Latin square designs

In this plan, the effects of both automobile and wheel position are controlled by blocking. It should, however, be kept in mind that for the Latin square design, as for other blocking plans, it is generally assumed that the blocking variables do not interact with the primary variable to be evaluated. 

Statistical experimental design is characterized by the three basic principles Replication, Randomization and Blocking (block division, planned grouping). Latin square design is especially useful to separate nonrandom variations from random effects which interfere with the former. An example may be the identification of (slightly) different samples, e.g. sorts of wine, by various testers and at several days. To separate the day-to-day and/or tester-to-tester (laboratory-to-laboratory) variations from that of the wine sorts, an m x m Latin square design may be used. In case of m = 3 all three wine samples (a, b, c) are tested be three testers at three days, e.g. in the way represented in Table 5.8 ... 

Meals were consumed by the subjects following a Latin Square Design. Statistical analysis was performed by a General Linear Models Procedure (20) using split-plot in time analysis with the following non-orthogonal contrasts ... 

In this chapter we explore factorial-based experimental designs in more detail. We will show how these designs can be used in their full factorial form how factorial designs can be taken apart into blocks to minimize the effect of (or, if desired, to estimate the effect of) an additional factor and how only a portion of the full factorial design (a fractional replicate) can be used to screen many potentially useful factors in a very small number of experiments. Finally, we will illustrate the use of a Latin square design, a special type of fractionalized design. 

In some applications, Latin square designs can be thought of as fractional three-level factorial designs that allow the estimation of one main factor effect while... 

Latin square design as a fractional factorial design. 

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

If there are three types of blocking factors, Graeco-Latin square designs can be used to minimize their effects. The following is a 4 x 4 Graeco-Latin square. What do a, p, y, and o represent ... 

Figure 5.5 Illustration of a 3/3 Latin Square design trial of two different drugs and...

All potency assays, from the simplest designs to the most complex Latin square design, necessitate potency estimation by computer. Low-precision assays employing plotting of zone sizes (response) against concentration of standards must be dealt with using computerized regression analysis, with the potency (standard equivalent) estimation calculated from the computed equation of the line. In this way, all opportunity for operator subjectivity is minimized. 

Latin square design — three factors at four levels. This is a 1/4 replicate of a 43 = 64 factorial... 

Fractional replicates of experimental designs in which all factors are at the same number of levels can be partially replicated in fractions whose denominators are multiples of the number of levels. These designs are the so-called Latin square designs. 

Latin square design three factors at three levels. Run the indicated experiment at the levels of A, B, and C shown in the box This is a l/3 replicate of a 38= 27 factorial design. 

Latin square designs, 1,52 simplex designs, 56,57,58 Experimental designs for specific problems, 61,62,63... 

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

Experimental designs are square in forms (mxm), and the researched factor is tested once in each step. Table 2.58 shows an example of 4x4 Latin square design. 

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