Analyse results from one of the following tests: 2-AFC,
3-AFC, Duo-Trio, Triangle, Tetrad.

- Discrimination.xlsx
- Results of the discrimination test are binary (1 = correct answer, 0 = incorrect answer)

This is an alternative forced
choice (AFC) discrimination test where panellists are presented with 2, 3 or
more products and asked to select one product based on a pre-specified
attribute. The 2-AFC test, also known as a directional difference
test, is used to establish if a directional difference exists in the perceived
intensity of a specified attribute between 2 products. The panellist
is required to state if a 2^{nd} product is more or less intense
in the specified attribute compared to the 1^{st} presented
product.

The guessing probability (probability of getting a correct
answer by guessing only) is ½.

This is an alternative forced choice (AFC) discrimination
test where panellists are presented with 2, 3 or more products and asked to
select one product based on a pre-specified attribute. The3-AFC test
is used to establish if there is a discernible difference between 2 products in
respect of a specified attribute. The panellist is required to
select 1 product from the set of 3 that differences in the specified attribute.

The guessing probability (probability of getting a correct answer by guessing only) is ⅓.

The guessing probability (probability of getting a correct answer by guessing only) is ⅓.

A discrimination (difference) test to determine if an
unspecified difference exists between two products. The panellist is presented with 2 products (A
and B) and a reference product (R), and asked to determine which of A or B is *most
similar* to R. Useful for products that are fairly similar but not totally
identical.

The guessing probability (probability of getting a correct answer by guessing only) is ½.

The guessing probability (probability of getting a correct answer by guessing only) is ½.

During a triangle test, a panellist is presented with three
samples of which two are equal and one is different. The panellist must state
which sample is different. The results indicate whether a detectable difference
exists between two samples. The method is statistically more efficient than the
duo trio test but has limited use with products that have a strong and/or
lingering flavour.

If there is no difference detected between sample A and B the panellist must choose a random sample. The chance a panellist chooses the odd sample is 1/3. If there is no difference between the samples you would expect one third of the panellists to choose the odd sample, while two third of the panel chooses one of the equal samples. If there is a detectable difference more than one third of the panellists will choose the right sample.

The guessing probability (probability of getting a correct answer by guessing only) is ⅓.

If there is no difference detected between sample A and B the panellist must choose a random sample. The chance a panellist chooses the odd sample is 1/3. If there is no difference between the samples you would expect one third of the panellists to choose the odd sample, while two third of the panel chooses one of the equal samples. If there is a detectable difference more than one third of the panellists will choose the right sample.

The guessing probability (probability of getting a correct answer by guessing only) is ⅓.

An unspecified or specified attribute discrimination test
which aims to establish if 2 products are different or
similar. Panellists are presented with 2 samples of the 1st product
and 2 samples of the 2^{nd} product and asked to sort them into
two groups of 2 products where products in a group are more similar to each
other.

There is a ⅓ chance of selecting of selecting any combination of 2 groups of 2 products.

There is a ⅓ chance of selecting of selecting any combination of 2 groups of 2 products.

The statistical
principle behind every discrimination test should be to reject a null
hypothesis (H_{0}). For a *difference* test the null hypothesis
states there is no detectable difference between two (or more) products. The
alternative hypothesis H_{1 }is that there is a detectable difference.
If there is sufficient evidence to reject H_{0} in favour of the
alternative hypothesis H_{1}, then a difference can be recorded.

For a *similarity*
test the null hypothesis states that there is a non-negligible difference. The
size of difference that will be considered non-negligible must be
pre-specified. The alternative hypothesis is that there is no difference. If
there is sufficient evidence to reject H_{0} in favour of the
alternative hypothesis H_{1}, then it can be concluded the products are
similar.

The data is processed using the binomial test to test for
difference among the samples.

The number of correct and incorrect responses are
counted. The proportion of correct
responses is calculated and from there the proportion of true distinguishers is
calculated as follows: where p_{c} is the proportion of correct
responses. P_{g} is the guessing probability and p_{d} is the
proportion of distinguishers.

p_{c} = p_{d} + (1-p_{d})*p_{g }

p_{d} =(p_{c}-p_{g})/(1-p_{g})

**Treat Sessions/Replicates separately:**If the data has been gathered over different sessions, or there are different replicates, these can be analysed separately.**Type of test:**Similarity or difference test.**Model:**Guessing or Thurstonian model.**Prop of Discriminators Threshold (Pd):**If the test is a similarity test and the Guessing Model is used, the threshold that will be considered non-negligible. That is, H_{0}is that Pd is greater than this threshold.

Or**D-prime Threshold (d’):**If the test is a similarity test and the Thurstonian Model is used, the threshold that will be considered non-negligible. That is, H_{0}is that d’ is greater than this threshold.**Confidence level:**The probability for the confidence intervals. That is, a 0.95 confidence interval means that in 95% of population samples, the true value would lie in this confidence interval.**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.

