3. Sensory discrimination (exact) analysis - This analysis is a statistical non-inferiority test (which in this case is a binomial test of the lower tail) and it aligns with the ASTM standard E3009-23a. This analysis type is used in the following Discrimination tests: Triangle, Tetrad, and Duo-Trio.
   
   These options are selected by default. Any changes in the selections and values will be saved for the next time you run the report.
   
   
1. Difference Test – Enter the Alpha you wish to use for this test or turn off the Difference Test analysis by removing the checkmark from the checkbox. Update the d' (d prime) by typing directly in the box. You will notice that the Pd and Pc values will automatically recalculate.
   
   
   
   Difference thresholds:
   
   Update the d' (d prime) by typing directly in the box. You will notice that the Pd and Pc values will automatically recalculate.
   
   
   
   If you update the Pd, then the d' and Pc values will automatically recalculate. Likewise, if you update the Pc value, the d' and Pd values will automatically recalculate. 
   
   
   
   
2. Equivalence Test – An equivalence test is a statistical method used to demonstrate that two samples are practically the same within acceptable limits. Unlike traditional hypothesis tests, which assume equality and look for differences, an equivalence test starts by assuming the samples are different and seeks to prove they are “close enough.”
   
   Control whether the Equivalence test analysis is included in the report by adding in or removing the checkmark from the checkbox.
   
   
3. Equivalence test for replications - This option is only compatible with Triangle tests, Tetrad test, and Duo-trio test, and these tests have to have an experimental design where the same samples were presented to panelists at least twice (i.e the test includes repetitions). In other words, if your test is a single Duo-Trio or a back to back Duo-Trio with more than two samples, even if you select this option, the equivalence analysis for reps is not applicable and therefore will not be included in the report.
   
   The Equivalence test for replications analysis is based on Meyners, M., Carr, B. T., & Kunert, J. (2023). Equivalence and non‐inferiority tests using replicated discrimination and preference data. Journal of Sensory Studies, 38(6), e12882. https://doi.org/10.1111/joss.12882
   
   Control whether the Equivalence test for replications analysis is included in the report by adding in or removing the checkmark from the checkboxes.
   
   
   Equivalence thresholds: 
   
1. Alpha. The Alpha value is applicable to both the Equivalence test and Equivalence test for replications. The default value is 0.05. Update as necessary. 
   
   
2. d'. The d-prime value is applicable to the Equivalence test only. Update as necessary. You will notice that the Pd and Pc values will automatically recalculate.
   
   
3. Pd. The Proportion of distinguishers value is applicable to both the Equivalence test and Equivalence test for replications. If you update the Pd, then the d' and Pc values will automatically recalculate. 
   
   
4. Pc. The Proportion correct value is applicable to the Equivalence test only. If you update the Pc value, the d' and Pd values will automatically recalculate. 
   
   
4. Discrimination analysis - This analysis follows the formulas published in the Sensory evaluation techniques by Meilgaard et al. This analysis has been supported in Compusense since the original implementation of this test type. 
   
   These analysis options are not selected by default, but any changes you make will be saved for future use until modified. 
   
   
1. Difference Test - This is the default analysis. Change the Alpha value if desired, or turn off the Difference Test analysis by removing the checkmark from the checkbox.
   
   
   
2. Similarity Test - Analysis type used in Discrimination tests (Triangle, Tetrad, Same/Different,  3-AFC, Duo-Trio, 2-out-of-5, A-not-A, and Torgerson's) when high confidence is required that the samples are perceived the same. This analysis can be used in quality control tests, for example. Turn the Similarity Test analysis on or off when generating the report.
   
   Set the Alpha and Beta values according to your company standards.

1. Above the table, the following information is displayed:
   
1. The threshold values specified by the user before generating the report.
   
   
2. Statement on how conclusions are made based on the selected alpha. The confidence % is the only value that will change in this statement depending on the Alpha value specified before the report was generated.
   
   
2. The table displays the following details:
   
1. p-value: The p-value for each Duo-trio test.
   
   
2. Responses Required: The maximum number of correct responses permitted to reach the conclusion of Equivalent.
   
   
3. Conclusion: A conclusion is made based on whether the difference between samples is significantly larger than the equivalence threshold.
   
   
4. Triad number: The example screenshot above, annotated with numbered callouts, indicates that a back-to-back Duo–Trio test was executed, resulting in the inclusion of both Triad 1 and Triad 2 rows.
   
   
5. Pooled: In the analysis where two samples (see the Samples table in our example above) were evaluated back to back, the N is increased by multiplying the actual N by the number of tests. Each test is treated as done by different panelists even though they were seen back to back by the same panelists. Pooled analysis is not available in single tests and in any other variation of back to back tests (e.g. more than two tests on two samples, or more than two sample tests).
   
