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Department of Biology St. Francis Xavier University Antigonish, NS Canada B2G 2W5 |
Biology 201
An example showing the difference in usage between unpaired and paired t-tests
Hibernating Bears
Do they loose weight?
"Do they loose weight?" This is an ambiguous question, in and of itself. It could mean, "Do individual bears loose weight?" or "Is the mass of these seven bears significantly different after dormancy when compared with their masses prior to dormancy?" Make sure you know which question you are addressing!
|
Bear Number |
mass before (kg) |
mass after (kg) |
|
1 |
298 |
276 |
|
2 |
152 |
140 |
|
3 |
166 |
151 |
|
4 |
305 |
279 |
|
5 |
90 |
81 |
|
6 |
121 |
107 |
|
7 |
225 |
199 |
|
mean |
193.9 |
176.1 |
Numbers are easily crunched in a spreadsheet set up like this:
|
Bear Number |
mass before dormancy (kg) |
mass2 |
|
mass after dormancy (kg) |
mass2 |
|
mass difference (kg) |
(X-Y) 2 |
|
1 |
298 |
88804 |
|
276 |
76176 |
|
22 |
484 |
|
2 |
152 |
23104 |
|
140 |
19600 |
|
12 |
144 |
|
3 |
166 |
27556 |
|
151 |
22801 |
|
15 |
225 |
|
4 |
305 |
93025 |
|
279 |
77841 |
|
26 |
676 |
|
5 |
90 |
8100 |
|
81 |
6561 |
|
9 |
81 |
|
6 |
121 |
14641 |
|
107 |
11449 |
|
14 |
196 |
|
7 |
225 |
50625 |
|
199 |
39601 |
|
26 |
676 |
|
mean |
193.9 |
|
|
176.1 |
|
|
17.7 |
|
|
sum |
1357 |
305855 |
|
1233 |
254029 |
|
124 |
2482 |
|
sum2 |
1841449 |
|
|
1520289 |
|
|
15376 |
|
|
SS |
42791 |
|
|
36845 |
|
|
285 |
|
|
s2 |
7132 |
|
|
6141 |
|
|
48 |
|
|
|
|
|
|
|
s |
(SD) |
6.9 |
|
|
t Student's |
0.4068 |
|
|
|
|
|
t paired |
6.795 |
Has the average mass of the bears changed? i.e. Is there a significant difference between the average masses of the bears before and after the dormancy? Use the t-statistic from the Student's t-test to determine this.
Is there a tendency for individual bears to lose weight during dormancy? Use the paired t-test to determine this.
What are the degrees of freedom for this example? Look up the critical value of t, using an α=0.05.
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Department of Biology St. Francis Xavier University Antigonish, NS Canada B2G 2W5 |