The primary reason to use triads is to limit the cognitiveburden on respondents by giving them a very simple set of tasks which can be analyzed to reveal their perceptions of the degree of similarity between all pairs of items.

 

A triads questionnaire consists of a series of triples (triads) of items. For each triad, the respondent is asked to indicate which pair of items is most similar, or alternatively, which one item is the most different. For example, consider the following two triads:

 

       1.       DOG           SEAL         MOSQUITO

 

       2.       BEAR          SHARK        DOLPHIN

 

For the first triad, most north-americans would choose mosquito as the most different, which is equivalent to choosing {dog,seal} as the most similar pair. In the second triad, there will be some people choosing "bear" because sharks and dolphins are similar in shape and habitat, and some people choosing "shark" because dolphins and bears are mammals. Very few north-americans are likely to choose "dolphin" because the pair {bear,shark} do not seem as similar as either {bear,dolphin} or {shark,dolphin}.

 

Ideally, all possible combinations of items are presented to the respondent for judgement.  For example, "dog" and "seal" would appear against "dolphin", "bear", "shark" and every other animal in the set. Thus, each pair of items would occur n-2 times, where n is the number of items in the domain. However, since the number of triads increases roughly with the cube of the number of items, this usually results in too many triads to reasonably administer. The exact formula is

 

where t is the number of triads. For example, a questionnaire with 10 items has 120 triples. A questionnaire with 20 items has 1140 triads.

 

Consequently, instead of a full factorial design it is common to use a fractional factorial design known as a balanced incomplete block (BIB). (A design is a pattern or template that specifies which triads should appear and in what order.) BIB designs reduce the number of triads by presenting each pair of items only a limited number of times. BIB designs are classified by the number of times each pair occurs. This number is known as "lambda" (λ). For example, a λ=2 design is a BIB that has each pair of items occur exactly twice. The highest lambda possible is N-2, since that is the case where all possible triples occur.

 

An example of a λ=1 BIB design for 9 items is given below:

 

 

 

The numbers refer to items. Accordingly, the first row specifies that the 2nd, 3rd and 8th items in the domain will occur together in a triad. Note that each pair of items occurs together in a triad only once throughout the design. To construct the actual questionnaire, you arbitrarily number each item in the domain, then substitute the corresponding item for each number in the design. For example, if the list of items is

 

1.     Shark

2.     Dolphin

3.     Whale

4.     Frog

5.     Seal

6.     Dog

7.     Eel

8.     Snake

9.     Hippo

 

then the questionnaire created by the design above would be:

 

 

Since the example uses a λ=1 design, each pair of items occurs together only once in the questionnaire, and therefore only 12 triads are needed in total. The lower the value of lambda, the greater the reduction in the number of triads that a respondent must endure. For example, for the case of a domain with 15 items, the full factorial λ=13 design has 455 triads. The λ=3 design has 105 triads. The λ=2 design has 70 triads and the λ=1 design has 35 triads. (Each block has 35 triads: the λ=13 design has 13x35=455 triads.)

 

Unfortunately, this reduction in triads is accompanied by a reduction in accuracy. Consider, for example, the case of λ=1. In this design, each pair of items occurs only once, "against" a single, randomly assigned item. If that item happens to be extremely unusual, most respondents will choose that item as the most different, even though the other two items are not particularly similar. In fact, if a different third item had been assigned (such as one very similar to one of the other two items), then most respondents might have chosen one of the other two items as the most different. Thus, in a λ=1 design the similarity to any two items is completely determined by their similarity to a single third item.