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An automotive engineer is investigating two different types of metering devices for an electronic fuel injection system to determine whether they differ in their fuel mileage performance. The system is installed on 12 different cars, and a test is run with each metering device on each car. The observed fuel mileage performance data, corresponding differences, and their signs are shown in Table 15-2. We will use the sign test to determine whether the median fuel mileage performance is the same for both devices using 0.05. The eightstep-procedure follows: 1. 2. 3. 4. 5. 6. 7. 8. The parameters of interest are the median fuel mileage performance for the two metering devices. H0: H1:

The matrix you provide a ColorMatrixFilter is 4 5. This is multiplied by the input color, resulting in the output color:

1 1 2, 2,

| | | | a f k p b g l q c h m r d i n s e j o t | | | | | | | | | R G B A 1 | | | | | = | | | | output output output output red green blue alpha | | | |

or, equivalently, H0: or, equivalently, H1:

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0.05 We will use Appendix Table VII to conduct the test, so the test statistic is r min(r , r ). Since 0.05 and n 12, Appendix Table VII gives the critical values as r*.05 2. 0 We will reject H0 in favor of H1 if r 2. Computations: Table 15-2 shows the differences and their signs, and we note that r 8, r 4, and so r min(8, 4) 4. Conclusions: Since r 4 is not less than or equal to the critical value r*.05 2, we 0 cannot reject the null hypothesis that the two devices provide the same median fuel mileage performance.

Multiplying the 4 5 lter matrix by the 5 1 input color matrix results in a 4 1 output color matrix. If you do the matrix multiplication by hand, you see that each channel of the output color is a linear combination of the input color channels. In other words, by choosing the contents of the lter matrix you create equations that de ne each output color channel as a combination of the input colors. Now you ll expand the matrix multiplication to see that in action:

Table 15-2 Performance of Flow Metering Devices Metering Device Car 1 2 3 4 5 6 7 8 9 10 11 12 1 17.6 19.4 19.5 17.1 15.3 15.9 16.3 18.4 17.3 19.1 17.8 18.2 2 16.8 20.0 18.2 16.4 16.0 15.4 16.5 18.0 16.4 20.1 16.7 17.9 Difference, dj 0.8 0.6 1.3 0.7 0.7 0.5 0.2 0.4 0.9 1.0 1.1 0.3 Sign

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output output output output red green blue alpha = = = = aR fR kR pR + + + + bG gG lG qG + + + + cB hB mB rB + + + + dA iA nA sA + + + + e j o t

578 15-2.3

The power of this method of transforming colors comes from the fact that you can tweak just how each channel relies on the other ones. The extra 1 that pads the input color matrix allows for the addition of a fth column of the lter matrix that can add a color offset to each channel that is independent of the input color. You can see that the column [e, j, o, t] and the terms e, j, o, and t in the preceding equations are not multiplied by any of the input color channels. When using a ColorMatrixFilter, you specify the 4 5 matrix in the matrix property of the ColorMatrixFilter instance. Instead of using a two-dimensional array, you should provide the matrix contents as a one-dimensional array in row-major order. That is, lay out the matrix terms left to right and top to bottom in an Array of size 20:

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