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.