In Section 6.5 .2 Computation Lab: Normal Plots in Unreplicated Factorial Designs, the factorial effects were sorted based on their magnitudes before plotting the normal quantile plot shown in Figure 6.7 .

a. Create the normal quantile plot without sorting the factorial effects. What is wrong with the plot?

b. Instead of using geom_qq() and geom_qq_line(), construct a normal quantile plot using geom_point () and add an appropriate straight line to the plot that connects the first and third quantiles of the theoretical and sample distributions.

c. Suppose the absolute values of factorial effects are used in a normal quantile plot. Will the result be an interpretable plot to assess the significance of factorial effects in an unreplicated design? Explain.

Data from Section 6.5 .2

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Data from Figure 6.7

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Consider the data from the 23 design in Example 6.1. The factorial effects were estimated in Example 6.1 via a linear regression model in Section 6.4.1 and stored in fooddiary_mod. A vector of ordered factorial effects can be obtained using dplyr::arrange(). The normal quantile plot of factorial effects in Figure 6.7 was created us- ing ggplot. To create the plot using the factor labels, we pass geom = "text" and label = rownames (effs) to ggplot2: : geom_qq(). This tells ggplot2: geom_qq() to draw text using the rownames() of effs instead of the default geom = point. Finally, distribution = stats: : qnorm specifies the distribution function to use.