Systematic Random Sampling

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.

👁 Systematic-Random-Sampling

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:

1. Determine Population Size: Identify the total number of elements in the population you want to sample from.
2. Decide Sample Size: Determine the size of the sample required for your study or survey.
3. Calculate Sampling Interval: Divide the population size by the desired sample size. This gives the sampling interval (k).
4. Sampling Interval (k) = Population Size / Sample Size
5. Select a Random Start: Choose a random number between 1 and the sampling interval (k). This number determines the starting point.
6. Systematic Selection: Begin from the randomly selected starting point and select every kth element until you reach the desired sample size.
7. 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.
8. 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

Systematic Random Sampling is a statistical technique used to select elements from a population at regular intervals through a systematic and structured approach.

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

• Probability Theory
• Introduction to Statistics

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.