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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.

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    $\begingroup$ Is this a homework problem? $\endgroup$
    – gung - Reinstate Monica
    Apr 15, 2014 at 1:09
  • $\begingroup$ Why? I am trying to understand the concept $\endgroup$
    – user39531
    Apr 15, 2014 at 1:26
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    $\begingroup$ Ask yourself this, "if each phone is a separate variable, then in what what is it varying?" $\endgroup$
    – John
    Apr 15, 2014 at 4:45
  • $\begingroup$ so it will be one independent variable (mobile phone) with four levels (types of mobile phones). $\endgroup$
    – user39531
    May 30, 2014 at 18:11

2 Answers 2

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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).

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  • $\begingroup$ My understanding was that if you take one variable (black color mobile device) and modify it (apply a blie skin), then it is considered as one variable with two levels (black and blue color). However, if you take four "different" mobile phones (same brand: Nokia) - Lumina 930, Dual Slim, Nokia XL Dual, Asha 503), then we are dealing with 4 different variables. This is because one model may be touch screen, one works with two simcards, the other may have keypads etc. $\endgroup$
    – user39531
    Apr 15, 2014 at 14:56
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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).

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