This page is under construction; stay tuned for FlowJo Version 10 with Population Comparison.

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 (not in the control). Two algorithms (Kolmogorov-Smirnov and Probability Binning) are used to determine the statistical difference between samples.

Percent (%) Positive Algorithms

The Overton cumulative histogram subtraction1 algorithm 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.

The Super-Enhanced Dmax Subtraction (SED) is a sophisticated algorithm developed by Bruce Bagwell to compute percent positives when comparing histograms. A detailed overview of the algorithm can be found here.

This post on the daily dongle provides some additional information on differences between the two models.

Confidence Interval Algorithms

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. In other words, it states a confidence interval for the assertion that the two populations are NOT drawn from a common distribution. For a detailed look at the algorithm, go here.

*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. Furthermore, this statistic is ideal for comparing differences in small populations (e.g. n=100).  In flow cytometry, we compare values of much higher magnitude (e.g. 1024, 262,000, 16.7 million).  Therefore, chances are extremely high that this algorithm with indicate that there is a 99% difference between two channels of two populations.  The channel where this occurs may or may not be meaningful and must be observed in biological context.

The Probability Binning (T(x))(3-5) comparison is related to the Cox Chi Square6 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. In more detail, the algorithm divides the control sample into bins with the same number of events, divides the test sample along the same boundaries and calculates the Chi Square of the two binned data sets. The X2 is converted into a metric (T(X) that can be used to estimate the probability that a test population is different from a control population.  The Probability Binning algorithm was designed for use with flow cytometry data.

Note: K-S and T(X) will very readily label two samples as MATHEMATICALLY different. It’s up to the user to determine whether this difference is BIOLOGICALLY meaningful.  Hence, controls are important!

References:

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.