Example of the Variance (F) Test for Two Independent Samples Student's t Test
Biostatistics BI 45, Saint Anselm College
Biologists are interested in whether there is a difference in the average number of moths caught by one type of moth trap versus a second type of trap. They are using a Student's t test and are testing whether the variances of the two samples are equal. Their question is: are the two variances equal?
Step 1) Develop the statistical hypotheses.
Step 2) State the alpha level: p<0.05 is considered significant
Step 3) State the statistical test.
Because we are working with two independent samples and a Two Independent Samples t test we use the Variance of F test.
Step 4) State the assumptions of the test. The data should come from normally distributed populations.
Step 5) Calculate the observed t statistics from your data.
|
|
Trap
type 1 |
d1 |
d12 |
ss |
var1 |
|
|
41 |
6.55 |
42.9025 |
218.7275 |
21.87275 |
|
|
34 |
-0.45 |
0.2025 |
|
|
|
|
33 |
-1.45 |
2.1025 |
|
|
|
|
36 |
1.55 |
2.4025 |
|
|
|
|
40 |
5.55 |
30.8025 |
|
|
|
|
25 |
-9.45 |
89.3025 |
|
|
|
|
31 |
-3.45 |
11.9025 |
|
|
|
|
37 |
2.55 |
6.5025 |
|
|
|
|
34 |
-0.45 |
0.2025 |
|
|
|
|
30 |
-4.45 |
19.8025 |
|
|
|
|
38 |
3.55 |
12.6025 |
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|
|
|
|
|
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|
|
Sum |
379 |
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|
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|
|
Mean |
34.45 |
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|
|
|
|
n |
11 |
|
|
|
|
|
df |
10 |
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|
Trap
type 2 |
d2 |
d22 |
ss |
var2 |
|
|
52 |
-5.25 |
27.5625 |
107.5 |
15.3571 |
|
|
57 |
-0.25 |
0.0625 |
|
|
|
|
62 |
4.75 |
22.5625 |
|
|
|
|
55 |
-2.25 |
5.0625 |
|
|
|
|
64 |
6.75 |
45.5625 |
|
|
|
|
57 |
-0.25 |
0.0625 |
|
|
|
|
56 |
-1.25 |
1.5625 |
|
|
|
|
55 |
-2.25 |
5.0625 |
|
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|
|
|
|
|
|
|
|
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|
|
|
|
|
|
|
|
|
Sum |
458 |
|
|
|
|
|
Mean |
57.25 |
|
|
|
|
|
n |
8 |
|
|
|
|
|
df |
7 |
|
|
|
|
Step 6) Find the df and critical value of F from the table of critical values.
Step 7) Compare the critical and observed t values and reject or do not reject the null hypothesis.
Find the actual P value
Fobs=1.42<
F .50(2)10,7=
P>.50
Step 9) Interpret the results of the analysis as it relates to the biological question raised in 1). We did not reject the null hypothesis. The variances are equal so use the Student's t test. There is no need to report the variance of this test unless they are different.
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.