I use the IOWA test. It's just the easiest to implement in the home. The Stanford will let you test your own child, but you have to have a minimum number of kids to test and that number has to include kids other than your own. I bought my IOWA tests via Bob Jones University Press.
We used to pay a small fee to a homeschooling mom who would supervise a number of children taking the test at the same time. She used the Bob Jones test materials.
We use the PASS test from www.hewitthomeschooling.com . You can administer it from home without a supervisor.
We use the CAT-E. In NY kids test in 5th and 7th grades (and 9th -12th). The CAT-E includes only math and language. That's all the state requires. It costs $25. After mailing back the test, the result come back in less than 2 weeks.
My homeschool group offers The Stanford test in may. My kids will be taking it. This is our 1st year home schooling and I need it for my own peace of mind. My kids have taken this test in the past.
When I was working in the school system, I used the Woodcock-Johnson battery for ds -- I could just borrow it from work for the weekend. When we started schooling Other People's Kids, I was able to get the Iowa from Bob Jones, even though our state used the Iowa as their test-of-choice so I had to use an older version. I used that one year, but then there was this big "hoo-rah" about people getting the Iowa - even an older edition - and using it as '"test prep" for their kids in public school. So that year you had to start sending in your proof of homeschooling documentation, which I couldn't do because I was not homeschooling these kids. So I found Crosspointe in North Carolina as a source for the CAT, and I used that. THEN I got hooked up with the SAT/10 through a curriculum/school company -- I had to get recognized as a school, rather than a homeschooler, though. They even sent a representative to visit our school to make sure that we're schooling Other People's Kids. But now I am recognized as a school, not a homeschool, so I can actually BUY the tests (and keep them under lock and key until needed), and only have to buy the answer documents each year which also pays for the scoring. There are several different ways, still, to get your children tested if you want/have to. You can still locate companies that "rent out" the CAT or CAT/5 (Seton Homeschool, I think, does too), or hook up with a co-op that does group testing annually, or locate a teacher-evaluator to do it privately, or get one from Hewitt or from BJU. You might also, if you live near a university with a psychology department or an education department, find a grad student who needs to do a certain amount of testing of individuals in order to meet their requirements for their degree OR even one of their professors might do it. They would most likely use a Woodcock-Johnson, PIAT, Kaufman TEA, or other individually-administered tests, rather than an achievement test like the Stanford or the Iowa.
In most if not all states your kids have the same rights to public school services as other students in the system full time. This means you can have your kids tested at the same time they are testing other kids. I believe all schools receive funding for your kids whether they actually attend or not.
I forgot about having your kids tested with the public school kids -- because we choose to have as little as possible to do with the public schools... Here, however, you have to notify them by January that you'll want to test with them in March/April, and it'll cost you $35. Our state uses the Iowa, but with "tweaks" to match our particular state's benchmarks and such, and Riverside has made some sort of special arrangement that they give the results in a completely different format than the old familiar one. And you'll only get National Percentile scores, never a Grade Equivalent score (they say parents don't really understand GE scores and get way too excited when their student scores above grade level). Then in grades 4, 8, and 10/11, they only give the State test which is only "standardized" for our state, and it only tells you whether the student scored in Unsatisfactory, Approaching Basic, Basic, Proficient, or Advanced - not really a score like "85th percentile, x.x grade equivalent score" like other tests. Oh, and schools only receive funding if your child is actually enrolled there. That's the big deal why they don't like people to homeschool!