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A fictitious plant ecologist sampled 90 shrubs of a dioecious plant in a forest, and each plant was classified as being either male or female. The ecologist was interested in the sex ratio and whether it differed from 50:50. The observed counts and the predicted (expected) counts based on a theoretical 50:50 sex ratio follow.
Note, it is not necessary to open or create a data file for this question.
Lets now extend this fictitious endeavor. Recent studies on a related species of shrub have suggested a 30:70 female:male sex ratio. Knowing that our plant ecologist had similar research interests, the authors contacted her to inquire whether her data contradicted their findings.
Here is a modified example from Quinn and Keough (2002). Following fire, French and Westoby (1996) cross-classified plant species by two variables: whether they regenerated by seed only or vegetatively and whether they were dispersed by ant or vertebrate vector. The two variables could not be distinguished as response or predictor since regeneration mechanisms could just as conceivably affect dispersal mode as vice versa.
Open the french data file. HINT.
Arrington et al. (2002) examined the frequency with which African, Neotropical and North American fishes have empty stomachs and found that the mean percentage of empty stomachs was around 16.2%. As part of the investigation they were interested in whether the frequency of empty stomachs was related to dietary items. The data were separated into four major trophic classifications (detritivores, omnivores, invertivores, and piscivores) and whether the fish species had greater or less than 16.2% of individuals with empty stomachs. The number of fish species in each category combination was calculated and a subset of that (just the diurnal fish) is provided.
Open the arrington data file (HINT).
Note the format of the data file. Rather than including a compilation of the observed counts, this data file lists the categories for each individual. This example will demonstrate how to analyse two-way contingency tables from such data files. Each row of the data set represents a separate species of fish that is then cross categorised according to whether the proportion of individuals of that species with empty stomachs was higher or lower than the overal average (16.2%) and to what trophic group they belonged.
Here is an example (13.5) from Fowler, Cohen and Parvis (1998). A field biologist collected leaf litter from a 1 m2 quadrats randomly located on the ground at night in two locations - one was on clay soil the other on chalk soil. The number of woodlice of two different species (Oniscus and Armadilidium) were collected and it is assumed that all woodlice undertake their nocturnal activities independently. The number of woodlice are in the following contingency table.
Open the woodlice data file. HINT.
Polis et al. (1998) were intested in modelling the presence/absence of lizards (Uta sp.) against the perimeter to area ratio of 19 islands in the Gulf of California.
Open the polis data file (HINT).
Roberts (1993) was intested in examining the interaction between the presence of dead coolibah trees and the position of quadrats along a transect.
Open the roberts data file (HINT).
Open the sinclair data file (HINT).
A marine ecologist was interested in investigating whether hermit crabs on North Stradbroke Island (what a wet ecologist does on holidays I guess!). He intended to score shells according to whether or not they were occupied and whether they what type of gastropod they were from (Austrocochlea or Bembicium). Shells with living gastropods were to be ignored. Essentially, the NERD wanted to know whether or not hermit crabs occupy shells in the proportions that they are available. A quick count of shells on the rocky shore revealed that approximately 40% of available gastropod shells were occupied and that Austrocochlea or Bembicium shells were approximately equally available. The ecologist scratched his sparsely haired scalp, raised one eyebrow and contemplated performing a quick power analysis to determine how many observation would be required to have an 80% chance of detecting a 20% preference for Austrocochlea shells.
This task is best broken down into parts.