You should also keep a full backup of your site on your local hard drive. Then if you wish, you can make your edits locally on those files and FTP the changed file to your site.
This is always good practice, whether you have a test/development installation of your site on your home computer or not. If you make all file edits on your home computer first and then FTP them to your site, you will always have an up-to-date backup in case of catastrophe on your site. (You still need to back up your database regularly.)