KNOWLEDGEBASE - ARTICLE #148

How do I make XY plots showing "dilution factor", instead of concentration, on the X axis?

When working with unknown concentrations, perhaps of an impure substance, some prefer to plot concentrations in relative terms, such as "dilution factor" (DF). One approach is to enter the fold-dilution value in the X column, do an X=1/X transformation (because higher dilution factors correspond to lower concentrations), and plot the results (i.e., Y vs. 1/DF). Then, to give the X axis meaningful labels, substitute the 1/DF values with DF itself using Custom Ticks. If, as is often the case, your graph is a log-dose-response (sigmoidal) curve, remember that you still have to do a log transformation of 1/DF, just as if it were a concentration. Suppose you've performed an assay where the "final" or "into-the-assay" dilutions range from 10- to 1,000,000-fold. You want to construct a log-dose-response curve. Enter the dilution factors in the X column of your data table as shown here:

 

Find the reciprocals of DF by using the transform X=1/X. Then transform the X values of the Results sheet to X=Log(X), choosing to "Create a new graph of the results". If you prefer, you can do this as a single "User-defined" transform, X=Log(1/X). The graph looks like this:

 

The X axis labels are not very useful, so substitute the original DF values. Double click on the X axis, then select "Custom Ticks". Choose to "Show custom ticks only". For each "Position (X)=", enter the transform value Log(1/X), and for the "Label", the corresponding DF value. You can skip some of the labels to avoid overlapping. Here are the entries for this example:

 

The tick labels now look those in this graph (which contains, additionally, a fitted curve and some formatting):

 

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