35.7 Confidence intervals
Reporting the CI for the slope is also useful, which can be obtained from software or computed manually.
CIs have the form statistic±(multiplier×standard error), The multiplier is two for an approximate 95% CI, so (using the standard error reported by the software), we obtain −0.181±(2×0.029), or −0.181±0.058, or from −0.239 to −0.123.
Software can be asked to produce exact CIs too (jamovi: Fig. 35.11; SPSS: Fig. 35.12). The approximate and exact 95% CIs are very similar.

FIGURE 35.11: jamovi output for the red-deer data, including the CIs

FIGURE 35.12: SPSS output for the red-deer data, including the CIs
We write:
The sample presents very strong evidence (P<0.001; t=−6.275) of a relationship between age and the weight of molars in male red deer (slope: −0.181; n=78; 95% CI from −0.239 to −0.124) in the population.
Example 35.5 (Emergency department patients) In Example 35.4, the jamovi output does not give the 95% CI for the slope.
However, since CIs have the form
statistic±(multiplier×standard error),
the CI is easily computed:
−0.34790±(2×0.046672),
or −0.34790±0.093344.
This is equivalent to −0.441 to −0.255.
Combining with information from Example 35.4, we write:
The sample presents very strong evidence (P<0.001; t=−7.45) of a relationship between the mean number of ED patients and the numbers of days after welfare distribution (slope: −0.348; n=30; 95% CI from −0.441 to −0.255) in the population.