Description: This is a small data set used to illustrate the failure of an inappropriate use of an independent means test compared with a paired test on the same data.
The story is that we have before and after weights for 6 customers of a weight loss clinic. Visual observation makes it clear that the clinic is effective (except in one questionable case). Students can discuss what sources there are for the variation found in the data set and relate them to the assumptions of the independent versus paired analysis models. Application of classical techniques will produce an extremely large p_value for the independent analysis and a significant p_value for the paired analysis.
To illustrate the difference with simulation techniques, first do a randomization for two means between the before and after data groups. This will spectacularly fail to show a difference, when in fact there is a clear difference. Then use a bootstrap to examine the 6 differences and it is clear that a zero difference is highly unlikely.