# Population Comparison - Overview

Comparing distributions of FACS data is an important goal in many applications. For example, to determine whether two samples are statistically significantly different (control vs. test sample) in order to detect a response, or to provide feedback regarding instrument stability by detecting when collected data varies significantly over time.

##### Comparison Algorithms

FlowJo's comparison platforms support four different comparison algorithms. Two algorithms (Overton and SED) are used to calculate the percentage of positive cells found in the sample and not the control). Two algorithms (K-S and Chi(T) / PB) are used to determine the statistical difference between samples.

The **Overton cumulative histogram subtraction**^{1} algorithm essentially subtracts histograms on a channel-by-channel basis to provide a percent of positive cells. This method does not provide an indication of the probability with which two distributions are different; nor does it provide confidence intervals.

The Super-enhanced Dmax Subtraction (SED) is a new sophisticated algorithm by Bruce Bagwell to compute %Positives when comparing histograms.

Several algorithms can be used to compare FACS data. The Kolmogorov-Smirnov (K-S) algorithm is a commonly used method to determine the confidence interval with which one can make the assertion that two flow cytometric univariate histograms are different. Caution must be exercised with this statistic as it will erroneously report that two halves of the same population (every other cell makes up one of the halves while the cells in between make up the other half) are distinct.

A new comparison algorithm was recently developed for the comparison of distributions, called Probability Binning (Chi(T) or PB)^{(3-5)}. The PB comparison is related to the Cox chi-square^{6} approach, but with modified binning such that it minimizes the maximal expected variance. This algorithm has been shown to detect small differences between two populations and it does so in a quantitative way.

##### FlowJo Population Comparison Platforms

FlowJo contains two platforms that allow the direct comparison between different populations, Population Comparison (Uni- and Multivariate) and Multi-sample Comparison. The compared populations can either be subsets of the same sample, or more commonly, equivalent populations in different samples.

Method | # Parameters | Statistic | Create Gates? | Compare |

Univariate | 1 | K-S, Overton, PB, SED Subtraction | no | Individual Populations |

Multivariate | 1 or more | PB | yes | |

Multi-sample | Individual or aggregates of Populations |

The Univariate Comparison platform compares single parameters using the Overton, SED, K-S, and Chi(T) statistics.

The Multivariate Comparison platform compares a single test sample to a single control for multivariate data using the Chi(T) statistic.

The Multi-sample platform compares either univariate or multivariate data of single samples to composites of control samples using the Chi(T) statistic.

1) Overton WR. *Modified histogram subtraction technique for analysis of flow cytometry data*. Cytometry. 1988 Nov;9(6):619-26.

3) Roederer M, Treister A, Moore W, Herzenberg LA. *Probability binning comparison: A metric for quantitating univariate distribution differences.* Cytometry. 2001 Sep 1;45(1):37-46.

4) Roederer M, Moore W, Treister A, Hardy RR, Herzenberg LA. *Probability binning comparison: a metric for quantitating multivariate distribution differences.* Cytometry. 2001 Sep 1;45(1):47-55.

5) Roederer M, Hardy RR.* Frequency difference gating: A multivariate method for identifying subsets that differ between samples.* Cytometry. 2001 Sep 1;45(1):56-64.

6) Cox C, Reeder JE, Robinson RD, Suppes SB, Wheeless LL. *Comparison of frequency distributions in flow cytometry.* Cytometry. 1988 Jul;9(4):291-8.