R-index Analysis

R-index Analysis

Purpose 

To analyse the results of an R-index test. 

Data Format

  1. R_index_rank_withMD.xlsx

Background 

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.

Options

  1. Reference Product: Select which product should be used as a reference.
  2. Type of test: Similarity or Difference test
  3. Difference: 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 this threshold.
  4. Significance level: Type-I error
  5. 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.
  6. Number of Decimals for Values: Required number of decimals for values given in the results.
  7. Number of Decimals for P-Values: Required number of decimals for any p-values given in the results. 

Results and Interpretation

Frequency table

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.

R-index table 

The second tab is the R-Index table showing the estimated R-Index for each product. The following values are given:

  1. N. The number of times each sample was evaluated.
  2. 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.
  3. The critical value Z (at the significance threshold).
  4. The p-value to conclude whether each product was significantly different from the reference product.

Interpretation 

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. 

Technical Information

  1. The R-index is calculated manually. 

References 

  1. Bi & O’Mahony (2007) Updated and extended table for testing the Significance of the r-index Journal of Sensory Studies 22 713–720.
  2. Lawless & Heymann (1998) Sensory Evaluation of Foods Chapter 5 Discrimination Theories and  advanced topics 140-159.
  3. Macmillan N & Creelman C D (2004) Detection Theory A User’s Guide.  Lawrence Arlbaum Associates Inc.
  4. 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.
  5. O’Mahony M & Rousseau B (2002) Discrimination testing: a few ideas, old and new. Food Quality and Preference 14 157-164.
  6. Rousseau B (2011) Measuring product similarities: Are two indices, R-Index and d′, interchangeable? IFT Annual Meeting, New Orleans, USA
  7. Brown J (1974) Recognition assessment by rating and ranking. Brit J Psycho 65 13-22.
  8. Lee H-S, van Hout D Quantification of Sensory & Food quality: The R-Index Analysis Journal of Food Science 2009.
  9. Bi, J. (2006).  Statistical Analyses for R-Index.  Journal of Sensory Studies, 21, 584-600.
  10. Lawless, H.T. and Heymann, H. (2010).  Sensory Evaluation of Food – Principles and Practices.  Springer.
  11. O’Mahony, M. (1986).  Sensory Evaluation of Food – Statistical Methods and Procedures.  CRC Press.

    • Related Articles

    • R-Index

      Introduction The R-index is a tool in sensory science that helps quantify the difference between two samples. The R-index is designed to quantify the area under an empirical Receiver Operating Characteristics (ROC) curve within the framework of ...

    • R-Index (ranked data)

      Purpose R-index is a signal detection measure that assesses the degree to which assessors can discriminate between a pair of products for a given attribute. R-index is expressed as a proportion that represents the probability that the one product is ...

    • Penalty Analysis

      Purpose To provide a penalty analysis of a consumer data set, that is to investigate how liking or acceptability of product decreases when product attributes are not at the optimal intensity. Data Format Consumer.xlsx Note: for EyeOpenR to read your ...

    • Quality Index Analysis

      Available from version: 5.4.4 Purpose The Quality Index is an ANOVA based analysis, with the idea based on the paper by Verhoef (2015) for the purpose of measuring the reliability of univariate sensory descriptive data. Data format profiling.xlsx The ...

    • Napping Analysis

      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 ...