Youdens Squares

Observe the design of an incomplete random block with four blocks and four levels of researched factor. 

This kind of design of experiment is known as Youdens square and is in essence an incomplete design of a Latin square as the fourth column with D factor levels in the first block, B in the second, C in the third and A in the fourth are missing. Design of experiment from Table 2.74 may be written differently, as shown in Table 2.75. 

The design of experiment written in this form is a reconstructed Latin square design where one of the diagonals has been left out. Generally speaking, Youdens square is a symmetrically balanced incomplete random block where each factor level appears once and only once in each block position. 

Youdens square is always a Latin square where one or more columns (or rows or diagonals) have been left out however, the opposite is not true a Latin square where one or more columns (or rows or diagonals) have been left out is not always a Youdens square, for by leaving out columns from a Latin square the balance in design is lost. It is, however, possible to construct designs of Youdens squares from all symmetrical balanced random blocks [26]. Youdens squares have the same number of rows and levels of a researched factor but quite a different number of columns. 

Following Youdens squares may be used for practical needs  

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How is the following Youden square design related to the Latin square design of Problem 15.15 ... 

Another useful experimental design for minimizing the effects of two types of inhomogeneity is the Youden square design. Latin squares must have the same number of levels for both of the blocking factors and the treatment factor Youden squares must have the same number of levels for the treatment factor and one of the blocking factors, but the number of levels for the other blocking factor can be... 

What is the relationship - Youden square designs Latin square designs balanced incomplete block designs randomized complete block designs ... 

Youdens square I=J=7 K=b=4 is transformed into a balanced incomplete random block for easier calculation ... 

Analysis of variance for Youdens squares is shown in Table 2.84. 

In researching resistance on rubber abrasion, a Martindale tester is used for com-parasions of various rubber samples. Five types of rubbers have been tested in five cycles on four tester positions. Design of experiment for five rubber types and five test cycles is the Youdens square shown in Table 2.85... 

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