Levels or Independent Variables in ANOVA There are four different types of mobile phones (same brand) that are used as stimuli in an experiment.


*

*In the first example, if "mobile phone" is the independent variable
in the study, which one  of the two is appropriate? (i) mobile phone
is the independent variable with four levels or (ii) this study has 4
independent variables (since there are 4 different mobile phones)


The same webpage is modified into two versions: one with a blue background, and the other version with an orange background. 


*

*In the second example, if webpage is the independent variable, can we
say that the study has one independent variable with 2 levels or does it
have two independent variables?


Kindly clarify.
 A: Since this can be a confusing issue for new statistics students, I will direct you to the following link which talks about independent variables and levels. Hopefully this helps you answer the question. As they note on this site regarding variables:

"Variables are properties or characteristics of some event, object, or person that can take on different values or amounts (as opposed to constants such as $π$ that do not vary). When conducting research, experimenters often manipulate variables. For example, an experimenter might compare the effectiveness of four types of antidepressants. In this case, the variable is "type of antidepressant"." 

Addition, in terms of understanding what a level is (to help you understand your question on levels):

"If an experiment compares an experimental treatment with a control treatment, then the independent variable (type of treatment) has two levels: experimental and control. If an experiment were comparing five types of diets, then the independent variable (type of diet) would have 5 levels. In general, the number of levels of an independent variable is the number of experimental conditions." 

You can think of many different examples to reinforce this. If, for example, you were doing an experiment comparing the effects of varying dosages (eg. high, medium, and low), of a drug on performance or behavior, then your independent variable would be the DRUG, and the levels are the DOSAGES - high, medium, and low. Now, high, medium, or low seems to suggest some order. That said, it doesn't have to. One could imagine it (in your case), extending or classifying the brand as different "levels" of the mobile device (albeit a categorical, rather than ordinal based level type). 
A: You can think of levels as specific values of an independent variable. Applying it to your first example: mobile phone is a variable with specific values (levels) representing different types of mobile phones. Likewise in your second example it'll be correct to say that there's a single independent variable (webpage version) with two levels (red and orange background).
