Variables are things you are studying, basically. A good way to think about dependent versus independent variables is that the dependent variable depends upon the independent variables. The dependent variable is the one that changes, and is the focus of your study. The independent variable(s) is the cause of the...
Variables are things you are studying, basically. A good way to think about dependent versus independent variables is that the dependent variable depends upon the independent variables. The dependent variable is the one that changes, and is the focus of your study. The independent variable(s) is the cause of the change. So, for instance, if I am studying how women got the right to vote in two or more countries, my dependent variable would be voting laws in those two countries. My independent variables would be things that resulted in a change in those voting laws (dependent variable), such as: political system in each country, history of women's rights in each country, protests by women in each country, etc. Anything that affected the laws that allowed women to vote is an independent variable. The voting laws themselves, the laws that define who can vote, is my dependent variable. I want to know what made the voting laws (dependent variable) change, so I examine things that might have caused that change (independent variables).
Many people are confused when we use mathematical terminology, such as the word "variable." Thus, it might be easier to think of the dependent variable as a change you want to explain, and the independent variables as things that caused that change.
Deductive versus inductive reasoning are basically whether you examine something from the top down or the bottom up. Deductive reasoning is examining something from the top down: you have a theory, and based upon that theory, you assume, predict, or deduce something about a particular subject. For example, you have a theory that everyone who lives in California has a suntan. Your friend Brenda lives in California. Therefore, based upon your theory, Brenda has a suntan. Jake also lives in California. Based upon your theory, Jake also has a suntan. Deductive reasoning is taking a broad statement/assumption (theory), and applying it to more specific subjects.
Inductive reasoning is the opposite, a bottom up approach to reasoning. Here, you begin with a specific observation or fact, and assume more general things because of that specific observation/fact. Taking the example above, using inductive reasoning, you would observe that your friend Brenda is from California and she has a suntan. Jake is also from California and also has a suntan. You would conclude from this information that all of the people who live in California have suntans.
So, with deductive reasoning, you go from the general to the specific, and with inductive reasoning, you go from the specific to the general.