Is the navigational behavior of cockroaches scavenging for food random or linked to a chemical trail? In an attempt to answer this question, an entomologist designed an experiment to test a cockroach’s ability to follow a trail of its fecal material (Explore, Research at the University of Florida, Fall 1998). A methanol extract from roach feces—called a pheromone—was used to create chemical trail on a strip of white chromatography paper at the bottom of a plastic container. German cockroaches were released into the container at the beginning of the trail, one at a time, and a video surveillance camera was used to monitor the roach’s movements. 

In addition to the trail containing the fecal extract (the treatment), a trail using methanol only was created. This second trail served as a “control” to compare back against the treated trail. Since the entomologist also wanted to determine if trail-following ability differed among cockroaches of different age, sex, and reproductive status, four roach groups were utilized in the experiment: adult males, adult females, gravid (pregnant) females, and nymphs (immatures). Twenty roaches of each type were randomly assigned to the treatment trail and 10 of each type were randomly assigned to the control trail. Thus, a total of 120 roaches were used in the experiment. The design is a factorial with two factors—Trail (extract or control) and Group (adult males, adult females, gravid females, or nymphs). The response (dependent) variable of interest was the average trail deviation (measured in “pixels,” where 1 pixel equals approximately 2 centimeters). The data for each of the 120 cockroaches in the study are stored in the ROACH file. 

The entomologist wants to determine whether cockroaches in different age–sex groups differ in their ability to follow either the extract trail or the control trail. In other words, how do the two factors, age–sex group and trail type, impact the mean trail deviation of cockroaches? Answer this question by conducting a two-way factorial analysis of variance on the data. Fully interpret the results.