## Sampling for NCA

**What sampling methods can be used for NCA?**

**How can I obtain a census for NCA?**

**How can I obtain a probability sample (random sample) for NCA?**

**How can I obtain a convenience sample for NCA?**

**How can I obtain a purposive sample for NCA?**

**Can I estimate population parameters with a purposive sample?**

**Does NCA require a minimum sample size?**

**What sampling methods can be used for NCA?**

Sampling is the selection of cases from a population of cases for subsequent measurement and data analysis. For NCA the common sampling methods are the same as for any other research approach and data analysis technique (e.g., census, probability sampling, convenience sampling). Only purposive sampling is performed differently.

**How can I obtain a census for NCA?**

A census is a “sample” in which all cases of the population become part of the “sample” (and the data base). With a census statistical inference from sample to population is not relevant and unnecessary because the population information is available in the “sample”. For NCA the census is the same as for any other research approach and data analysis technique.

**How can I obtain a probability sample (random sample) for NCA?**

A probability sample (random sample) is a sample in which all cases of the population had the same probability to become part of the sample (and the data base). This can be achieved by random sampling from a complete list of cases of the population (sampling frame). A probability sample is a requirement for statistical inference from sample to population. For NCA the probability sample is the same as for any other research approaches and data analysis technique.

**How can I obtain a convenience sample for NCA?**

A convenience sample is a sample in which cases from the population are selected for convenience of the researcher, for example, because cases are easily accessible. When a convenience sample is used as a substitute of a probability sample, statistical inference is flawed. For NCA the convenience sample is the same as for any other research approach and data analysis technique.

**How can I obtain a purposive sample for NCA?**

A purposive sample is a sample in which cases from the population are specifically selected with a certain purpose. In NCA purposive sampling can be applied for testing necessity theory by sampling only cases with the outcome present. With an necessity experiment this sample is used to observe if the outcome disappears when the condition is removed. In an necessity observational study this sample is used to observe if the condition is present in all sampled cases.

**Can I estimate population parameters with a purposive sample?**

With a purposive sample, estimations for general parameters of the population (e.g., mean) cannot be obtained because these estimations require information about the entire population.

**Does NCA require a minimum sample size?**

The short answer is “**At least 1, but the larger the better**”.

NCA may be performed with a __single case__. This is possible when the condition and outcome can have only two values (absent/present, low/high, 0/1, etc.). For testing the hypothesis that the presence of X is necessary for the presence of Y, a case with the outcome present should be selected. Then the researcher observes if the condition is present or not. If the __condition is not present__, the __hypothesis is rejected__ (falsification). This is one test of the hypothesis with a single case. Such test could be replicated with multiple cases, but the test itself is done with a single case.

In most NCA applications X and Y can have several levels, and samples are drawn from a population for the estimation of the NCA parameters, for example the effect size. Like with other methods, the __estimation becomes better when sample size increases__.

There is no recommended minimum, optimum or maximum sample size. The quality of the estimation depends on many factors.