what is multistaged sampling exaplain in detail with example use simple wording

Multistage sampling is a complex form of probability sampling. It's a type of sampling method that involves dividing the population into groups (or stages). Then, individuals are randomly selected from these groups for the sample. This method is usually used when a complete list of all members of the population is difficult to establish.

Let's break it down:

1. Step 1: Divide the Population into Groups (First Stage) The first stage involves dividing the entire population into distinct groups. These groups are often geographically defined. For example, a country could be divided into states, then cities, then neighborhoods.

2. Step 2: Select Groups (Second Stage) In the second stage, some of these groups are randomly selected. For example, you might randomly select 5 neighborhoods from a city.

3. Step 3: Select Individuals from Groups (Third Stage) In the third stage, individuals are then randomly selected from these chosen groups. For example, you might randomly select 20 households from each of the 5 neighborhoods.

Let's take an example:

Suppose you're conducting a survey on the reading habits of high school students in the United States. It would be impractical to create a list of all high school students in the U.S. Instead, you could use multistage sampling.

1. First Stage: Divide the U.S. into states. You now have 50 groups.
2. Second Stage: Randomly select 5 states from the 50.
3. Third Stage: In each selected state, divide the high schools into public and private. Randomly select 3 public and 2 private high schools from each state.
4. Fourth Stage: Randomly select 30 students from each chosen high school to participate in your survey.

This way, you get a sample that is representative of the entire population, but you didn't have to list out every single high school student in the U.S. That's the beauty of multistage sampling!