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.

**Ways to detect**before performing the t test whether your data violate any assumptions.**Ways to examine**t test results to detect assumption violations.**Possible alternatives**if 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:

- two-sample problem
- independent samples
- residuals
- Gaussian (normal) distribution
- equality of variance (homoscedasticity)
- transformations

- 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. 1986.
*Beyond ANOVA, Basics of Applied Statistics.*New York: John Wiley & Sons. - 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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