Statistics for Environmental Engineers

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n = 2(‘-8П’-645— I-282+ 1 „ 15


(3.0 — 1.0)2

Confidence Interval for an Interaction


Here we insert an example that does not involve a t-test. The statistic to be estimated measures a change that occurs between two locations and over a span of time. A control area and a potentially affected area are to be monitored before and after a construction project. This is shown by Figure 23.2. The dots in the squares indicate multiple specimens collected at each monitoring site. The figure shows four replicates, but this is only for illustration; there could be more or less than four per area.


The averages of pre-construction and post-construction control areas are yB1 and yB2. The averages of pre-construction and post-construction affected areas are yA1 and yA2. In an ideal world, if the construction caused a change, we would find yB1 = yB2 = yA1 and yA2 would be different. In the real world, yB1 and yB2 may be different because of their location, and yB1 and yA1 might be different because they are monitored at different times. The effect that should be evaluated is the interaction effect (I) over time and space, and that is:


I = (Уа2 — yA1) — (yB2 — yB1 )





FIGURE 23.2 The arrangement of before and after monitoring at control (upstream) and possibly affected (downstream) sites. The dots in the monitoring areas (boxes) indicate that multiple specimens will be collected for analysis.

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