SGM Journals
Research Article

The Statistical Analysis of Slope-Ratio Assays

FINNEY, D. J.

Journal of General Microbiology 1951; 5(2):223 · https://doi.org/10.1099/00221287-5-2-223

Download PDF View at publisher PubMed

Summary auto-generated

This paper by D. J. Finney presents an improved statistical method for analyzing slope-ratio assays, commonly used in microbiological testing. In slope-ratio assays, the potency of a test preparation is estimated by comparing the slopes of dose-response relationships between a standard and test substance. Previous statistical analyses relied on composite tests of residual variation without explicitly testing fundamental assumptions. Finney introduces an analysis of variance approach using orthogonal coefficients that distinguishes between tests of statistical validity (whether linearity assumptions hold) and fundamental validity (whether the assay's basic premises are sound). The method is illustrated using a 5-point riboflavin assay and extended to 7-, 9-, and 11-point designs. The analysis partitions the sum of squares between doses into components for regression, blanks, intersection, and higher-order terms. Validity tests can reveal whether assumptions about linear dose-response relationships and proper intersection of regression lines at zero dose are violated. Finney emphasizes that explicit validity tests are essential for biological assays and argues that confidence in assay results requires demonstrating the soundness of underlying assumptions.

Key findings

  • Proposed analysis of variance method using orthogonal coefficients separates statistical validity tests (linearity) from fundamental validity tests (proper intersection at zero dose) in slope-ratio assays.
  • Extended the analytical approach from 5-point to symmetrical (2k+1)-point assay designs (7, 9, and 11-point), with provided tables of orthogonal coefficients for each design.
  • Demonstrated the method on a riboflavin assay example, showing how to partition variation and interpret validity test results to determine if assay conclusions are reliable.
  • Emphasized that explicit validity testing should be mandatory in biological assays rather than relying on investigator judgment or accepting assumptions without verification.
  • Method is more rigorous than previous approaches while remaining computationally feasible through use of standard orthogonal coefficient tables.

This summary was generated automatically from the article PDF and is not part of the original publication. Refer to the PDF for the authoritative text.

Abstract

SUMMARY: In the past, the statistical analysis of slope-ratio assays has failed to make specific tests of the validity of assumptions essential to the validity of the conclusions to be drawn, and has instead relied upon a composite test of residual variation. The technique introduced in, this paper enables the analysis of variance of assay data to be developed in a manner analogous to that customary for parallel line assays. The paper illustrates the calculations for a 5-point assay, and shows how the analysis of variance, completed with the aid of a set of orthogonal coefficients, gives the required validity tests. Similar analyses for other assay designs, symmetrical and unsymmetrical, are, briefly described, and tables of the orthogonal coefficients for 5-, 7-, 9-, and 11-point designs are given. A final section discusses the need for vatidity tests in biological assays.