Kastner et al. studied how the brain recognizes the shape and color of an object. They found that the process of identifying the shape and color of an item is carried out not simultaneously but in steps. Two students decided to investigate the impact of color distraction on a shape matching game called Shapesplosion. In this game, subjects are asked to match shapes by placing specifically shaped pegs into the matching hole as quickly as possible. These student researchers selected eight female science majors and eight female non- science majors at their college. Each of the 16 subjects played four games (each of the following four games in random order): Factor 1 (game complexity): the Shapesplosion game with 15 pieces (pegs) or the game with 18 pieces Factor 2 (color distracter): the Shapesplosion game where the peg color matches the hole color or the game where the pegs are a different color than the hole The Time it took (in seconds) to complete each game was recorded.
a. List each factor in the study and specify whether it is fixed or random and whether it is crossed or nested with all other factors.
b. Calculate an appropriate ANOVA for this study using Time as the response. Check the model assumptions. Create a plot to check if the data appear to be skewed or have outliers. Is there reason to doubt the equal variance assumption? Are the error terms approximately normally distributed?
c. Calculate an appropriate ANOVA for this study using log (Time) as the response. Does log(Time) better fit the model assumptions? Would you suggest using Time or log(Time) when presenting the results?
d. State your conclusions for the six hypotheses that can be tested with this study. Provide appropriate plots and take into account random sampling and random allocation when stating your conclusions.
e. Draw a Hasse diagram corresponding to this study.