# Does the total of ordinal scores on a questionnaire become scale in SPSS?

I have a questionnaire whose data I've inputted into SPSS. I wanted to ask that do the total scores of likert items become scale and no more ordinal?

• In order to form a total in the first place you had to assign numbers to your results, thereby making them more than ordinal! – whuber Mar 17 at 23:29
• So basically the individual number assignment is ordinal but when a total is found, it is scale? – W. Bruce Mar 18 at 0:11
• The individual items are ordinal because it is categorical but there is a ranking among them – W. Bruce Mar 18 at 0:19
• Just a thought: item response theory is a plausible alternative to treating a sum of Likert items as an interval variable in a linear regression. – Weiwen Ng Mar 18 at 15:21

It is quite common to add Likert items, even though this (as both WHuber and Sal have noted) requires that we are treating them as interval data. The trouble is that Likert scales are really in-between ordinal and interval. Suppose, for example, your questionnaire has questions with answers that can be "Strongly agree", "agree", "neutral", "disagree" and "strongly disagree" (fairly typical Likert scale, but substitute as you wish).

These would usually be given numeric labels such as 1,2,3,4,5, or perhaps 2,1,0,-1,-2 and, if you had a lot of questions, you would add them up. It wouldn't matter much which of the above codings you used (as long as you were consistent). Technically, though, "ordinal" means that you could just as well code them 1,2,301,301,400010019. Worse, it means that the coding could be different on different items and different for different people. Maybe I use "strongly" more easily than you do.

But, while that's how it works mathematically, no one codes Likert items that way because it doesn't make sense. That is, we assume that the gaps between the items are about equal. We don't know this. We assume it. We also assume that different items are about equal and that any differences between people are about equal. There has actually been some work on this (I looked at some of it 20+ years ago when working on my master's project) and it seems about right (at least on the cases that were studied). There's also been work on the meanings people tend to assign to words such as "very", "extremely" and so on (sorry, but I don't have citations - it's been a long time since I looked at this).

So, we can't know that adding Likert items is OK, but it seems to be.

It's another source of measurement error, but probably not a huge one, at least in most cases. My intuition is that it might be more problematic if the questions are very emotionally laden.

The answer is given by the initial comment by @whuber. In order to be able to add up the individual responses, those responses have to be assumed to be interval. If you have truly ordinal values, there’s no logical way to add or subtract the values, unless you assume the intervals between the categories.

Imagine I rank chocolate, vanilla, and strawberry ice cream as strawberry < vanilla < chocolate. Let’s say there’s a fungible quantity of the amount of pleasure I get from eating each ice cream. If it were the case that chocolate gives me 9 pleasure points, vanilla 6, and strawberry 3, then, for example we could add up the points, and say, for example, that eating strawberry twice gives me the same amount of pleasure as eating vanilla once. But given the same ordinal variable, it could be that chocolate gives 9 points, vanilla 8, and strawberry 2. Then it’s the case that I need four strawberries to equal one vanilla. In the first case we could code the flavors -1, 0, 1. In the second case we could code the flavors -6, 0, 1.

With Likert-type items, if we want to add the results into a scale, we need to assume the intervals between the categories. I think probably with Strongly disagree, Disagree, Neutral, Agree, Strongly agree, it does make sense to assume equal spaced categories. That is, if we were to translate these to a continuous Agree-ness variable on the scale of 1 to 100, Neutral might be 40 to 60, Agree 60 to 80, Strongly agree 80 to 100. So coding the categories as -2, -1, 0, 1, 2, or 1, 2, 3, 4, 5. But maybe not everyone views these categories this way.

If we had different categories, for example if we change Strongly agree to This is more important than my family and friends, and health, and money, it might make sense change this coding to reflect that Agree is closer to Neutral than it is to This is more important than my family….

The upshot here is that in order to do the addition, you had to implicitly convert those categories to numeric values. Often, if we analyzing individual Likert-type items we try to treat the data ordinal, but if we have several items summed into a scale, we treat the result as interval.