An observational study gathered data on the rate of progression of multiple sclerosis in patients diagnosed with the disease at different ages. Differences in the mean rate of progression were tested among several groups that differed by age-of-diagnosis using ANOVA. The results gave P=0.12.

From the following list, choose all of the correct conclusions that follow from this result (Borenstein 1997). Explain the basis of your answers.

a. The mean rate of progression does not differ among age groups.

b. The study has failed to show a difference among means of age groups, but the existence of a difference cannot be ruled out.

c. If a difference among age groups exists, then it is probably small.

d. If the study had included a larger sample size, it probably would have detected a significant difference among age groups.