The Statistics of Bioassay - 1st Edition - ISBN: 9781483256627, 9781483277011

The Statistics of Bioassay

1st Edition

With Special Reference to the Vitamins

Authors: C. I. Bliss
eBook ISBN: 9781483277011
Imprint: Academic Press
Published Date: 1st January 1952
Page Count: 188
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The Statistics of Bioassay: With Special Reference to the Vitamins, Volume II focuses on the processes, reactions, principles, and approaches involved in the biological assay of vitamins.

The publication first offers information on the general principles of biological assay, dosage-response curve and its error, and designs for segregating nonrandom variation. Discussions focus on replacement of missing values, randomized groups, calculation of the line, analysis of the variation about the line, comparative biological assays, analytical biological assays, and determination of activity. The text then ponders on measurement of relative potency and correction of quantitative variables.

The manuscript takes a look at assays where the variation in response is a function of the dose and slope-ratio assays. Topics include microbiological assays and the slope-ratio technique, analysis of balanced slope-ratio assays, analysis of assays with an all-or-none response, and graded response with unequal variance. The publication then tackles multiple or repeated assays, including quality control in repeated assays and combination of independent assays of a single unknown.

The publication is a valuable source of information for researchers interested in the biological assay of vitamins.

Table of Contents

I. General Principles of Biological Assays

1. Determinations of Activity

2. Comparative Biological Assays

3. Analytical Biological Assays

4. Inspection Assays

II. The Dosage Response Curve and Its Error

1. The Calculation of the Line

A. Computation from Individual Observations

B. Computation with Several Responses at Each Dose

C. Computation with Coded Doses

2. Analysis of the Variation About the Line

A. The Standard Deviation About the Computed Line

B. Tests for Heterogeneity of Dose Means

C. Test for Simple Curvature

3. The Precision of the Line

A. The Standard Errors of the Computed Line

B. The Standard Deviation in Terms of the Log Dose, λ

C. The Use of λ in Planning Assays

III. Designs for Segregating Nonrandom Variation

1. Randomized Groups

2. The Latin Square

3. The Replacement of Missing Values

IV. Measurement of Relative Potency

1. Determinations of Potency without Restrictions in Dose

A. Assays with One Dosage Level of Each Unknown

B. Assays from Two Dosage-Response Curves

2. Factorial Determinations of Potency

A. The Factorial Design in Biological Assays

B. Two-Dose Factorial Assays

C. Three-Dose Factorial Assays

D. Factorial Assays with More than Three Doses

3. The Precision of the Assayed Potency

A. The Standard Error of Potency

B. Confidence or Fiducial Limits

4. Extensions of the Two-Dose Factorial Assay

A. Abbreviated Computation of Assay Results

B. Assays from Paired Observations

C. Assays with Two Unknowns in Groups of Six

D. Assays with Two Unknowns in Groups of Three

V. The Correction of Quantitative Variables: Covariance

1. The Covariance Between a Concomitant Measure and the Besponse

2. The Adjusted Estimate of Potency

3. The Error of the Estimated Potency

VI. Assays Where the Variation in Eesponse Is a Function of the Dose

1. The Analysis of Assays with an All-or-None Response

A. The Provisional Dosage-Effect Curve

B. The Graphic Estimation of Potency

C. The Computed Dosage-Effect Curve

D. The Computed Potency and Its Precision

2. A Graded Response with Unequal Variance

A. The Dosage-Response Curve

B. The Estimation of Potency

VII. Slope-Ratio Assays

1. Microbiological Assays and the Slope-Ratio Technique

A. Requirements for an Efficient Assay

B. The Design of Balanced Assays

2. Analysis of Balanced Slope-Ratio Assays

A. The Calculation of Potency from Balanced Assays

B. The Calculation of Potency from a Four-Dose Assay

C. Analysis of Variance for Slope-Ratio Assays

D. Standard Error of Potency

VIII. Multiple or Repeated Assays

1. The Combination of Independent Assays of a Single Unknown

A. The Combination of Homogeneous Log Potencies

B. The Combination of Heterogeneous Log Potencies

C. The Combination of Assays Computed with a Common Error Variance and Slope

2. Quality Control in Repeated Assays

A. Control Charts for the Error Variance

B. Control Chart for Slope

C. Control Chart for λ

3. Collaborative Experiments

Glossary of Symbols


A. Homogeneity of the Error for Randomized Groups

B. The Precision of an Estimated Potency with Two Error Variances

C. Relative Potency from All-or-None Assays


Index to Equations

Subject Index


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© Academic Press 1952
Academic Press
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About the Author

C. I. Bliss

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