Statistics 3N03/3J04 - Assignment #2

2006-09-13

Do your graphs and calculations in R. Create a report, pasting the graphs into a word processor and adding comments and discussion. The first question is from Montgomery & Runger, Applied Statistics and Probability for Engineers.

Question 1: 14-8 (p F555, T520)

Do graphical analyses using comparative box plots to compare fatigue crack growth rate between the cyclic loading frequencies and between the environments. Give "interaction plots" like the one in Figure 14-8 (p 516): plot the mean fatigue crack growth rate against cyclic loading frequency, giving a separate trace for each environment, and plot the mean fatigue crack growth rate against environment, giving a separate trace for each cyclic loading frequency. Repeat the graphs with fatigue crack growth rate on a log scale. State your conclusions. (The question asks for a two-factor analysis of variance but you will do that in Assignment #3.)

Hints: Enter the data as three columns in a data frame, putting the fatigue crack growth rate in the first column, a code for cyclic loading frequency in the second, and a code for environment in the third. To plot on a log scale, you can add the option log="y" to the plot or boxplot command to transform the Y-axis, or you can compute a new column of log-transformed crack growth rates.

Question 2: Skidders

Do an exploratory data analysis on the Effects of Skidders on Two Types of Forest Soil. Using only the graphical methods we have learned so far, can you start to answer the questions posed in the Case Study?

Question 3: Niagara River Pollution

Do an exploratory graphical analysis of the data in the Niagara River Pollution Case Study. Specifically,

  1. Use box plots to compare the discharge at Fort Erie with discharge at Niagara on the Lake.
  2. Give a time series plot of discharge at Niagara on the Lake, smoothed with exponential smoothing, plotted against Julian date. Explain why putting discharge on a log scale does not make much difference to the plot.
  3. Smooth the times series of discharge at Fort Erie and plot it against Julian date, adding it to the graph you created in (b). What does this tell you that the box plots in (a) couldn't tell you?
  4. In the Niagara on the Lake data, are there any relationships between discharge, sediment concentration and the concentration of PCB in solids? Use a scatterplot matrix. Do log transformations help?
  5. Does the log of PCB concentration in solids at Niagara on the Lake follow a Normal distribution?
Statistics 3N03/3J04