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 ${\beta }_1$?

CIs have the form $$\text{statistic}\pm (\text{multiplier}\times \text{standard error}),$$ The multiplier is two for an approximate 95% CI, so (using the standard error reported by the software), we obtain $-0.181\pm (2\times 0.029)$, or $-0.181\pm 0.058$, or from $-0.239$ to $-0.123$.

Software can be asked to produce exact CIs too (jamovi: Fig. 35.9; SPSS: Fig. 35.10). The approximate and exact 95% CIs are very similar.

FIGURE 35.9: jamovi output for the red-deer data, including the CIs

FIGURE 35.10: 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.