Thurstonian Scaling for Sensory Discrimination Methods
Thurstonian scaling, i.e., Thurstonian discriminal distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi></mrow></semantics></math></inline-formula> or <...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
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| Series: | Applied Sciences |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2076-3417/15/2/991 |
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| Summary: | Thurstonian scaling, i.e., Thurstonian discriminal distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>δ</mi></mrow></semantics></math></inline-formula> or <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula>, can be used as a sensory measurement index to measure and monitor food sensory difference/similarity between test and control samples due to potential food contamination. It can be obtained from any one of the sensory discrimination methods. Thurstonian scaling is theoretically independent of the methods or scales used for its estimation. This paper discusses statistical inference including estimations and tests of hypothesis for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula>. Ten basic sensory discrimination methods including six forced-choice methods and four methods with response bias are used in this paper to estimate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> values and their variances. Statistical tests are conducted based on the estimated <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> values and their variances. The statistical tests include difference testing and equivalence/similarity testing for individual <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> values for test and control samples and for two or multiple <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> values for test samples. The application and significance of Thurstonian scaling for sensory discrimination methods are discussed generally. R codes for estimations and tests for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mo>′</mo></msup></semantics></math></inline-formula> values are provided in the paper. |
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| ISSN: | 2076-3417 |