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I am working on a survey analysis looking at the effect of an intervention with three components (each having multiple sub-parts). Questions ask respondents how frequently they used each component. Two of the questions have scales ranging from 1 to 5 (never/rarely/often/almost always/always), while the other question has a scale ranging from 1 to 4 (never/1-2 times/3-4 times/5 or more times).

Here are my questions:

  1. Is it okay to sum all three questions together despite being on different scales? If not, how should I remedy the scale differences given that they are all measuring the same underlying construct (how the overall intervention was adopted)?

  2. Each question has a different number of sub-parts (Q1 has 4, Q2 has 5, and Q3 has 6) b/c the number of items in each part of the intervention varies. Therefore, since the answer scale of Q1 is 1 to 5 and it has 4 sub-parts, the theoretical sum for any respondent could range from 4 (lowest) to 20 (highest), but for Q2, the range is obviously different (5 to 25). Q3 is on a different range (6 to 24) because the answer scale range is 1 to 4 and it has 6 sub-parts. How can I standardize the ranges? Do I even need to?

I hope these questions make sense and thanks in advance for any help! It is greatly appreciated!

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  • $\begingroup$ What is the purpose of your analysis? $\endgroup$ – StasK Aug 22 '13 at 13:34
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Old question but I'd like to answer this one anyway.

Adding Likert Data can create data that is no longer nominal. Two people who score the same in terms of the summed scores probably did not obtain those scores by having the same responses to every question. In fact, they can be very different. Doing certain parametric statistics in this type of space can be misleading and inadvisable. If you can defend it, go for it, but the more complicated the statistical method that you use, the more difficult your work will be to justify.

If you want to reduce the effect of this, make sure your Likert Items are measuring the same phenomenon in similar ways. There are ways to attempt to do this including factor analysis, but literature is scarce because no mathematician in their right mind would try to understand all of the strange properties that go on in such a odd space...

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  • $\begingroup$ "Adding Likert Data can create data that is no longer nominal" - I find this claim odd. Why would Likert data be nominal in the first place, rather than ordinal? $\endgroup$ – Silverfish Jun 30 '15 at 15:32
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In the wonderful book Statistics as Principled Argument Robert Abelson notes that often, in statistics, it's not a question of what you "can" do but what you can defend sensibly.

Technically, adding Likert scales is wrong - we don't know that the intervals between levels are equal, so they are only ordinal variables and we could just as well code them 1 2 4 8 12 or even 1 1.1 1.2 1.3 4000 as the more usual 1 2 3 4 5.

But people add them all the time, because although we don't know that the intervals are equal, we can posit that they are and have sensible results. So, for your first question, think about whether it makes sense in your situation to say that a 1 in the first scale is like a 1 in the second, and so on. Certainly "never" = "never" but is "1 to 2 times" = "rarely"? Well, "rarely" is context driven; in your context, does it mean something like 1 to 2 times? (Think about the question you're asking.... "How often do planes crash?" vs. "How often are planes delayed?" the response "rarely" will mean different things!

For your second question, you could take the average value per question (if adding the questions makes sense, taking their average should, as well).

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