## NCA statistics

**What statistical methods are used in NCA?**

NCA currently uses descriptive statistics (data summary and description) and inferential statistics (by null-hypothesis testing).

**What statistical descriptives are used in NCA?**

NCA summarizes and describes the data for a given ceiling technique in terms of ceiling line, effect size and other NCA parameters.

**What point estimates are used in NCA?**

A point estimate is the single guess value of an unknown population parameter, calculated from the sample that was selected from that population. For a given ceiling technique, NCA’s point estimates are the sample’s ceiling line, effect size and other NCA parameters.

**How is NCA's statistical significance test done?**

NCA’s significance test has the following parts (Dul et al., 2018):

- Calculate the necessity effect size for the sample.
- Formulate the null-hypothesis that suggests that X and Y in the population are not related. Any effect size is a random effect.
- Create a large set of random resamples (e.g., 10,000) using approximate permutation. In a permutation test the X and Y values that are observed in the sample are shuffled to create new resamples (same sample size) with ‘cases’ where X and Y are unrelated.
- Calculate the effect size of all resamples. The set of effect sizes comprises an estimated distribution of effect size under the assumption that X and Y are not related.
- Compare the effect size of the observed sample (see part 1) with the distribution of effect sizes of the random resamples. The fraction of random resamples for which the effect size is equal to, or greater than the observed effect size (
*p*value) informs us about the statistical (in)compatibility of the data with the null hypothesis.