## 7.5 CIs for mean differences (paired data)

A study (Guirao et al. 2017) examined the difference between 2-minute walk times (2MWT) for \(10\) patients before *and* after receiving a prosthetic implant.
(The 2MWT measures how far participants can walk in two minutes.)

The 2MWT for ten amputees *with* and *without* an implant are shown in Fig. 7.5.

- What type of RQ is implied: descriptive, relational, repeated-measures or correlational?
- What do \(\mu_d\) and \(\bar{d}\) represent in this context?
- Explain why these data should be analysed as
*paired*data. - Compute the
*changes*in 2MWT for each patient. - Although it doesn't really matter,
*why*does it probably makes more sense to compute the**With Imp**values minus the**Without Imp**values? - Using the statistics mode on your calculator, compute the sample mean difference \(\bar{d}\) and the sample standard deviation of the differences \(s_d\).
- Compute the standard error of the mean difference \(\text{s.e.}(\bar{d})\). Explain what this tells us in this context.
- If another sample of ten subjects were studied, would the same sample mean difference \(\bar{d}\) be computed? How much variation would be expected in the sample mean differences found from different samples?
- Draw the approximate sampling distribution of \(\bar{d}\).
- Compute an approximate \(95\)% confidence interval for the population mean difference in 2MWT.
- Construct a one-sentence statement that communicates a \(95\)% CI for the population change in 2MWT.
- What conditions must be met for this CI to be statistically valid?
- Is it reasonable to assume the CI is statistically valid? Construct a stem-and-leaf plot to help.
- Suppose the researchers wished to estimate the change in 2MWT to within \(5\)m, with \(95\)% confidence. What size sample would be necessary?
- Do you think the population 2MWT changes because of the prosthetic, on average? Explain and discuss.

### References

Guirao L, Samitier CB, Costea M, Camos JM, Majo M, Pleguezuelos E. Improvement in walking abilities in transfemoral amputees with a distal weight bearing implant. Prosthetics and Orthotics International. 2017;4(26–32).