Open the project named Example2.vsp.
Note that the samples are arranged in a systematic grid. They were produced using Sampling Goals / Compare Average to Fixed Threshold and selecting the Systematic grid sampling radio button on the Sample Placement tab. Position the cursor near one of the samples and right-click with the mouse. Note that the type is Systematic Sample rather than a Random Sample as in the previous example.
Note that the grid is aligned with the axis of the map rather than being aligned with the building. To change the alignment of the grid click select Edit / Sample Areas / Select Grid Angle on the menu.
The cursor becomes a crosshair, indicating you are in angle selection mode. Position the crosshairs on the lower left corner of the sample area. Hold down the Shift key and click with the mouse. (Holding the Shift key attaches the angle selector to the corner point on the building. This results in the most accurate method of angle selection.)
A stretching line is now attached to the cursor indicating the angle of the grid. Select the second point of the angle by positioning the cursor over the lower right corner of the building. Hold down the Shift key and click with the mouse. (As before, holding the Shift key attaches the other end of the angle selector to the corner of the building.)
The sample grid is now aligned with the bottom edge of the building rather than with the axis of the map. This simplifies the process of locating samples inside a building.
Simultaneously show all the views for this sample plan by choosing Window / Quad Window from the menu.
Choose Sampling Goals / Compare Average to Fixed Threshold from the menu.
Note that this sampling design calls for a minimum of 57 samples. Also note that the report view probably shows that there are more or fewer than 57 samples in the sample area. This discrepancy exists because a systematic grid cannot always produce the minimum number of samples needed. There were 57 samples when you first opened the project, but realigning the grid angle caused the number of samples to change. The grid defaults to a random-start option, which varies the position of the first sample and evenly spaces the remaining samples from that position.
The systematic grid sampling designs try several times to get the exact minimum number of samples needed. Press the Apply button to resample. You should now see 57 samples. If not, you will see more than 57 samples. The systematic grid sampling designs keep resampling until you have at least the minimum number of samples required by the design.
VSP provides three different types of grids: square, triangular, and rectangular. View the grid options by clicking on the Sample Placement tab of the True Average vs. Fixed Threshold dialog. The triangular grid typically provides the best coverage (the smallest unsampled spot) for a given number of samples. Click on the Triangular grid radio button and press the Apply button. You should now see 57 samples. If not, press the Apply button again.
Once you have a grid that is acceptable, you can keep it by pressing the small Close button on the upper right corner of the dialog window or by pressing the large Close button at the bottom of the dialog.
Click the Maximize button on the upper right corner of the Graph view window. The graph that corresponds to the Parametric / True Mean vs. Action Level sampling design is the typical EPA Decision Performance Goal Diagram (DPGD).
Choose Sampling Goals / Compare Average to Fixed Threshold from the menu. Drag the dialog to the left until you can see the vertical red line on the graph. This red line is the Action Level that is entered by the user. Type 100 in the Action Level text box on the dialog (it currently contains the number 1) and click the Apply button. Notice that the vertical red line is now located at 100 on the x-axis.
The dashed blue line near the top of the graph represents the Confidence level (or 1 - Alpha error rate). This is where the decision function crosses the Action level. In this case, Confidence is 0.95 (and the remaining 0.05 is the Alpha Error). Type 85 in the Confidence text box (it currently contains 95.0[%]) on the dialog and click the Apply button. Notice that the decision function now crosses the action level at 0.85.
Drag the dialog box up until you can see the bottom blue line. This dashed blue line represents the Beta error rate. This is where the decision function crosses the outer bound of the gray region. In this case, Beta is 20% and is offset from 0 (resulting in a value of 0.20). Type 25 in the Beta text box (it currently contains 20.0) on the dialog and click the Apply button. Notice the decision function now crosses the edge of the gray region at 0.25.
The decision function is based on the null hypothesis. In this case, the null hypothesis is that the true mean is greater than or equal to the action level (i.e., the site is dirty). The resulting decision function is the probability of deciding that the mean is greater than or equal to the action level when the true mean is a particular level. Change the drop-down list option under the Specify Null Hypothesis section to acceptable (clean) and press the Apply button. Now, the null hypothesis is that the site is clean and the decision function is the probability of deciding that the true mean is greater than the action level when the true mean is a particular level.
The decision function of the DPGD is not very intuitive. VSP provides an option that makes the meaning of the decision function more clear. Choose Options / Graph / Probability of Correct Decision from the menu. The DPGD decision function is now the probability of making the correct decision when the true mean is a particular level.
Each of the parameters can be modified by manipulating the graph as follows:
(Confidence/Alpha): drag the horizontal blue dashed line up or down
Beta: drag the horizontal blue dashed line up or down
Delta (and lower or upper bound of the gray region; i.e. LBGR, UBGR): drag the vertical edge of the shaded gray area left or right
Standard Deviation: drag the vertical section of the green line left or right
Action Level: drag the vertical red line left or right
Null Hypothesis: click on the y-axis title
As you change these parameters, you can see the new value of the parameter on the status bar. The sampling design is updated based on the parameter you modified, and new samples are placed on the map. For modifying design parameters, you can use the interactive DPGD as an alternative to the sampling design dialog boxes.
Close any existing projects before proceeding (use File / Close Project on the menu or click the Close button on the project windows).