas random sampling involves selecting individuals randomly from a population without any order or sequence.
What is the Formula for Random Sampling?
The formula for random sampling is often expressed as P(E)= n/N, where P(E) is the probability of selecting a specific individual, n is the number of individuals to select and N is the total population size.
What is Stratified Random Sampling?
Stratified random sampling involves dividing a population into subgroups (strata) based on specific characteristics and then randomly selecting individuals from each subgroup, ensuring representation from each subgroup in the sample for a more comprehensive analysis.
What is Solvin Formula?
“Solvin Formula” is not a familiar term in the context of sampling or statistics. If it refers to a specific formula or concept, providing more context would help clarify its meaning.