Calculate the Pearson correlation coefficient
Calculate the Pearson correlation coefficient
Simmons and Roberts (2005) examined the idea that males will trade off the ability to fight diseases with the ability to reproduce. To test this in field crickets (Teleogryllus oceanicus), they measured sperm viability (a measure of reproductive success) and lysozyme numbers (a measure of disease-fighting ability). The data are given below; sperm viability is given as percent of sperm that were mobile, and lysozyme numbers are given in units of number per mm2. I have divided the data into two columns just so that it will all fit on one page; you should include all of the data in your analysis!
|
Sperm Viability |
# of Lysozymes |
Sperm Viability |
# of Lysozymes |
|
72.6 |
18.1 |
83.1 |
17.3 |
|
79 |
16.6 |
83.3 |
15.6 |
|
80 |
20.5 |
83.7 |
16.6 |
|
80 |
16.4 |
83.8 |
16 |
|
80 |
16.7 |
83.9 |
17.5 |
|
80.5 |
18.1 |
84 |
17.2 |
|
81 |
16.8 |
84 |
13.8 |
|
81.7 |
16.8 |
84.3 |
19 |
|
81.8 |
16.4 |
84.4 |
18.3 |
|
81.8 |
14.1 |
84.6 |
17.6 |
|
82.2 |
17.3 |
84.6 |
15.6 |
|
82.3 |
19.8 |
84.8 |
14.7 |
|
82.8 |
19.9 |
84.9 |
14.3 |
|
82.8 |
17.4 |
85.6 |
16.9 |
|
82.8 |
16.5 |
86.2 |
15.5 |
|
82.8 |
15.6 |
86.5 |
13.1 |
|
82.8 |
14.3 |
87.3 |
15.6 |
|
83 |
17.6 |
87.6 |
13.5 |
|
83 |
16.6 |
87.7 |
17.5 |
|
88.2 |
16.1 |
87.8 |
13.7 |
|
88.1 |
18.5 |
A) Calculate the Pearson correlation coefficient between these two variables, and then determine whether this correlation is significantly different from zero.
B) Calculate the Spearman’s rank-order coefficient between these two variables, and then determine whether this correlation is significantly different from zero. For this part, you need to include your ranked data and your values of D calculated from these ranks. However, you do not need to hand-calculate the actual correlation coefficient!
