STAT 600 - Assignment #5 General Factorial Experiments
Problem 1 – Environmental Factors Influencing Shrimp Weight Gain
The California brown shrimp spawn at sea and the hatched eggs undergo larval
transformations while being transported to shore. By the time they transform to postlarval stage they enter estuaries, where they grow rapidly into subadults and migrate back
offshore as they approach sexual maturity.
The shrimp encounter wide temperature and salinity variation in their life cycle as a result
of their migrations during the cycle. Thus, a knowledge of how temperature and salinity
effect their growth and survival is of great importance to understanding their life history
and ecology.
There was at the time of this experiment great interest in commercial culture of the
shrimp. From the standpoint of mariculture (farming shrimp) another important factor
was stocking density in the culture tanks that affects intraspecific competition.
Research Objective: The investigators wanted to know how water temperature, water
salinity, and density of shrimp populations influenced the growth rate of shrimp raised in
aquaria and whether the factors acted independently (main effects only) on the shrimp
populations. If they do not act independently, understanding the potential interactions
between these factors is also very important.
Experimental Design: For the three factors they used the following settings:
Temperature: 25 Co and 35 Co
Density: 80 shrimp/40 liters or 160 shrimp/40 liters
Salinity: 10%, 25%, and 40%
These levels were chosen to reflect those most likely to exhibit an effect if the factor was
influential on shrimp growth.
The experimental design consisted of three replicate aquaria for each of twelve treatment
combinations (2 X 2 X 3 = 12 treatment combinations). The 36 aquaria were stocked
with post-larval shrimp at the beginning of the test. The weight gain of the shrimp in four
weeks for each of the 36 aquaria was measured on a per-shrimp basis.
The data collected are in the file: Shrimp-Growth.JMP
a) Perform a complete analysis to identify the effects are significant. Cite
appropriate p-values and include appropriate plots of the most important effects
and discuss. (10 pts.)
b) Which aquaria condition(s) would you recommend if the goal is to maximize the
weight gain of shrimp in a mariculture operation? Explain. (3 pts.)
c) Look at a plot of the residuals vs. the fitted values. Comment on model violations
suggested by this plot. (3 pts.)
d) Construct a normal quantile plot of the residuals. Comment the normality
assumption. (3 pts.)
e) Finally, plot the residuals vs. the individual factors. Comment on the any
violations suggested by these plots. Do any of these plots make you potentially
reconsider your recommendation from part (b)? Explain. (4 pts.)
Problem 2 – Gauge R & R Study
An article by Hoof and Berman (“Statistical Analysis of Power Module Thermal Test
Equipment Performance”, IEEE Transactions on Components, Hybrids and
Manufacturing Technology Vol. 11, pg. 516-520, 1988) describes an experiment
conducted to investigate the capability of measurements in thermal impedance (Co/w ×
100) on a power module for an induction motor starter. There are 10 parts, three
operators, and three replicates. The data are contained in the file Gauge RRImpedance.JMP.
a) Analyze the data from this experiment, assuming that both parts and operators are
random effects. What effects are statistically significant? (4 pts.)
b) Examine residuals for checking model assumptions. Comment. (4 pts.)
c) Estimate the variance components using E(MS) method. Discuss the important
sources of variation identified from this analysis. Does this seem to contradict the
results from part (a)? Explain. (4 pts.)