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Paired Experiments

When we try to compare methods, treatments, etc. by applying each to the same population, these two values are no longer independent. Think e.g. of comparing analytical methods applied to environmental samples. The variation among the different samples will probably be larger than the difference between the individual methods. Due to the large pooled variance sp2, we cannot use the independent sample t-test to distinguish between the two methods. We can calculate the pairwise differences, di, and consider the di as a new variable that follows a t-distribution. The mean and standard deviation of the di are , and sd, respectively. nD is the number of pairs. Depending on the sample size nD we use the one-sample tests based on t scores.

Assumption: the distribution of the differences is normal and the differences are a random sample.

The paired difference experiment is often more powerful, since it can eliminate differences in the samples that increase the total variance, s2. When the comparison is made between groups (of similar experimental units), it is called blocking. The paired difference experiment is a simple example of a randomized block experiment.

NOTE: The blocking has to be done before the experiment is performed.

When the normality assumption is not fulfilled, one can use the non-parametric Wilcoxon sign rank test for paired difference designs.

Last Update: 2005-Jul-16