The Scientific Method/Independent and Dependent Variables

Relationships Between Variables
In any experiment, the object is to gather information about some event, in order to increase one's knowledge about it. In order to design an experiment, it is necessary to know or make an educated guess about cause and effect relationships between what you change in the experiment and what you are measuring. In order to do this, scientists use established theories to come up with a hypothesis before experimenting.

Hypothesis
A hypothesis is a conjecture, based on knowledge obtained while formulating the question, that may explain any given behavior. The hypothesis might be very specific or it might be broad. "DNA makes RNA make protein" or "Unknown species of life dwell in the ocean," are two examples of valid hypothesis.

When formulating a hypothesis in the context of a controlled experiment, it will typically take the form a prediction of how changing one variable effects another, bring a variable any aspect, or collection, open to measurable change. The variable(s) that you alter intentionally in function of the experiment are called independent variables, while the variables that do not change by intended direct action are called dependent variables.

A hypothesis says something to the effect of:

Changing independent variable X should do something to dependent variable Y.

For example, suppose you wanted to measure the effects of temperature on the solubility of table sugar (sucrose). Knowing that dissolving sugar doesn't release or absorb much heat, it may seem intuitive to guess that the solubility does not depend on the temperature. Therefore our hypothesis may be:

Increasing or decreasing the temperature of a solution of water does not affect the solubility of sugar.

Isolation of Effects
When determining what independent variables to change in an experiment, it is very important that you isolate the effects of each independent variable. You do not want to change more than one variable at once, for if you do it becomes more difficult to analyze the effects of each change on the dependent variable.

This is why experiments have to be designed very carefully. For example, performing the above tests on tap water may have different results from performing them on spring water, due to differences in salt content. Also, performing them on different days may cause variation due to pressure differences, or performing them with different brands of sugar may yield different results if different companies use different additives.

It is valid to test the effects of each of these things, if one desires, but if one does not have an infinite amount of money to experiment with all of the things that could go wrong (to see what happens if they do), a better alternative is to design the experiment to avoid potential pitfalls such as these.

Corollary to Isolation of Effects
A corollary to this warning is that when designing the experiment, you should choose a set of conditions that maximizes your power to analyze the effects of changes in variables. For example, if you wanted to measure the effects of temperature and of water volume, you should start with a basis (say, 20oC and 4 fluid ounces of water) which is easy to replicate, and then, keeping one of the variables constant, changing the other one. Then, do the opposite. You may end up with an experimental scheme like this one:

Test number     Volume Water (fl. oz.)    Temperature (oC) 1                 4                       20    2                  2                       20    3                  8                       20    4                  4                       5    5                  4                       50

Once the data is gathered, you would analyze tests number 1, 4, and 5 to get an idea of the effect of temperature, and tests number 1, 2, and 3 to get an idea of volume effects. You would not analyze all 5 data points at once.