To analyse the
results of an R-index test.

- R_index_rank_withMD.xlsx

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**Difference:**If the test is a similarity test, the threshold that will be considered non-negligible. That is, H_{0}is that the difference is greater than this threshold.**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.

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
evaluated.
- 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
threshold).
- 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
comparative judgement.

R index values can
be analysed using parametric statistics e.g. ANOVA (as can d’).

Significance of
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 calculated manually.

- 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.

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