Example of Two Dependent Samples Student's t Test
Biostatistics BI 45, Saint Anselm College
Step 1) State the biological question.
The biological question is whether there is a difference between the amount of time spent looking for predators by seals at the beginning of a haul-out compared to the end of a haul-out?
Step 2) Translate the biological question into statistical hypotheses.
Step 3) State the alpha level: p<0.05 is considered significant
Step 4) State the statistical test.
Because we are working with two dependent samples (each seal is exposed to two different scan treatments: beginning versus end of a haul-out) we use the two-tailed Two Dependent Samples t test.
Step 5) State the assumptions of the test.
The subjects in each sample must be randomly selected from a population. The differences between scans must come from a population of differences that are normally distributed.
Step 6) Calculate the observed t statistics from your data.
| Seal # | Scan - B | Scan - E |  |
 |
 |
| 1 | 110 | 45 | 65 | 44.417 | 1972.870 |
| 2 | 67 | 59 | 8 | -12.583 | 158.332 |
| 3 | 115 | 44 | 71 | 50.417 | 2541.874 |
| 4 | 90 | 67 | 23 | 2.417 | 5.842 |
| 5 | 45 | 21 | 24 | 3.417 | 11.676 |
| 6 | 23 | 29 | -6 | -26.583 | 706.656 |
| 7 | 76 | 62 | 14 | -6.583 | 43.336 |
| 8 | 88 | 79 | 9 | -11.583 | 134.166 |
| 9 | 49 | 39 | 10 | -10.583 | 112.000 |
| 10 | 67 | 60 | 7 | -13.583 | 184.498 |
| 11 | 56 | 49 | 7 | -13.583 | 184.498 |
| 12 | 86 | 71 | 15 | -5.583 | 31.170 |
| Sum | 247 | 6086.917 |
Step 7) Find the df and critical value of t from the table of critical values. n = the number of pairs of data.
Step 8) Compare the critical and observed t values and reject or do not reject the null hypothesis.
Find the actual P value
t.02(2)11=2.718<tobs=3.031<
t.01(2)11=3.106
0.01<P<0.02
Step 9) Interpret the results of the analysis as it relates to the biological question raised in 1).
We rejected the null hypothesis in Step 8. The duration of the first scan is different from the last scan (t=3.031, df=11, two-tailed, p<0.02). There is a difference between the first and last times spent scanning for predators by seals at haul-outs.
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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.