Kenneth Ault wrote: > > As someone who made extensive use of the K-S test in a past life I would > like to point out one important issue that is not dealt with in > statistics text books, and I think was not explicitly mentioned in Ted > Young's excellent paper that introduced K-S to the flow community. > > The K-S test is typically used to compare two frequency distributions > non-parametrically. The number of degrees of freedom that one uses to > calculate a p value from a K-S statistic is based upon the number of > bins in the frequency distribution histogram. For flow cytometry data > one is tempted to use the number of channels, i.e. 256 or 1024 etc. as > the degrees of freedom. Doing this will result in any two histograms > that are not identical being highly statistically significantly > different. In other words using channels as degrees of freedom makes > the K-S test ridiculously too sensitive to trivial differences in the > histograms. > In fact our flow histograms have far fewer degrees of freedom than > they have channels. The correct value is based upon the CV of your > histogram, i.e. how many distinct distinguishable histograms can you fit > into the number of channels that you have? For most of our data we have > no way (that I know of) to estimate the correct number of degrees of > freedom. > For this reason I have always used the K-S statistic as a measure of > the difference between two histograms, but have not used it to calculate > a p value. I am sure there are others listening to this discussion who > are better qualified to discuss how one calculates degrees of freedom > for a flow histogram - I for one would be interested in such a > discussion. There is some argument as to whether the K-S test even fits the conditions required for flow cytometric histogram analysis. Chris Cox in his paper on flow cytometry frequency distributions makes a good case for using the chi-square test for statistical histogram comparisons (Cytometry 9:291-298, 1988). Scott
This archive was generated by hypermail 2b29 : Wed Apr 03 2002 - 11:50:22 EST