using normal probability paper [78] or quantile-quantile (Q-Q) plots. Since the Q-Q plots can easily be generated by many software packages, the procedure to use them in assessing the importance of effects will be outlined. Assume that the data (effects of all factors and interactions in this case) are represented as a set of values j/j, i = 1,2,..., n.

1. Order the data according to magnitude: y^ < y(2) < • • ■ < 2/(n)-

2. For each ordered data, set Qy(fi) = y(¿), i = 1,2, ...,n where Q denotes a quantile.

3. Calculate the quantiles for a standard Normal distribution (Qsn) using the empirical relation

QsN{fi) = 4.91 f/0'14 — (1 — /)°'14| Where fi = (3-13)

4. Plot Qy(fi) versus QsN(fi)- Approximate linearity indicates that data are consistent with standard Normal distribution. Significant deviation of specific effects from linearity indicates that they are important effects.

Example. Develop the Q-Q plot for the main effects and interactions computed for the penicillin fermentation data in Tables 3.1 and 3.2.

The second and fourth columns of Table 3.7 provide the quantiles of the main effects and interactions. The last column of the table displays the corresponding quantiles of the standard Normal distribution computed using Eq. 3.13. The two sets of quantiles are plotted in Figure 3.3. The

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