The data set monarch from Computer-Active Data Analysis by Lunn andMcNeil (1991) contains the years lived after inauguration,election, or coronation of U.S. presidents, popes, and Britishmonarchs from 1690 to roughly the present (Nixon, Carter, Reagan,etc., are not included). Do the groups differ? Thestats output is
>> stats(monarch.years,monarch.group)
pres popes K&Qs
N 35.0000 23.0000 14.0000
Mean 14.5429 12.5652 22.7143
Std. Dev. 9.4662 8.7221 18.6028
suggesting that the monarchs tend to live longer than presidents orpopes. This is not experimental data (but instead observational)and one could claim that the data is nearly the population.Nevertheless, we have run the ANOVA and the results look like
Source df SS MS F p-val
group 2 x x 3.5880 ?
Error 69 x x
Using the fact that this F statistic has an F density with 2 and 69degrees of freedom under random sampling and the null hypothesis ofequal means, find the p value using Splus or MATLAB and the factthat Pr(F > y) = 1-pf(y,df1,df2) in Splus and Pr(F > y) =1-fcdf(y,df1,df2) in MATLAB, where df1 is the numerator degrees offreedom and df2 is the denominator degrees of freedom in the Fstatistic. p value =