Interviewing is more art than science. Some people are not good test takers but thrive under real life pressure. Others are great test takers but fold in real world conditions.
The most important thing is to find a method that works for your group.
The most important thing is to get the right number of candidates to each phase screening process. If you get too few to any one phase then you start feeling pressure to lower standards and expectations to fill positions. This often leads to poorly qualified people being over their heads and unable to perform. The result is a negative for both sides. If you get to many then it is difficult to make a good choice and you end up turning away great candidates many times unrealized. What is the right number is a subjective matter that varies. You need to find the right numbers for your organization
Most commonly I have seen a 4 phase process.
Prescreen: An initial check to make sure the applicant meets the bare minimum requirements. There is no point in interviewing someone that can not be brought on anyway. Some companies have used an automated test here as well.
Phone Screen: The initial interaction with the company, simple tech test, introduction to the company, verification of expectations and next steps.
Tech Test: Gauge the skill level of the candidate. I have seen the range of FizzBuzz to a Kobayashi Maru type(there was no way to actually solve it just about how you handle the test). Personally I dislike the former because I think it sets a bad tone for the relationship. I prefer that candidates come on board with a positive experience of success rather than failure but that is my preference.
Team Interview This is a test of the culture fit. This is not so much about what they know but how they interact with the key people on the team. Technical questions are asked not to probe knowledge so much as to gauge levels of interest and compatibility.
Hiring is expensive. Made more so if you hire to many people who do not work out. There is no golden bullet but getting the right number of people to each phase is important to keep your team/business healthy.