# Probability sampling

Probability sampling is about designing samples that allow for correct inferences representative for a population. Loosely speaking, it’s about designing a study that gives basis for correct inferences. It **reduces** **bias** compared to non-probability sampling.

## Simple random sample

In simple random samples **all elements in the population are equally likely to be chosen for the ****sample**. This is known as randomization. For example, if we wish to create a board consisting of 3 staff members out of a total of 50 staffs, each staff can get a random number between 1 to 50 and then a computer can generate three random numbers. **Randomization is considered the most efficient way to reduce bias in a sample**.

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## Systematic Sampling

**If we have 33 football players and we wish to create three teams of 11 players, we can count 1-2-3 eleven times** and the teams are divided each as to the numbers they have received: There is a team of number 1s, a team of number 2s, etc. This is systematic sampling. Not all elements have the same probability for being chosen for the different teams and as such**, this is not a simple random sample**.

## Cluster Sampling

**Cluster sampling is to select a cluster, or a sub-area, of a larger area*** in order to estimate for the population area. It can also make part of a multi-stage sample: Say we wish to study Spanish schoolteachers’ opinions as to the concept of un-schooling. We could choose for example 10 different schools in Spain and for each school run a simple random sample from each school. The choosing of the 10 schools together with the simple random sample is called multi-stage sampling. The simple random samples conducted on each school is called cluster sampling. *

## Stratified Sampling

In statistical analysis we can** split the population into similar groups (stratum) that have similar characteristics but that might respond differently in a survey.** The grouping, or the stratifying, of a population is done to assure that the outcome of each group is correctly represented in the sample.

**Example: **Say, we are going to survey Spanish schoolteachers. We could go to 10 different schools in different schools in the country. But one school might have 100 teachers and another 10 teachers. And opinions might very well differ from area to area especially in a “opinion-divided” country as Spain.

If we survey 10 teachers in each school, it will equal 100% of the teachers in the 10-teacher school and only 10% of the larger 100-teacher school. In order to solve for this, we can make a fix sample of (say a total 100 teachers) and divide these into the corresponding proportions for each school. This is stratified sampling.

## Non-probability summarized

The four sampling methods described above visualized together:

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## Proability sampling learning resources

- Towards Data Science: Sampling techniques
- QuestionPro: Types of sampling for social research

#### Carsten Grube

Freelance Data Analyst

##### Normal distribution

##### Confidence intervals

##### Simple linear regression, fundamentals

##### Two-sample inference

##### ANOVA & the F-distribution

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