**What is sampling with replacement?**

He **sampling with replacement** It is a sampling technique in which, after selecting a sample of items, they are returned to the population and can be selected again.

This means that, once an element is chosen to be part of the sample, this element re-enters the selection process for the following iterations.

This method is useful when you want to obtain a representative sample of the population, since by replacing each element in the population after it has been selected for the sample, selection bias is avoided.

**Characteristics of sampling with replacement**

– It is a sampling technique in which each element of the population has an equal probability of being selected for the sample.

– This technique ensures that all elements of the population have an equal chance of being included in the sample.

– The size of the sample obtained by this method is determined by the size of the population and the number of elements to be included in the sample.

– This method is suitable for sampling large populations, since it guarantees that all elements have the same probability of being selected.

**Differences between sampling with replacement and sampling without replacement**

In replacement sampling, once selected, an item can be chosen again. In non-replacement sampling, each item in the population has only one chance of being selected for the sample. This means that once selected, an item cannot be chosen again.

**Advantages of Sampling with Replacement **

The process is simpler and requires less time and effort than sampling without replacement.

There is no bias in the selection of items, since all items have the same probability of being selected.

It is possible to obtain multiple samples from the same population using the same initial data set, which is useful for performing statistical tests.

**Disadvantages of Sampling with Replacement**

A biased sample can be obtained if the sample size is small or if it is not done randomly.

You cannot get data on items that are not in the sample.

It can be expensive or time consuming if the population size is large.

**Examples of sampling with replacement**

– Select a random coin from a bag full of coins. Then, return it to the bag, being able to take out the same coin again. This is repeated until the desired number of coins has been selected.

– Select marbles from a pocket. Each time a marble is drawn, it is put back into the pocket before another is drawn.

– Clicking random buttons on a website until 100 pieces of data have been collected. Each time a button is clicked, this button becomes available for selection again.