# 4.Sampling

# 4.2 Probability Sampling

**Require knowledge about the population**

### Simple Random Sampling & Systematic Sampling

**Require knowledge about the population**

**Simple Random Sampling**

- Each element in the population has a known and equal probability of selection
- Each possible sample of a given size (n) has a known probability of being the sample actually selected
- This implies that every element is selected independently of every other element

**Systematic Sampling**

- The sample is chosen by selecting a random starting point and then picking every i-th element in succession from the sampling frame
- The sampling interval, i, is determined by dividing the population size N by the sample size n, i.e., i=N/n

### Stratified Sampling

**Require knowledge about the population**

Stratified sampling is obtained by separating the population into non-overlapping groups called strata and then obtaining a proportional simple random sample from each group. The individuals within each group should be similar in some way.

Good for:

- highlighting a specific subgroup within the population
- observing existing relationships between two or more subgroups
- representative sampling of even the smallest and most inaccessible subgroups in the population
- a
**higher statistical precision**

**Proportionate**

Stratum |
A |
B |
C |

Population Size | 100 | 200 | 300 |

Sampling Fraction | 1/2 | 1/2 | 1/2 |

Final Sample Size | 50 | 100 | 150 |

**Disproportionate**

Stratum |
A |
B |
C |

Population Size | 100 | 200 | 300 |

Sampling Fraction | 1/5 | 1/2 | 1/3 |

Final Sample Size | 20 | 100 | 100 |

### Cluster Sampling

**Require knowledge about the population**

Cluster sampling the target population is first divided into mutually exclusive and collectively exhaustive subpopulations, or clusters. Than a random sample of clusters is selected, based on SRS.

Good for:

- covering large geographic areas
**reducing survey costs**- when constructing a complete list of population elements is difficult
- when the population concentrated in natural clusters (e.g., blocks, cities, schools, hospitals, boxes, etc.)

*For each cluster, either all the elements are included in the sample (one-stage) or a sample of elements is drawn probabilistically (two-sage).*