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[Phys-L] Tetrad excel equation

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
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
> collected from the tetrad Test.
> Difference Methods Maurice G. O'Sullivan, in A Handbook for Sensory and
> Consumer-Driven New Product Development, 2017
> *The Tetrad Test: *
> 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:
> 35 person double tetrad
> 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%
> Here are two links with further depiction of the tetrad test.
> Meeting/Presentations/Ennis_Christensen_2012.pdf
> biological-sciences/tetrad-test