# A not A Analysis

## Purpose

Analyse results from the A-not-A test.

## Data Format

1. Discrimination_AnotA.xls
2. Data type is binary.

## Background

The A-not-A discrimination test is a variation of the paired comparison test.  It is an unspecified test with a probability of guessing of 0.5.

The panellist is presented with the first product (A), which is then removed after evaluation.

A second product is then presented, and the panellist decides whether it is the same as A or not.  As part of the test design multiple products may be compared with A in a monadic protocol. The order of the samples is randomized.

## Options

1. Treat Sessions/Replicates separately: If the data has been gathered over different sessions, or there are different replicates, these can be analysed separately.
2. Reference Product: Select which product should be your reference product. This is the first product in the test(A).
3. Correction:  If yes, apply the continuity correction for 2x2 contingency tables.
4. Number of Decimals for Values: Required number of decimals for values given in the results.
5. Number of Decimals for P-Values: Required number of decimals for any p-values given in the results.

## Results and Interpretation

1. Contingency table: This is a n x 2 contingency table of the responses, where n is the number of products.
The first row totals the responses when the reference product (A) was tested.
Subsequent rows total the responses when the other products were tested.

2. A chi-squared test is then performed on the contingency table. The following values are returned:
1. Chi-squared value
2. The Critical Chi-Squared value at a 5% significance
3. Degrees of freedom
4. P-value at 5% significance
If the p-value is < 0.05 for the chi-squared test, it can be concluded that the reference product (A) is significantly different to the other products. Note that even if you conclude a difference, this does not imply similarity.
1. D-prime.  D-prime indicates the size of the difference between the products. The following values are returned:
1. d-prime
2. Lower and upper 95% confidence intervals for d-prime
3. P-value for Fisher’s Exact Test performed on the contingency table.
Note that if one of the cells in the contingency table is zero, the d-prime cannot be calculated.

## Technical Information

1. The R package sensR (Rune Christensen and Per B. Brockhoff) is used.
2. The AnotA function is used to calculate d-prime.
1. ISO 8588:1987 – Sensory Analysis – Methodology – ‘A’ – ‘not A’ Test
2. ​Lawless, H.T. and Heymann, H. (2010).  Sensory Evaluation of Food – Principles and Practices.  Springer.