Testing differences between two samples with similar variance

Pooling similar variance

If the F test for variance does not test significantly different, you can calculate a pooled variance as:

$$ s^2_p = \frac{df_1 s^2_1 + df_2 s^2_2}{df_1 + df_2} $$

Testing the difference between two means

The means of two samples can be tested for difference by:

$$ t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s^2_p}{n_1} + \frac{s^2_p}{n_2}}} $$

Also See:

Chapter 9 - Significance of a Difference between Two Means pages 108-124 in:

Phillips, J. L. 2000. How to think about statistics. W. H. Freeman and Co. New York. 202 pp. ISBN 0-7167-3654-3

Chapter 9 - Two-Sample Hypotheses pages 126-130 in:

Zar, J. H. 2007. Biostatistical Analysis. Prentice-Hall, Inc. Englewood Cliffs, New Jersey. 718 pp.
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Natural Resources Biometrics by David R. Larsen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License .

Author: Dr. David R. Larsen
Created: July 19, 2000
Last Updated: December 14, 2019