The quantiative method is about using numbers. In order to test a hypothesis the researcher will use data, with the goal of formulating laws that will apply the "whole" that is being researched - the "whole" could be a population, an event, etc.
The Scientific Method is not one single thing. It refers to the ideas, rules, techniques, and approaches that the scientific community uses.
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Why a literature review? You are trying to determine what evidence exists on your research idea.
A literature review is a component of the research process in which the author summarizes or synthesizes the ideas and arguments made by scholars. In the social sciences a literature review can be organized in a number of ways including by topic, chronological, or by methodology . The more focused your research topic the more straightforward the literature review will be.
Remember that the literature review (a.k.a. the lit. review) is, in essence, a paper in and of itself. It has an introduction; a body and a conclusion. It is NOT an annotated bibliography.
Caution: Make sure that the choices you make in writing a literature review reflect the requirements of your assignment. Be sure to consult with your Professor.