How systematic sampling is differ from Stratified Random Sampling

Systematic sampling and stratified random sampling are both probability sampling techniques used to select a representative sample from a population, but they go about it in different ways:

Stratified Random Sampling:

• Divides the population: Here, you first divide the entire population (let's say, all students in a school) into subgroups (strata) based on shared characteristics (like grade level). These subgroups should be mutually exclusive and collectively exhaustive (every member of the population belongs to exactly one subgroup).
• Random selection within subgroups: Then, you randomly select a sample from each subgroup. This ensures all relevant subgroups are represented in the final sample.

Systematic Sampling:

• Ordering the population: This method treats the population as a single list in some order (like a list of students in alphabetical order).
• Fixed interval selection: You decide on a sampling interval by dividing the total population size by your desired sample size. Then, you pick a random starting point from the list and select every nth element thereafter based on the interval.

Here's a table summarizing the key differences:

Feature	Stratified Random Sampling	Systematic Sampling
Divides population	Yes, into subgroups (strata)	No
Basis for selection	Random selection within subgroups	Fixed interval selection from ordered list
Risk of bias	Lower, ensures all subgroups are represented	Higher if the ordering coincides with a pattern in the population

Choosing the right method:

• Use stratified random sampling if you have a diverse population with subgroups you want to be sure are represented in the sample.
• Use systematic sampling if ordering the population is easy and there's no underlying pattern or cyclical trend within the population that might bias your selection. It can also be slightly more efficient to implement than stratified sampling.

Example:

Imagine you want to survey students about their preferred lunch options.

• Stratified Random Sampling: You could divide the students into subgroups by grade level (strata). Then, randomly select a sample from each grade level to ensure all grade levels have a voice.
• Systematic Sampling: If the student list is in alphabetical order (not ideal, but possible), you could choose a random starting student and then survey every 10th student on the list (assuming you want a 10% sample). However, this could be biased if, for example, taller students tend to be placed alphabetically later (and perhaps have different lunch preferences).