Journal of Probability and Statistics

Research Article

Simultaneous Inference on All Linear Combinations of Means with Heteroscedastic Errors

Table 3

The simultaneous Scheffé intervals and Generalized Scheffé’s intervals on means and pairwise mean differences in the cigarette example.
Parameters Scheffé Generalized Scheffé
Mean
  𝜇 P C (20.66, 28.94) (20.76, 28.84)
  𝜇 𝐶 (10.95, 22.25) (11.08, 22.12)
  𝜇 𝑃 (26.02, 31.58) (26.09, 31.51)
  𝜇 𝐴 (10.08, 17.32) (10.16, 17.24)
Pairwise comparisons
  𝜇 P C − 𝜇 𝐶 (1.19, 15.21) (1.36, 15.04)
  𝜇 P C − 𝜇 𝑃 (−8.98, 0.98) (−8.87, 0.87)
  𝜇 P C − 𝜇 𝐴 (5.59, 16.60) (5.73, 16.47)
  𝜇 𝐶 − 𝜇 𝑃 (−18.49, −5.90)(−18.35, −6.05)
  𝜇 𝐶 − 𝜇 𝐴 (−3.81, 9.61) (−3.65, 9.45)
  𝜇 𝑃 − 𝜇 𝐴 (10.53, 19.67) (10.64, 19.56)