Example of One-tailed Two Independent Samples Student's t Test
Biostatistics BI 45, Saint Anselm College
Step 1) State the biological question. Does a new fertilizer improve plant growth by making plants grow taller?
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 independent samples and we want to test the direction of the difference between two independent means, we use the one-tailed Two Independent Samples t test.
Step 5) State the assumptions of the test.
The subjects in each sample must be randomly selected from a population. The sample data must come from a normally distributed populations of observations for the variable under study and the variances from the two samples must be equal.
Step 6) Calculate the observed t statistics from your data.
|
|
oldfert |
dold |
dold2 |
ssold |
|
|
48.2 |
-3.71 |
13.7641 |
102.229 |
|
|
54.6 |
2.69 |
7.2361 |
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|
58.3 |
6.39 |
40.8321 |
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|
|
47.8 |
-4.11 |
16.8921 |
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|
|
51.4 |
-0.51 |
0.2601 |
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|
|
52 |
0.09 |
0.0081 |
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|
|
55.2 |
3.29 |
10.8241 |
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|
49.1 |
-2.81 |
7.8961 |
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|
|
49.9 |
-2.01 |
4.0401 |
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|
52.6 |
0.69 |
0.4761 |
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Sum |
519.1 |
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Mean |
51.91 |
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n |
10 |
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|
|
df |
9 |
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|
newfert |
dnew |
dnew2 |
ssnew |
|
|
52.3 |
-4.25 |
18.0625 |
69.2 |
|
|
57.4 |
0.85 |
0.7225 |
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|
|
55.6 |
-0.95 |
0.9025 |
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|
53.2 |
-3.35 |
11.2225 |
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|
|
61.3 |
4.75 |
22.5625 |
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|
|
58 |
1.45 |
2.1025 |
|
|
|
59.8 |
3.25 |
10.5625 |
|
|
|
54.8 |
-1.75 |
3.0625 |
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|
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|
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|
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Sum |
452.4 |
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|
|
|
Mean |
56.55 |
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|
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n |
8 |
|
|
|
|
df |
7 |
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|
|
Step 7) Find the df and critical value of t from the table of critical values.
Step 8) Compare the critical and observed t values and reject or do not reject the null hypothesis.
Find the actual P value
t.005(1)16=2.921<tobs=2.99<
t.0025(1)16=
0.0025<P<0.005
Step 9) Interpret the results of the analysis as it relates to the biological question raised in 1). Plants grown on the new fertilizer grow significantly taller than plants on the old fertilizer (t=-2.99, df=16, one-tailed, p<0.005).
Blackboard at Saint Anselm College
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.