Testing differences between two samples with different variance

If the two variance are significantly different, we test them with this procedure.

Testing the difference between two means

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

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

You will need to calculate the degrees of freedom for the critical value with the following formula:

$$ v = \frac{\left(\frac{s^2_1}{n_1} + \frac{s^2_2}{n_2} \right)^2}{\frac{\left( \frac{s^2_1}{n_1} \right)^2}{n_1 - 1} + \frac{\left( \frac{s^2_2}{n_2} \right)^2}{n_2 - 1}} $$

If this formula produces a decimal value, truncate the value to an integer.

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