Sampling

# Sampling

To choose samples, we use **sampling** and its different types:

In a random or probability sampling, each individual in the population has the same probability to be chosen for the sample.

The different types of random sampling are:

–

**Simple random sampling**(the base for the other types of sampling) consists in listing the elements of the population and choosing the n elements of the sample randomly–

**Systematic random sampling**consists in choosing the n elements of the sample k in k where:–

**Stratified random sampling**, also sometimes called proportional or quota random sampling, involves dividing your population into homogeneous subgroups and then taking a simple random sample in each subgroup.–

**Cluster random sampling**. The problem with random sampling methods when we have to sample a population that's scattered across a wide geographic region is that you will have to geographically cover a very large ground in order to get to each of the units you sampled. In cluster sampling, we follow these steps: •divide population into clusters (usually along geographic boundaries)

•randomly sample clusters

•measure all units within sampled clusters

The number of samples of size n in a population of N individuals is:

–Without replacement:

–With replacement: N

^{n}If you make an error in the sampling process, the results of the sample won’t match the population. This error can be:

–

**Random sample error**: in order to reduce this error, you must increase the size of the sample–A

**systematic error**is associated to the process of selection of the sample and it is reduced by improving the selection**Exercise**: A library has 5 sections, in each one there is a certain number of books as is shown in the table:

Section | 1 | 2 | 3 | 4 | 5 |

Books | 500 | 860 | 1200 | 700 | 740 |

In order to try to estimate the number of books published in Spanish, we want to extract a sample of 5% of the total books by doing a stratified random sampling with the sections as strata. How many books in each section do we have to select?

Solution: 25, 43, 60, 35 and 37 books

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