An Example of Correlation Analysis
Biostatistics BI 45, Saint Anselm College
1) Biological question
Is there a relationship between wing length and tail length and what is the strength of this relationship?
2) Statistical hypotheses
3) Assign alpha level
Step 4) State the statistical test and the number of tails.
Because we are trying to determine whether there is a relationship between tail length and wing length and we are only trying to measure the strength of this association, we will use a correlation analysis. This is a two-tailed test.
5) Observed test statistics and critical values
5a) Correlation Coefficient (Wing L - X variable, Tail L - Y variable for calculating r)
5b) Test statistic - correlation coefficient
Find the actual P value
r.05(2)10=.576<
r.001(2)10=
P<0.001
5c) Test statistic - F test
Find the actual P value
F.05(2)10,10=3.72<=F.001(2)10,10=10.3<Fobs=13.93
P<0.001
5d) Test statistic - t test
Find the actual P value
t.05(2)10=2.228<t.001(2)10=
P<0.001
6) Reject the null hypothesis for each test.
7) Interpret
There is a positive relationship between wing length and tail length (r = .866, two-tailed, df = 10, p<0.001) or tail length (r=0.866, F=13.93, two-tailed, df = 10, 10, p<0.001) or tail length (r=0.866, t = 5.48, two-tailed, df = 10, p<0.001).
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Trademark and Disclaimers
Copyright © 2001 Jay Pitocchelli. All rights reserved. The contents of this page are the intellectual property of Dr. Jay Pitocchelli for distribution to students enrolled in Biostatistics BI 45 at Saint Anselm College. These pages may not be copied, photocopied, reproduced, translated, or published in any electronic or machine-readable form in whole or in part without prior written approval of Jay Pitocchelli. Students enrolled in Biostatistics BI 45 at Saint Anselm College have permission to print this material for their lecture notes. All formulae and critical values from: Zar, J. H. 1999. Biostatistical Analysis. (4th ed.). New Jersey, Prentice Hall.