**N total:**The total number of tests in the results set**N correct:**The number of correct tests**N incorrect:**The number of incorrect tests (N incorrect + N correct = N total)**Proportion correct:**The proportion of correct tests as a percentage (100 x N correct/N tot)**P-value:**The p-value indicates the probability of obtaining the result if the Null hypothesis is true.**Min correct (0.1%):**The minimum number of correct responses for the result to be significant with 99.9% probability.**Min correct (1%):**The minimum number of correct responses for the result to be significant with 99% probability. (For a similarity test this is the maximum number).**Min correct (5%):**The minimum number of correct responses for the result to be significant with 95% probability.**Min correct (10%):**The minimum number of correct responses for the result to be significant with 90% probability.**p < 0.1%:**Is the p-value less than 0.001 i.e. Is the result significant at 99.9% level?**p < 1%:**Is the p-value less than 0.01 i.e. Is the result significant at 99% level?**p < 5%:**Is the p-value less than 0.05 i.e. Is the result significant at 95% level?**p < 10%:**Is the p-value less than 0.1 i.e. Is the result significant at 90% level?

**Proportion correct:**The proportion of correct responses (within the bounds of the guessing probability) and confidence interval, calculated using the exact method.**Proportion Discriminators:**The proportion of responses that are true distinguishers and confidence interval, calculated using the exact method.**D-prime:**is an estimation of the distance between the products according to the Thurstonian scale. It is the difference between the mean values of the two signals divided by the standard deviation.

When testing for a difference, the p-value indicates if the
samples are significantly different, and at what level. You will
decide whether to conclude if the samples are different based on the risk you
want to take.

In the case of similarity, the interpretation is similar,
but will be in the context of the pd or d-prime value you specified as a
non-negligible difference.

If the data contains 3 or more replicates the Beta-Binomial
model is fitted. This is to check for loss of independence in the replicates.
This is also called over-dispersion in the data.

The beta-binomial model is parameterized
in terms of mu and gamma, where mu corresponds to a probability parameter
and gamma measures over-dispersion. Both parameters are restricted to the
interval (0, 1).

The parameters of the standard (i.e. not
corrected) beta-binomial model refers to the mean (i.e. probability) and
dispersion on the scale of the observations, i.e. on the scale where we talk of
a probability of a correct answer (Pc).

The following parameters are
returned, with estimate, standard error, and confidence interval limits.

- Probability (mu)
- Over-dispersion (gamma)
- Pc – the probability of a correct response.
- Pd – the probability of true discrimination.
- d-prime – the ‘distance’ between the products.

The test shows:

- a likelihood ratio test of over-dispersion on
one degree of freedom.
- and a likelihood ratio test of association (i.e.
where the null hypothesis is "no difference" and the alternative
hypothesis is "any difference") on two degrees of freedom (chi-square
tests).
- If the data is over-dispersed, the p-value for the test for over dispersion should be smaller than the desired alpha.

- The R package
*sensR*(Rune Christensen and Per B. Brockhoff) is used. - The confidence intervals are calculated using the ‘exact’ binomial method.

- ISO 4120:2004 Sensory Analysis – Methodology – Triangle
Test
- ASTM-E1885-04 (2011) Standard Test Method for Sensory
Analysis – Triangle Test
- Lawless, H.T. and Heymann, H. (2010). Sensory
Evaluation of Food – Principles and Practices. Springer.
- Ennis. J. M., and Jesionka, V. (2011) – The Power of
Sensory Discrimination Methods Revisited. Journal of Sensory
Studies, 26, 371-382.
- Ennis. J. M. (2012). Guiding the Switch from
Triangle Testing to Tetrad Testing. Journal of Sensory Studies, 27,
4, 223-231.
- Garcia, K., Ennis, J.M. and PrinyawIwatkul, W.
(2013). Reconsidering the Specified Tetrad Test. Journal
of Sensory Studies, 28, 6, 445-449.
- O’Mahony, M. (2013). The Tetrad Test – Looking
Back, Looking Forward. Journal of Sensory Studies, 28, 4, 259-263.
- ISO 10399:2004 Sensory Analysis – Methodology – Duo-Trio
Test
- ASTM-E2610-08 (2011) Standard Test Method for Sensory
Analysis – Duo-Trio Test
- Christensen, R.H.B. (2014). Statistical Methodology for Sensory
Discrimination Tests and Its Implementation in SensR.
- Christensen, R.H.B. and Brockhoff, P.B (2014). Package ‘sensR’.
- http://cran.r-project.org/web/packages/sensR/sensR.pdf
- Christensen, R.H.B. and Brockhoff, P.B (2014). Sensory Discrimination Testing with the sensR
Package.
- http://user2014.stat.ucla.edu/abstracts/talks/125_Christensen.pdf

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