To analyse the
results of an R-index test.
The R-index applies signal detection theory as an alternative approach to discrimination testing. It is often used where there are a large number of products requiring a ‘yes/no’ response relative to a control or reference product.
It is also applicable where the ‘yes/no’ response is broken down into ‘degrees of certainty’ – e.g., ‘different, I am sure’; ‘different, I am not sure’; ‘different, I do not know and guess’; ‘the same, I do not know and guess’; ‘the same, I am not sure’; ‘the same, I am sure’.
In the above scenario, the R-index results from converting the rating data to a measure related to the area under the ROC (receiver operation characteristics) curve.
- Reference Product: Select which product
should be used as a reference.
- Type of test: Similarity or Difference test
If the test is a similarity test, the threshold that will be considered
non-negligible. That is, H0 is that the difference is greater than
- Significance level: Type-I error
- Order of the Scale: Increase or Decrease.
Should an increase or decrease in scores in the data set result in an increase
in the certainty of difference. By default, a score of 1 means the assessor is
sure the samples are the same, and a score at the top of the scale means the
assessor is sure the samples are different.
- Number of Decimals for Values: Required number
of decimals for values given in the results.
- Number of Decimals for P-Values: Required number
of decimals for any p-values given in the results.
Results and Interpretation
This is a contingency table gives a summary of how many responses given
for each of the scale categories. The products form the rows and there is a column
for each level of the scale.
It is a useful
visual look see. It is also the basis for calculating the R-index
using the traditional psychophysics principles from Thurstone.
The second tab is
the R-Index table showing the estimated R-Index for each product. The following
values are given:
- N. The number of times each sample was
- An estimate of the R-index. R-index is
expressed as a proportion. It
is equivalent to the probability of correctly choosing one of two samples in a
paired comparison, but is calculated from theoretical paired comparisons
between each possible signal/noise pairing.
- The critical value Z (at the significance
- The p-value to conclude whether each product
was significantly different from the reference product.
At a basic
interpretation level, the p-values are used to establish if each product is
statistically different from (or similar to) the reference product.
The key point to
note with the R-index is that it is based on Thurstonian scaling and the law of
R index values can
be analysed using parametric statistics e.g. ANOVA (as can d’).
R-index can be determined from critical value tables for ‘n’ responses.
‘Equivalent’ d’ can
be determined for r-index values from published tables.
- The R-index is
- Bi & O’Mahony (2007) Updated and extended table for testing the Significance of the r-index Journal of Sensory Studies 22 713–720.
- Lawless & Heymann (1998) Sensory Evaluation of Foods Chapter 5 Discrimination Theories and advanced topics 140-159.
- Macmillan N & Creelman C D (2004) Detection Theory A User’s Guide. Lawrence Arlbaum Associates Inc.
- O’Mahony M (1992) Understanding Discrimination Tests: A user friendly treatment of response bias, rating and ranking R-index tests and their relationship to signal detection. Journal of Sensory Studies 7 1-47.
- O’Mahony M & Rousseau B (2002) Discrimination testing: a few ideas, old and new. Food Quality and Preference 14 157-164.
- Rousseau B (2011) Measuring product similarities: Are two indices, R-Index and d′, interchangeable? IFT Annual Meeting, New Orleans, USA
- Brown J (1974) Recognition assessment by rating and ranking. Brit J Psycho 65 13-22.
- Lee H-S, van Hout D Quantification of Sensory & Food quality: The R-Index Analysis Journal of Food Science 2009.
- Bi, J. (2006). Statistical Analyses for R-Index. Journal of Sensory Studies, 21, 584-600.
- Lawless, H.T. and Heymann, H. (2010). Sensory Evaluation of Food – Principles and Practices. Springer.
- O’Mahony, M. (1986). Sensory Evaluation of Food – Statistical Methods and Procedures. CRC Press.
Quality Index Analysis
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Purpose To provide an analysis of data collected using the napping methodology. Data Format Napping.xlsx For EyeOpenR to read your data the first five columns must include the following in the specified order: Assessor, Product, Session, Replica and ...
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Purpose This analysis looks at the overall panel performance in terms of Discrimination, Agreement and Repeatability or Reproducibility, and then the performance of each individual in the panel in these terms. Using a more sophisticated model, than ...