PHARM/PCS V5 · Procedure 6 Dosage and Statistics
Parallel Lines I: Test for Parallelism
Test whether two or more regression lines share a slope, the check that must pass before any relative potency calculation.
What it computes
Tests whether the slopes of two (or more) regression lines differ significantly. A Student's t is computed from the difference of slopes and the pooled residual standard error. This test is the prerequisite for Procedure 7 (constructing the best common slope) and for the relative potency calculations in Procedures 10 and 11.
Inputs and outputs
You provide
- Two or more lines, each a block of x and y pairs, optionally labeled
- A confidence level
PHARM/PCS reports
- A t statistic and degrees of freedom for each line compared with the first
- Significant or not, with an exact p-value
- A plot of the fitted regression line for each group
When to use it
Before any analysis that assumes two dose-response lines are parallel, above all relative-potency work (Procedures 10 and 11), where a valid potency ratio depends on the lines sharing a common slope. Run this first, as the gatekeeper.
Reading the results
A non-significant t means you've failed to detect a slope difference (enough to proceed to a common slope, Procedure 7) but isn't positive proof the lines are parallel, especially with few or noisy points. A significant difference, by contrast, is a hard stop: potency ratios from non-parallel lines aren't meaningful.
An exact p-value, not just a verdict
The 1986 program only reported Significant or Not Significant against tabulated values. V5 adds the exact two-tailed p-value, so you can see how strong or marginal the evidence is. All the lines go into one entry, where the original read each from a separate file.
This page describes the procedure. Calculations run inside the licensed PHARM/PCS V5 application. PHARM/PCS is a trademark of MCS Scientific LLC.