The two-sample unpaired t test is used to test the null hypothesis that the two population means corresponding to the two random samples are equal.

### Assumptions:

- Within each sample, the values are independent, and identically normally distributed (same mean and variance).
- The two samples are independent of each other.
- For the usual two-sample t test, the two different samples are assumed to come from populations with the same variance, allowing for a pooled estimate of the variance. However, if the two sample variances are clearly different, a variant test, the Welch-Satterthwaite t test, is used to test whether the means are different.

### Guidance:

Ways to detectbefore performing the t test whether your data violate any assumptions.Ways to examinet test results to detect assumption violations.Possible alternativesif your data or t test results indicate assumption violations.

To properly analyze and interpret results of the *two-sample unpaired t test*, you should be familiar with the following terms and concepts:

Failure to understand and properly apply *two-sample unpaired t tests* may result in drawing erroneous conclusions from your data. If you are not familiar with these terms and concepts, you may wish to consult with a statistician. You may also want to consult the following references:

- Brownlee, K. A. 1965.
Statistical Theory and Methodology in Science and Engineering.New York: John Wiley & Sons.- Daniel, Wayne W. 1995.
Biostatistics.6th ed. New York: John Wiley & Sons.- Miller, Rupert G. Jr. 1996.
Beyond ANOVA, Basics of Applied Statistics.2nd. ed. London: Chapman & Hall.- Rosner, Bernard. 1995.
Fundamentals of Biostatistics.4th ed. Belmont, California: Duxbury Press.- Sokal, Robert R. and Rohlf, F. James. 1995.
Biometry.3rd. ed. New York: W. H. Freeman and Co.- Zar, Jerrold H. 1996.
Biostatistical Analysis.3rd ed. Upper Saddle River, NJ: Prentice-Hall.

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