Description

The data come from a graduate student, Lisa Ruemper, in the Department of Biology at the University of Waterloo. She is working in conjunction with researchers at the Canadian Centre of Inland Waters in Burlington, Ontario.

The researchers were interested in the effect of the effluents released over past years by a pulp mill on the Kapuskasing River in Ontario. In particular, they were interested in seeing if the effluent has affected the growth pattern of a particular species of fish, white sucker.

Using electro-fishing, they sampled fish from three different sites in September over three years, 94, 95 and 96. (Note that the sampling was destructive, so that different fish were obtained each year.) One site, up2, was 30 km upstream of the pulp mill and so remained unaffected by the effluent. The other two sites, downtb and downff, were downstream of the pulp mill, either directly below (downtb) or 15 km below (downff).

Many measurements were taken but those of interest are related to the growth of the fish. For each year of growth, a ring is laid down on the bony gill cover (opercula) similar to that on a slice from a tree trunk except that the opercula is fan shaped rather than circular. On each fish, the increment length (mm.) (i.e. the distance from the center of the opercula to the first ring or the perpendicular distance between successive rings) is measured; there will be one for each year of growth, so that a fish aged nine, say, will have nine such increments. While the researchers were able to determine exactly how many rings there were on each opercula, some of the increment lengths are missing, particularly for age 1 and 2, because the associated rings were not clearly visible. The total distance from the center to the edge of the gill cover is thought to be related to the fork length (cm.) (the length from the fish's 'nose' to the fork in its tail), a commonly used measure for size and age of the fish.

The primary objective of your analysis should be the testing of whether there is a difference in growth pattern among the three sites, allowing for possible environmental effects from year to year. Lisa was also interested in estimating the magnitude of these growth differences among the sites. You might assume that the fish in the three sites come from the same population of white suckers and that each sample taken is a random sample from that population.