GG413 Geological Data Analysis
Homework #9: Analysis of Variance (ANOVA)
Reading: Sections 4.4, 4.5 Due Tue Nov. 3.
Please include your Matlab scripts
In each of the following problems please be sure define the null and alternative hypothesis, write out an
ANOVA table, and perform an F test for the stated levels of significance.
1-way ANOVA
1) The data file “Hw9_hf.txt” on the webpage contains old (and hence less accurate) heat flow data taken
on old seafloor in the same format at the data in homework 7 (1st column is distance from a mid-ocean
ridge in km, 2nd column is heat flow in mW/m2).
(a) Using the same model for the decay of heatflow q with distance x as we did before,
q(x) = a0 + a1x + a2/x,
solve for the least-square solutions for the coefficients q0, q1, and q2.
(b) Plot the 95% confident interval for the true regression curve.
(c) Using ANOVA, fill in the appropriate ANOVA table, and test whether there is truly a trend that
follows the regression at 1% significance level.
(d) What fraction of the total variance can be attributed to the regression?
2) You have measured the chromium content 6 times in four shale units. The data are summarized in the
table below (values in ppm below and in “Hw9_Prob1_Chromium.txt”). At the 0.05 level of
significance, can the differences among the four sample means be attributed solely to measurement
errors + small-scale variability, or is there a real difference between the units sampled?
Unit A Unit B Unit C Unit D
181.3 160.6 163.2 132.3
176.8 179.9 154.1 140.8
182.7 170.9 158.6 124.5
186.0 151.3 137.8 123.2
188.4 163.4 158.7 121.1
160.2 185.8 191.8 163.2
(Matlab tip: If X is an (n x k) matrix, “mean(X)” is a row vector containing the k means of each
column, and hence will be a row vector of sample means).
2-way ANOVA
3) An engineering geology class had a lab in which a single core of sandstone was divided into four
sections (A, B, C, D) and the five students measured the porosity of each section. The results are shown
below (in %), and given in “Hw9_StudentPorosityMeasurements.txt”:
A
B
C
D
Student 1
22 18 19 13
Student 2
26 24 22 11
Student 3
19 13 22 10
Student 4
26 21 19 22
Student 5
19 27 28 22
(a) Students 1 and 3 are buddies and scrutinized each other’s work carefully. The mean of their 4
porosity measurements are lower than those of the other students, so the two buddies claimed their
measurements were distinguishably more accurate than those of the other students. Are they correct
at the 5% significance level?
(b) They also claimed that the porosity of section D is lower than the other sections. Are they correct at
the 5% significance level?
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