Exercise 13 in Chapter 11 looked at a gillnet experiment designed to determine the effect of net characteristics on the size of fish caught. The data are on the text Web site as datatab_11_fish. Using the methods of this chapter, we can see how the relative frequencies of species caught are related to net characteristics.
(a) The combinations of mesh size and net material form four groups. Does the proportion of fish caught that are gizzard shad differ for any of the groups? If so, create a table of the proportions using lettering to designate groups that are significantly different, similar to the tables used to summarize the results of pairwise comparisons in Chapter 6. Use a family-wise significance level of 5% to make the six comparisons.
(b) The overall median length for all fish in the sample was 193 mm. Does the proportion of fish whose length exceeds this value differ for any of the groups? If so, create a table of the proportions similar to that in part (a). How do you interpret the differences?
Exercise 13
It is of importance to the fishing industry to determine the effectiveness of various types of nets. Effectiveness includes not only quantities of fish caught, but also the net selectivity for different sizes and species. In this experiment gillnet characteristics compose a two-factor factorial experiment with factors:
SIZE: two mesh sizes, 1 and 2 in. and
TYPE: material, monofilament or multifilament thread.
Four nets, composed of four panels randomly assigned to a factor level combination, are placed in four locations in a lake. After a specific time, the nets were retrieved and fish harvested. Data were recorded for each fish caught as follows:
Species:
gs: gizzard shad
other: all other species
Size:
length in millimeters.
The data, comprising measurements of the 261 fish caught, are available on the
text Web site as datatab_11_fish. Of that total, 224 (85.8%) were gizzard shad.
(a) Using data for gizzard shad only, perform the appropriate analysis to determine the effects of net characteristics on the length of fish caught.
(b) Perform the same analysis for all other species.