Demetriades, A. and Argyraki, A., 2025. Tutorial: Analytical Precision - Plotting Thompson and Howarth Charts with Grapher. International Union of Geological Sciences, Commission on Global Geochemical Baselines, Tutorial Publication No. 2, 28 pp.; https://doi.org/10.5281/zenodo.15547988. Supplementary material.
Abstract
Thompson and Howarth developed a graphical method in the 1970s for the visual estimation of analytical precision even for a single duplicate-replicate pair of samples. The mean of the duplicate-replicate pair of samples is plotted against the corresponding absolute difference. A copy of the original precision control chart for replicate results used by the Imperial College Applied Geochemistry Research Group is presented for use in the laboratory and field.
Digital log-log base 10 and linear templates of Thompson and Howarth charts are provided, along with control lines plotted at the 90th and 99th percentiles for 10% and 20% precision at the 95% confidence level. These templates were generated using Golden Software’s Grapher™ (version 25). Instructions are provided for preparing the input replicate data set and plotting the results. Worked examples and the interpretation of the plotted results are also included.
Overview of plotting Thompson and Howarth Charts
Thompson and Howarth developed a graphical method in the 1970s that allows for the visual estimation of analytical precision using duplicate-replicate pairs of samples. The mean of these pairs is plotted against the absolute difference, providing a clear representation of data variability. The document includes a copy of the original precision control chart used by the Imperial College Applied Geochemistry Research Group for practical application in laboratory and field settings.
This comprehensive tutorial aims to enhance the understanding and application of analytical precision assessment in applied geochemistry surveys, making it a valuable resource for practitioners in the field, and especially university students and early career researchers.
Digital Templates and Instructions
The tutorial provides digital log-log base 10 and linear templates for plotting the Thompson and Howarth charts, including control lines plotted at the 90th and 99th percentiles for 10% and 20% precision at a 95% confidence level. Instructions for preparing input replicate data and plotting the results using Golden Software’s Grapher™ are included, along with worked examples to aid interpretation.
The software tools required for plotting Thompson and Howarth charts are Microsoft Excel® and Golden Software’s Grapher™.
Tutorial Structure
The tutorial is structured into various sections:
1. Introduction
This section introduces the Thompson and Howarth method and its significance in estimating analytical precision. It highlights the graphical approach’s utility even with a single duplicate-replicate pair.
2. Definitions
Key definitions are provided, including:
- Routine Sample: Collected per the sampling plan.
- Duplicate Sample: A sample collected from the same site, indicating within-site variability.
- Replicate Sample: A sample is split in the laboratory to identify laboratory errors.
3. Plotting Charts in the Field
The tutorial describes the procedure for plotting Thompson and Howarth charts in the field using log10-log10 paper and a hand-held calculator.
4. Customising Grapher’s Quick Access Toolbar
Instructions on customising the Grapher™ Quick Access Toolbar for efficient plotting are provided.
5. Worked Examples
The tutorial includes step-by-step examples of using log-log (base 10) and linear templates to plot replicate analytical data. Each step is detailed, ensuring clarity in the plotting process.
6. Interpretation of Charts
The interpretation section discusses how to evaluate the precision of analytical results based on the plotted charts. It emphasises the significance of the 90th and 99th percentiles in determining data conformity to analytical precision standards.
Supplementary Material
The tutorial includes supplementary material in a zip file. The file contains templates, example files, and relevant literature for further reading.
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