Problem 1.

The analysis of variance table (Table 1) and graph (Figure 2) below report some of the results of an Environmental Monitoring Program established to examine the effect of creating an artificial reef offshore from a beach (the reef was created by sinking old boats). Part of the study involved monitoring the diversity of the fish (i.e. number of species) in a bed of seagrass near the reef (Reef) and in two beds at some distance from it (Control site 1 and 2).

In this part of the study, numbers of species were recorded from three replicate quadrats in each of the beds at the six times shown in Figure 2. Note that new, randomly selected, quadrats were sampled at each of the six times. Three of the sampling times – 1, 2 and 3 –were before the reef was created and three – 4, 5 and 6 – were after.

Figure 1 illustrates the layout of this study.

Describe what the analysis (Table 1) indicates about the effects of the reef. Be sure to refer to the table (mention all the source rows except “Within”) and the graph (Figure 2) in your answer.

Figure 1: Design of study. The diagram below illustrates the physical arrangement of the system and the samples. Note that new, randomly selected, quadrats were sampled each sampling time. The white, black and grey objects represent the sunken ships (old boats).

Figure 2: Numbers of species over time. Each point is the mean number of species counted in the three replicate quadrats sampled in each bed at each time. On this graph, Time 4 is Time 1 after the impact, Time 5 is Time 2 after the impact, and Time 6 is Time 3 after the impact.

Table 1: Analysis of variance table. The df, MS and F-ratio for testing the significance of each factor are given, along with the p-value. Significant factors and interactions—where the p-level < 0.05—are labelled with an asterisk (*). † Note that the source (factor) “Time” is nested in the “Impact status” factor and refers to the first, second or third sampling time before or after the impact. There are only three times listed because there were only three times sampled in each period (before and after).

Further explanation of Table 1. The “Site” source of variation compares the three locations/sites sampled. The “Impact status” source of variation compares before to after the start of the impact (creation of reef). Finally, the “Time” source of variation compares times 1, 2 and 3 (before and after). The terms with “×” are interactions between the factors (or “main effects”): see the study materials for information on how to interpret these.