PROPHET StatGuide: Two-sample t test (unpaired)

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 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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Last modified: February 20, 1997