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Hi Jeremy,
- I am afraid that that one is too far outside the areas that I have
studied, but I will see if anyone on the Phys-L network might have any
remark(s).
Best, Uncle Bill

On Fri, Nov 10, 2017 at 7:42 AM, jeremy fair wrote:

Hi Uncle Bill,
When it comes to scientific “stuff” you are the family expert so perhaps
you can point me in the right direction. I need to build an equation by
which correct answers and incorrect answers are tabulated from a sample set
and a value given to the likelihood that a difference can be determined
between two different items.

Here is an explanation of the tetrad test. I am trying to create an excel
spread sheet where data can be entered and a value generated indicating
whether the *duplication* is equal to the *control* based on the data

Difference Methods Maurice G. O'Sullivan, in A Handbook for Sensory and
Consumer-Driven New Product Development, 2017
The tetrad method is a difference test involving four samples where the
assessor is presented with blind coded samples with two samples of one
product and two samples of another product. The assessors must then group
the products into two groups according to their similarity. Note that these
instructions are different from asking the subjects to identify the two
most similar samples (Ennis and Rousseau, 2012). The probability of
guessing the right answer is similar to the triangle test (33%). The tetrad
test has also received lots of interest due to its potential to provide
increased power without specification of an attribute. This greater power
means that for the same sample size, an existing difference is less likely
to be missed (Ennis and Jesionka, 2011; Ennis and Rousseau, 2012). The
tetrad method can thus reduce the likelihood of 'alpha' and 'beta' risk
sensory testing errors. Alpha risk is the risk of making a wrong decision.
If p is the decision point, then if p < alpha, then the 'null hypothesis'
is rejected. This is 'rejecting the null hypothesis', also called type I
error and occurs when differences are found between samples when really
there are not any. The opposite can also occur, by not rejecting the null
hypothesis and is called beta risk, or type II error. Here, no differences
are found between samples where differences really exist. Alpha and beta
risks can be reduced by increasing the number of observations or the amount
of data needed to make a decision. See Table 1.1 for sample sizes required
for significant differences.
A considerable advantage of the tetrad test is that far fewer assessors
are required compared to the triangle and duo-trio methods. According
to Ennis and Jesionka (2011), p. 87, assessors would be required to achieve
a significant (P < .05, 90% power, d′ = 1.5) difference between samples for
a duo-trio test, 78 for a triangle but only 25 for a tetrad panel.
Greater power means that smaller sample sizes can be used to achieve the
same performance as the triangle test as the sample sizes required by
the tetrad test are theoretically only one-third that required by the
triangle test (Ennis and Jesionka, 2011; Ennis and Rousseau, 2012). This
could be of great commercial benefit in the saving of time, money and
resources. However, the sensory scientist must determine through comparison
which of the triangle or the tetrad method best suits their products and
processes.

While I am only attempting a single tetrad Test, here is data collected
from a double tetrad meaning each participant took the test twice.
It is a “double tetrad Test” Fail:
0 out of 2 correct: 6
1 out of 2 correct: 24
2 out of 2 correct: 5
It’s a fail:

*Test Results*
Observed *Alpha*
*0.6%*
Observed *Beta*
*49.4%*

Beta needs to be at most 20%