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The F-ratios for all three main effects and the interactions are formed by dividing the mean square for the effect of interest by the error mean square. Since the experimenter has selected 0.05, the critical value for each of these F-ratios is f0.05,1,8 5.32. Alternately, we could use the P-value approach. The P-values for all the test statistics are shown in the last column of Table 14-11. Inspection of these P-values is revealing. There is a strong main effect of feed rate, since the F-ratio is well into the critical region. However, there is some indication of an effect due to the depth of cut, since P = 0.0710 is not much greater than 0.05. The next largest effect is the AB or feed rate depth of cut interaction. Most likely, both feed rate and depth of cut are important process variables. Obviously, factorial experiments with three or more factors can require many runs, particularly if some of the factors have several (more than two) levels. This point of view leads us to the class of factorial designs considered in Section 14-7 with all factors at two levels. These designs are easy to set up and analyze, and they may be used as the basis of many other useful experimental designs.

Example 35-11 illustrates the join styles and miter limits. The effect is shown in Figure 35-8.

Table 14-11 Minitab ANOVA for Example 14-2 ANOVA (Balanced Designs) Factor Feed Depth Angle Type xed xed xed Levels 2 2 2 Values 20 0.025 15 30 0.040 25

EXAMPLE 35-11

Analysis of Variance for Roughness Source Feed Depth Angle Feed*Depth Feed*Angle Depth*Angle Feed*Depth*Angle Error Total DF 1 1 1 1 1 1 1 8 15 SS 45.563 10.563 3.063 7.563 0.062 1.563 5.062 19.500 92.938 MS 45.563 10.563 3.063 7.563 0.062 1.563 5.062 2.437 F 18.69 4.33 1.26 3.10 0.03 0.64 2.08 P 0.003 0.071 0.295 0.116 0.877 0.446 0.188

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package { import flash.display.*; public class ch35ex11 extends Sprite { public function ch35ex11() { graphics.lineStyle(20, 0, 0.3, false, null, drawStrokes(40); graphics.lineStyle(20, 0, 0.3, false, null, drawStrokes(120); graphics.lineStyle(20, 0, 0.3, false, null, drawStrokes(200); graphics.lineStyle(20, 0, 0.3, false, null, drawStrokes(280); } protected function drawStrokes(y:Number):void graphics.moveTo(0, 0+y); graphics.lineTo(100, 0+y); graphics.lineTo(-20, 50+y); graphics.lineStyle(0); graphics.moveTo(0, 0+y); graphics.lineTo(100, 0+y); graphics.lineTo(-20, 50+y); } } }

EXERCISES FOR SECTION 14-5

14-11. The percentage of hardwood concentration in raw pulp, the freeness, and the cooking time of the pulp are being investigated for their effects on the strength of paper. The data from a three-factor factorial experiment are shown in the following table. (a) Analyze the data using the analysis of variance assuming that all factors are xed. Use 0.05. (b) Find P-values for the F-ratios in part (a). (c) The residuals are found by eijkl yijkl yijk.. Graphically analyze the residuals from this experiment. Cooking Time 2.0 hours Freeness 650 99.4 99.8 98.4 97.6 97.4 98.1 350 98.4 98.6 97.5 98.1 97.6 98.4 500 99.6 100.4 98.7 96.0 97.0 97.8 650 100.6 100.9 99.6 99.0 98.5 99.8

null, JointStyle.ROUND); null, JointStyle.BEVEL); null, JointStyle.MITER); null, JointStyle.MITER, 20);

Cooking Time 1.5 hours Freeness 350 96.6 96.0 98.5 97.2 97.5 96.6 500 97.7 96.0 96.0 96.9 95.6 96.2

FIGURE 35-8

14-12. The quality control department of a fabric nishing plant is studying the effects of several factors on dyeing for a blended cotton/synthetic cloth used to manufacture shirts. Three operators, three cycle times, and two temperatures were selected, and three small specimens of cloth were dyed under each set of conditions. The nished cloth was compared to a

Here I used a tiny shortcut. The string constant parameters to this method may be sent null, and they take their default values.

standard, and a numerical score was assigned. The results are shown in the following table. (a) State and test the appropriate hypotheses using the analysis of variance with 0.05. (b) The residuals may be obtained from eijkl yijkl yijk. . Graphically analyze the residuals from this experiment. Temperature

The drawing API lets you use gradients for both lls and strokes. The drawing API creates linear and radial gradients for you. When you use a gradient line style, it merely de nes how the gradient lls up the stroke. A call to lineStyle() is still required to set the basic parameters of the stroke. Once the basic line style is set, the drawing API knows how to draw the shape of the stroke; the gradient, bitmap, and shader line styles merely ll in the shape of the stroke that lineStyle() de nes. The methods to apply gradients to strokes and lls are very much the same, so I ll show them as a set.

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function beginGradientFill(type:String, colors:Array, alphas:Array, ratios:Array, matrix:Matrix = null, spreadMethod:String = "pad", interpolationMethod:String = "rgb", focalPointRatio:Number = 0):void function lineGradientStyle(type:String, colors:Array, alphas:Array, ratios:Array, matrix:Matrix = null,

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