First, the rules for writing any recommendations apply: the letter should be specific about your relationship to the student, and the length of time you have known them, and offer a candid and detailed assessment of their abilities. The most useful general rule I can give you to guide you as you write for the Rhodes is that the program is both academic and ambassadorial, and the program takes both functions very seriously. We will be sending our students out as individual scholars and as cultural ambassadors who we believe will have a productive experience and be good representatives of Willamette, of their home communities, and of their country. This much is true of the Fulbright and most other programs that take our graduates abroad. For the Rhodes you must also stress the student’s potential to be an important contributor to their discipline, and the ways in which their service and leadership are not just strong, but extraordinary. You may not be able to comment on all areas of their experience, but for the UK programs it is especially important to provide as much detail as you can in the areas where you know the student well. Finally, one of the key ingredients for the UK programs is that the applicant be able to make a strong case for why the program they wish to pursue is the absolute best way for them to receive the training and experience they desire; any information you can add to support that case can be helpful (this curriculum would be difficult or impossible to achieve in the . for example, or the UK program would allow them access to unique resources such as interdisciplinary or inter-institution collaborative projects).
Several programs and web sites perform sample size and power calculations for 1-way and factorial ANOVAs. They differ with respect to how "effect size" is specified - with some it can be generated for you from treatment means that you specify, with others it is calculated as the ratio of between group to within group MSE, and others it is specified via the non-centrality parameter of the F distribution. Usually the null hypothesis is that the treatment means are all equal, but this isn't always the case. Usually treatment effects are assumed to be fixed, but a couple of programs have a "random" choice.