Generally speaking, statistics is necessary if you want to describe quantitative data obtained from a sample (descriptive statistics) and to generalize your findings (inferential statistics) and for complexity reduction.
In linguistics, the field has shifted slightly away from one expert opinion who judges one or two linguistic examples and has oriented more towards judgments from more than one listener (and then you would count the listeners' responses and describe the sample and you would like to make inferences to other people that you haven't asked). Also, there is an increased interest in corpus data and statistical tools may also help you to determine patterns of interest. On the other hand, there are areas in linguistics in which statistics is not that important, possibly in developing grammar architectures or in formal semantics and pragmatics, but I don't know these fields well enough to judge. Having said that, you may need a basic understanding of statistics in these areas as well to evaluate more empirically oriented contributions. I am honestly curious about the responses you will get from others in the field.
(I am not sure I am allowed to recommend books here but you can ask me if you are interested - I have been teaching statistics to linguistic students for more than six years now)
What you are talking about can link to an area of linguistics called the Statistical Linguistics. It might not be necessary to possess ideas on statistics but if you have one, its extremely helpful in recording or observing linguistic data worldwide. The data collected by the procedures of statistical linguistics are used to reveal the stylistic features of authors, ascertain the sources of texts, decipher historical writings, and resolve problems in stenography, communications theory, and information science.
Research almost invariably involves the use of statistical techniques . Doing research without statistical provisions is like going hunting without having hunting tools. Although in typical types research such as reviews and evaluation reports, there might be no need statistical techniques, the application of psychometric principles adds vigor to linguistic research.
New trends of researching focus mainly on applied researches. As a result, knowledge of statistics is an obligation as I think to at least understand the kind of the relationships among variables.