One way to analyze children's semantics is to calculate the total number of words the child says (TNW) and consider the number of different types of words within that sample (NDW=number of different words). We can calculate a Type-Token Ratio (TTR) which will give us a measure of the variety of vocabulary the child is using. The more varied the vocabulary, the more semantic competency the child is showing. You can read more details about TTR here: TTR_Description.pdf