# Is 0 a valid value in a Likert scale?

I have carried out my pilot study on language learning motivation using a 6 point Likert scale but from 0 (strongly disagree) to 5 (very much agree). I noticed a colleague in his survey used 1 to 6. Will my computed variables (sum and mean) be the same as if I had used 1 to 6? Is it normally recommended to not use a 0 for some reason? I am new to SPSS but have managed to do most of what I need to do but I'm now worrying my values are 'distorted'. I don't understand how SPSS adds a 0 into an equation.

Thanks

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I suspect--but without being able to offer evidence--that there may be a psychological difference between the 1..6 and 0..5 scales, primary due to differences in how 0 is experienced and understood by people compared to their perceptions of positive integers, and perhaps because people may be thinking in terms relative to the maximum, so that in one case the change from 5 to 6 is 1/6 of the maximum whereas in the other case it would be (erroneously) considered equal to 1/5 of the maximum. Perhaps psychologists in our community could offer some thoughts about this? –  whuber Jul 16 '12 at 15:29
@whuber Indeed, this is a long standing topic in questionnaire design - especially with regards to uni- vs. bipolar scales. For an overview, see Schwarz. 1996. Cognition and communication: Judgmental biases, research methods, and the logic of conversation. Mahwah, NJ: Lawrence Erlbaum. Some more references. –  caracal Jul 16 '12 at 16:45
I think this previous post on Likert scale categories might help. –  David Jul 16 '12 at 19:14
5-point Likert-type item are often used, where response categories are "Strongly disag.", "Disag.", "Neither ag. nor disag.", "Ag.", and "Strongly ag.", without explicit numerical score. What's your 6th category? Response coding is immaterial, for regression, data checking, or summary statistics. Any scaling, linking or equating method can take that into account. What's really matter is the underlying measurement model you are ready to assume, because it will determine whether scores are to be treated as sample-dependent discrete scores or a 'reflection' of a latent trait on a discrete scale. –  chl Jul 16 '12 at 21:31
I am the poster of the original question. The entire quesitonnaire on motivation was made up of 80 items grouped into 16 subscales with a criterion measure of inended effort also rated on the likert scale. All reponses were 0 (totally disagree) to 5 (competely agree). thank you all very much for the insightful replies, based on these I maintained the original rating. –  Imelda May 2 at 8:03

Let me make a couple of points. First, if you just have 1 question, you don't technically have a likert scale, but just an ordinal rating. At any rate, I can't see as how there will be any meaningful difference. This is just a linear shift. This will neither make a difference whether you use an ordinal analysis like ordinal logistic regression or a Mann-Whitney U test, or a more standard option like OLS regression or a t-test.

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I must partially disagree with @MichaelChernick. While answers to a single Likert question (whether 0 to 5 or 1 to 6 or whatever) are clearly ordinal, usually there is a sum of several Likert scale items. At some point, the number of possible values becomes so high that it is essentially continuous.

As you know (but the poster of the question may not) OLS regression does not assume that the dependent variable is normally distributed, only that the errors (as estimated by the residuals) are.

