PHARM/PCS V5 · Procedure 7 Dosage and Statistics
Parallel Lines II: Construction of Parallel Lines
Combine two parallel lines into one best common slope, weighted by how well each line is determined, and redraw both lines with it.
What it computes
Given two regression lines whose slopes have been determined not to differ significantly (by Procedure 6), computes a single best-common slope as the weighted mean of the individual slopes, weighted by the reciprocal of each slope's squared standard error. The two lines are then redrawn through their own centroids (x̄, ȳ) using this common slope.
Inputs and outputs
You provide
- Two lines, each a block of x and y pairs, in the same format as Procedure 6
PHARM/PCS reports
- Each line's own slope
- The weighted common slope
- Both lines rewritten with the common slope through their own centroids
- A plot of the constructed parallel lines, with the individual fits dashed
When to use it
Right after Procedure 6 clears the lines as parallel, when you need the single shared slope that potency analysis requires. Procedures 10 and 11 use this common-slope construction to put the lines on equal footing before measuring the horizontal distance between them.
Reading the results
The weighting lets the better-determined line (smaller slope error) pull the common slope toward itself, which is what you want. Don't apply this if Procedure 6 flagged a real slope difference; forcing a common slope onto genuinely non-parallel lines buries the effect you should be reporting.
More accurate than the 1986 printout
The 1986 report printed a common slope of 60.2165; V5 gives 60.2139. The difference, in the fifth significant figure, comes from the single-precision arithmetic of the original BASIC interpreter, and the book's hand calculations agree with V5 as far as they are carried.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.