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*From*: Bill Norwood <bnorwood111@gmail.com>*Date*: Fri, 10 Nov 2017 15:58:25 -0500

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

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.

http://www.sensometric.org/Resources/Documents/2012/

Meeting/Presentations/Ennis_Christensen_2012.pdf

http://www.sciencedirect.com/topics/agricultural-and-

biological-sciences/tetrad-test

**Follow-Ups**:**Re: [Phys-L] Tetrad excel equation***From:*John Denker <jsd@av8n.com>

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