Anthropology is a social science and therefore has things in common with the other social sciences such as those you mention. However, it is a separate discipline and is different in many ways from the other disciplines. Let us look at two things that are key in making anthropology what it is.
First, anthropology has traditionally engaged in the study of what we might call “primitive” societies. In other words, anthropology has historically been about studying small tribes of people who are not part of modern societies. This differentiates it from sociology, which has typically been interested in studying large, modern, industrialized societies. You could say that sociology has been the study of “us” while anthropology has been the study of “them.” This difference is becoming blurred to some degree today, but it still holds in general.
Second, anthropology is different in its methodological focus. Anthropological studies typically involve a researcher immersing him or herself in a culture. The anthropologist personally observes the culture, trying to understand it in its entirety. He or she uses observational methods to try to understand the subject of the research. By contrast, researchers in such areas as economics and sociology typically use more quantitative methods. People in those disciplines are more likely to look at statistics than to go out and watch people to try to understand them.