Suppose you have defined a so-called bipolar Likert scale between -1 and +1, where as usual positive values mean a positive attitude and negative values mean a negative attitude towards the object or property to be scaled.
For example, you are asking people for their attitude towards some particular reform in the educational system in their country, where for each component or aspect of the reform you use the following 5-point bipolar Likert "ruler":
- -100% = absolutely against (encoded or labelled as "-2")
- -50% = more or less against (encoded or labelled as "-1")
- 0% = undecided (encoded or labelled as "0")
- +50% = more or less for (encoded or labelled as "+1")
- +100% = absolutely for (encoded or labelled as "+2")
My question is about how you would ADD scores on two or more scales about such a topic (or any other of your choice).
It is evident that you can't just add them as if they were usual real or decimal numbers. Why not? Because your scale is bounded on both sides! You can't be less than absolutely against something, can you? Nor can you be more than absolutely for something, can you?
- For instance: if a respondent would be strictly against two components on your questionnaire about the educational reform, he or she would give two times -1 on your Likert scale (equivalently: -100% or "-2" encoded). If you just add them, you will get -2 or -200%, but this is NOT foreseen on your scale (running from -1 to +1), so you would fall beyond the scale. Analogously if your respondent would answer two times +100%, which is +200%, but this doesn't correspond at all with a value between -1 and +1.
So my question is what to do? I suggest that you invent a new sort of addition of numbers between -1 and +1, which ALWAYS gives you again a plausible number between -1 and +1. Which addition would you propose? Why do you believe this addition is plausible?
P.S.: Don't bother about encoding or labeling the resulting sums, just assume that for any number between -1 and +1 we would be able to propose some sensible encoding or labeling. In particular, don't interpret e.g. "-2" as a number, it is just a convenient label, nothing else.
Dear Paulus, Another problem is that the keypoints may be expressed differently by different researchers. For example, -0.5 may be defined as almost dead against or slightly against. So the one researcher's score of -0.5 is different to another researcher's score.
However, the problem that you are raising is that even with one researcher having a respondent give an encoded -2, the question is: is it exactly canceled out (averaged out) by another respondent giving an encoded +1? I would say, yes. Also, you are asking, does an encoded -2.0 exactly cancel out two other respondents each giving a +1.0? I would say, not necessarily. However, it is a convenient fiction, that allows us to make generalizing statements like: “On average, the respondents were neutral.” If there is an average bias, then you would not report the grand sum of all the encoded responses, but divide by the number of respondents to get the average (and probably convert it to a percentage so that the politician can understand it!).
Similarity too for working out the average response of one respondent. You should not present the sum, but the average: “The average negativeness of respondent X was 0.333” (or 33.3%!). Of course, it is appropriate for the researcher also to report the “standard deviation”, but the politician will not be able to understand that! Best Regards, Ian.
Dear Ian, thanks for your comments, which give me the opportunity, to further point out the constraints and assumptions of my question:
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P.S.: For those who don't like "signed percentages" I have a good message: Yes, you may try to find a reasonable, plausible answer to the same question, assuming that your Likert scores shall be numbers between 0 and 1, or equivalently percentages between 0% and 100%, where n% is simply shorthand for the number n/100 and n runs from 0 to 100.
Given the above setting (including the preliminary assumptions and constraints) here are some further hints (in the form of questions with my favorite answers in parentheses) which may help you to find a solution for the problem that you can't simply add Likert scores as if they were decimal numbers:
- How to handle 0%? Is it reasonable to require of the general solution that the sum of any score s with 0% equals s again? [my favorite answer: yes, by default]
- What if the assessor is a little bit biased so that the role of 0% is played by a small negative or positive score s0 unequal to 0%? Should it suffice to "subtract" (in the Likert sense) s0 from any observed score s to get an unbiased score, on which the proposed Likert sum can be applied? [my favorite answer: yes, as long as subtraction is defined in a way which corresponds with Likert addition]
- Should scores be handled symmetrically around the 0% point, i.e. the Likert distance of -s% from 0% is equal to the Likert distance from 0% to s%? [my favorite answer: yes, given adequate training and calibration]
- What roles do -100% and +100% play, respectively? For instance, is it reasonable to require that the sum of -100% and -100% is still -100%? Same for +100%? [my favorite answer: -100% and +100% are absolute limits, so yes, adding more to it in a Likert sense should not change anything]
- Is it generally reasonable to assume that as scores "move" from 0% to 100%, they have to "travel" slower and slower to increase by the same amount of judgmental strength (same of course for: from 0% to -100%)? [my favorite answer: yes, it also explains why reaching -100% or +100% implies that scores will come to a halt, i.e. not change anymore upon "adding"]
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