### "How many events do you need to acquire?"

Assay variation can be a major source of error, therefore it is critical to understand the statistics behind rare event analysis. The cytometry friendly Gaussian distribution cannot be applied to the analysis of such a low number of events (the term "rare" is given to events with a frequency of 0.01% or less) and the best approach is to use Poisson statistics (Fig.1). Good experimental practice suggests to keep Coefficient of Variation (CV) below 5%, and thus the number of events to acquire should be defined in order to maintain the lowest CV possible and in any case below 5%.

The number of events that satisfy a given criterion (e.g they are positive for a marker, P) is defined as

the variance (V) is defined as

$P=R/N$

where
$N$=total events

$R$=events that meet a given criterion

and
$R$=events that meet a given criterion

$0<=P<=1$

As with all statistical distribution,the variance (V) is defined as

$V(R) = NP(1-P)$

The standard deviation (SD) is
$SD=√V=√(NP(1-P))$

and the coefficient of variation is
$CV=1/√V$

Figure 1. Poisson statistics defines the probability that a number of events will occur in a fixed interval of time/space/volume.
**Use the tool below to help define the ideal number of events to acquire for the expected frequency of rare population.**

**Step 1**: Input the expected frequency in the cell below; i.e. to identify a cell population that represents 0.01% of the total, input frequency is 0.001 (one positive event every ten thousands)

**Step 2**: Use the

**Events (N)**cells below to input the total number of events, CV% cells will automatically refresh allowing the identification of the ideal total events number or the interval required to achieve a CV below 5%; i.e. to identify a cell population that represents 0.01%, five million events should be acquired.

Events (N) | ||||||

Positive (R) | 0 | 0 | 0 | 0 | 0 | 0 |

Proportion (P) | 0 | 0 | 0 | 0 | 0 | 0 |

Variance (V) | 0 | 0 | 0 | 0 | 0 | 0 |

SD | 0 | 0 | 0 | 0 | 0 | 0 |

CV% | 0 | 0 | 0 | 0 | 0 | 0 |

**Where:**

Number of events | $$N$$ |

Positive events | $$R$$ |

Proportion (frequency) | $$P=R/N$$ |

Variance | $$V=NP(1-P)$$ |

Standard Deviation | $$SD=√V$$ |

Coefficient of Variation % | $$CV=(SDx100)/R$$ |