In Appendix Twe find that for a one-tailed test at a 5.025 (or a two-tailed test at
a5.05) with n 5 8, the entries are 3 (0.0195) and 4 (0.0273). This tells us that if we
want to work at a (one-tailed) a5.025, which is the equivalent of a two-tailed test at
a5.05, we can either reject for T 3 (in which case aactually equals .0195) or
we can reject for T 4 (in which case the true value of ais .0273). Since we want a
two-tailed test, the probabilities should be doubled to 3 (0.0390) and 4 (0.0546). Since
we obtained a Tvalue of 9, we would not reject , whichever cutoff we chose. We will
conclude therefore that we have no reason to doubt that blood pressure is unaffected by
a short (6-month) period of daily running. It is going to take a lot more than six months
to make up for a lifetime of dissipated habits.Ties
Ties can occur in the data in two different ways. One way would be for a participant to have
the same before and after scores, leading to a difference score of 0, which has no sign. In
this case, we normally eliminate that participant from consideration and reduce the sample
size accordingly, although this leads to some bias in the data.
In addition, we could have tied difference scores that lead to tied rankings. If both the
tied scores are of the same sign, we can break the ties in any way we wish (or assign tiedH 0
...
H 0 ...
680 Chapter 18 Resampling and Nonparametric Approaches to Data
Table 18.5 Critical lower-tail values of Tand their associated probabilities (Abbreviated
version of Appendix T)
Nominal a(One-Tailed)
0.05 0.025 0.01 0.005
NT T T T
5 0 0.0313
1 0.06256 2 0.0469 0 0.0156
3 0.0781 1 0.03137 3 0.0391 2 0.0234 0 0.0078
4 0.0547 3 0.0391 1 0.01568 5 0.0391 3 0.0195 1 0.0078 0 0.0039
6 0.0547 4 0.0273 2 0.0117 1 0.00789 8 0.0488 5 0.0195 3 0.0098 1 0.0039
9 0.0645 6 0.0273 4 0.0137 2 0.005910 10 0.0420 8 0.0244 5 0.0098 3 0.0049
11 0.0527 9 0.0322 6 0.0137 4 0.006811 13 0.0415 10 0.0210 7 0.0093 5 0.0049
14 0.0508 11 0.0269 8 0.0122 6 0.0068
Á Á Á Á Á Á Á Á Áa a a a