   
6. Both Triads: In a back to back Duo-trio analysis (true replicate of two samples), you can see how many panelists answered both Duo-trio tests correctly. The probability of panelists correctly identifying the sample that is the same as the control for both tests by chance decreases. Both Triads analysis is not available in single tests and in any other variation of back to back tests (e.g. more than two tests on two samples, or more than two sample tests).
   
   

Equivalence Test For Replications

1. Above the table, the following information is displayed: 
   
1. Pd. The proportion of distinguishers value.
   
   
2. Alpha. The Alpha value specified by the user before generating the report.
   
   
3. X. The total number of correct responses.
   
   
4. n. The total number of evaluations, not counting reps.
   
   
5. k. The number of reps included in the analysis.
   
   
2. The table displays the following details:
   
1. Samples. The pairs of samples analyzed for equivalence in reps. Your test may have multiple pairs of different samples, but only those that were evaluated as repetitions (or replicates) will be listed in the table.
   
   
2. Responses Required. The maximum number of correct responses permitted for a conclusion that the samples are equivalent. In our example screenshot above, we can see that there were 9 correct responses, which is greater than 7, which makes the samples not equivalent.
   
   
3. # of Correct Responses. The total number of correctly identified same as control samples.
   
   
4. p-value. The p-value.
   
   
5. Conclusion. A conclusion is made whether the samples evaluated in replicates are equivalent or not.

Supporting tables

1. N: Total number of evaluations included in the report.
   
   
2. Correct: Count of correct responses (where the sample same as reference was identified correctly (if that is what you selected in the Question options), or where the sample different from the reference was identified correctly (if that is what you selected in the Question options)).
   
   
3. Incorrect: Count of incorrect responses (where the same samples were not identified correctly same or different from the reference, depending on what you selected in the Question options.
   
   
4. Estimate Pc: Estimated proportion correct.
   
   Formula: Pc = c / n
   
   Where:
   c = number of correct responses.
   
   n = total number of evaluations.
   
   
5. SE: Standard error of the estimate of the proportion of (momentary) discriminators.
   
   
6. % LCL: Lower confidence limit at the Alpha specified before generating the report.
   
   
7. % UCL: Upper confidence limit.
   
   
8. Triad number: The example screenshot above, annotated with numbered callouts, indicates that a back-to-back Duo–Trio test was executed, resulting in the inclusion of both Triad 1 and Triad 2 rows.
   
   
9. Pooled: In the analysis where two samples (see the Samples table in our example above) were evaluated back to back, the N is increased by multiplying the actual N by the number of tests. Each test is treated as done by different panelists even though they were seen back to back by the same panelists. Pooled analysis is not available in single tests and in any other variation of back to back tests (e.g. more than two tests on two samples, or more than two sample tests).
   
   
10. Both Triads: In a back to back Duo-trio analysis (true replicate of two samples), you can see how many panelists answered both Duo-trio tests correctly. The probability of panelists correctly identifying the sample that is the same as the control for both tests by chance decreases. Both Triads analysis is not available in single tests and in any other variation of back to back tests (e.g. more than two tests on two samples, or more than two sample tests).

1. d' (read d prime): The measure of the extent of the overlap of panelist perception. It is the distance between the means of the two distributions measured in terms of their standard deviation.
   
   The larger the d’ value, the samples are more different. Where the d' value is 0 it means that the samples are indistinguishable. A d’ of 1 or less might be considered small and a d’ of 2 or more might be considered large, but it depends on various factors.
   
   This calculation is always done treating each response as independent, as if the test is unreplicated. For example, d' on a back-to-back test with 50 assessors who provide 2 responses, calculation is done as if there are 100 assessors who provide 1 response each.
   
   
2. SE: Standard error of the estimate of the proportion of (momentary) discriminators.
   
   
3. LCL: Lower confidence limit at the Alpha specified before generating the report.
   
   
4. UCL: Upper confidence limit at the Alpha specified before generating the report.
   
   
5. Triad test number: The example screenshot above, annotated with numbered callouts, indicates that a back-to-back Duo–Trio test was executed, resulting in the inclusion of both Triad 1 and Triad 2 rows.
   
   
6. Pooled: In the analysis where two samples (see the Samples table in our example above) were evaluated back to back, the N is increased by multiplying the actual N by the number of tests. Each test is treated as done by different panelists even though they were seen back to back by the same panelists. Pooled analysis is not available in single tests and in any other variation of back to back tests (e.g. more than two tests on two samples, or more than two sample tests).
   
   
7. Both Triads: In a back to back Duo–Trio analysis (true replicate of two samples), you can see how many panelists answered both Duo–Trio tests correctly. The probability of panelists correctly identifying the sample that is the same as the control for both tests by chance decreases. Both Triads analysis is not available in single tests and in any other variation of back to back tests (e.g. more than two tests on two samples, or more than two sample tests).

1. x-1 = number of correct responses minus 1
   
   
2. n = total number of evaluations included in the analysis