35.7 Confidence intervals

Reporting the CI for the slope is also useful, which can be obtained from software or computed manually.

Think 35.4 (Approximate 95% CI) Using the output (jamovi: Fig. 35.7; SPSS: Fig. 35.8), what is the approximate 95% CI for β1?

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.

jamovi output for the red-deer data, including the CIs

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

SPSS 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.