If we sum a bunch of Likert items, do we know that the intervals are really equal? No, not really. But do we know that for, say IQ? Or even income? Is the difference between an IQ of 130 and 140 the same as 100 and 110? Does that question even make sense? What about a \$10,000 raise for someone who makes \$10,000 vs. $100,000 per year? I wrote a whole blog post on this. In addition, it's not clear to me whether this Likert scale is going to be a dependent or independent variable. - I guess it depends on whether the OP wants to compare individual questions or groups of questions (commonly called domainsin the survey literature). But how do the sums of integers bscome continuous. They are larger but they are still integers and not continuous. Also the sum does not magically change from ordinal to nominal so I don't get what you are trying to say. OLS assumes the covariates are fixed and that the residuals are normal. In effect that means the dependent variable conditioned on the covariates is normal. – Michael Chernick Jul 16 '12 at 22:17 @Michael You may want to look at some earlier discussions on whether to treat Likert scales as continuous or discrete. Variable scoring sometimes reflect the way we envision the data. I can also recommend De Boeck, P., Wilson, M., and Acton, G.S. (2005). A Conceptual and Psychometric Framework for Distinguishing Categories and Dimensions. Psychological Review, 112(1): 129-158. – chl Jul 16 '12 at 22:41 @Chi Thanks for your suggestions. – Michael Chernick Jul 16 '12 at 22:45 In following up on @caracal's reference suggestions, I found an almost-direct answer (no, these two rating systems are not equivalent if presented as number options to respondents) from Schwarz, Knäuper, Hippler, Noelle-Neumann, and Clark (1991). They present data on responses to the question, "How successful have you been in life, so far?" One version gave rating options from 0–10 to 480 participants; the other version had options from (-5)–(+5) with zero as the midpoint, and was seen by 552 participants. The endpoints were labelled “not at all successful” and “extremely successful” in both versions. "Undecided" was also an option on both. Here's how things shook out: $$\begin{array}{ccc|ccc}&\text{0–10 Scale}&&&-5\text{ to +5 Scale}&\\\hline\small\text{Scale Value}&\small\text{Percentage}&\small\text{Cumulative}&\small\text{Scale Value}&\small\text{Percentage}&\small\text{Cumulative}\\\hline0&...&...&-5&1&1\\1&...&...&-4&...&1\\2&2&2&-3&1&2\\3&5&7&-2&1&3\\4&7&14&-1&1&4\\5&20&34&0&9&13\\6&14&48&+1&9&22\\7&20&68&+2&23&45\\8&20&88&+3&35&80\\9&6&94&+4&14&94\\10&3&97&+5&4&98\\\text{Undecided}&3&100&\rm{Undecided}&2&100\end{array}$$ Quite different, clearly! They also report$\chi^2(10)=105.1,p<.0001$for this difference. Of course, this difference won't appear if the difference is only behind the scenes in terms of how you code responses, not visible to participants as a way for them to provide responses. There are simple survey design methods that allow one to avoid worrying about the psychological effects of equating rating anchors with numbers. Basically, you can just avoid using numbers! E.g.: 1. Allow respondents to check cells in a table corresponding to their answer preference: each row can be a different item, and each column can be labeled with your rating anchor, or vice versa – no numbers involved. Here's how that might look (if one were to answer wisely):$\begin{array}{|c|c|c|c|c|c|c|}\hline&\tiny\text{Strongly Disagree}&\tiny\text{Disagree}&\tiny\text{Mildly Disagree}&\tiny\text{Mildly Agree}&\tiny\text{Agree}&\tiny\text{Strongly Agree}\\\hline\tiny\text{Tumblers: better than pumpers!}^*&&&&&&\checkmark\\\hline\tiny\text{I look fat in this dress.}&\checkmark\\\hline\end{array}\$*

Wikipedia gives another style using marked options (by Nicholas Smith):

2. Letter codes can also be substituted for numeric options if blanks are to be filled for a list of very many items; e.g., {SD,D,MD,MA,A,SA}. Just don't forget to include the legend!

Reference
Schwarz, N., Knäuper, B., Hippler, H. J., Noelle-Neumann, E., & Clark, L. (1991). Rating scales numeric values may change the meaning of scale labels. Public Opinion Quarterly, 55(4), 570–582.

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Any reason to view numberless scales as better? –  Scortchi May 8 at 8:49
@Scortchi: they at least ought to decrease ambiguity of responses. It seems unlikely to me that respondents and researchers would achieve a greater understanding of one another by mixing the languages of verbal and numeric anchors. It seems more likely that researchers would design their indices arbitrarily and naively, and respondents would decide how to respond inconsistently (in both an between- and within-subjects sense) based on whichever set of anchors makes more sense to them personally in general, or worse, for certain items. Thanks for your insightful edit BTW. Sharp eye! –  Nick Stauner May 8 at 15:45
This is just my intuition speaking now BTW, but for example, an item like, "This is a good answer," might appeal more to a 0–10 scale by association with the typical academic grading system that ranges from 0–100% credit...whereas, "Obama is a good president," might appeal more to a (-5)–(+5) system because it would give conservatives a way of expressing their sense of injury, not just their dissatisfaction. My guess is that the latter question would produce no preference between verbal and numeric rating systems, whereas the numeric system might be preferred slightly for the former question.. –  Nick Stauner May 8 at 15:50
...just in terms of how people would think about their answer choices, their choices between verbal and numeric rating systems probably being made on a preconscious / automatic / less-than-deliberate level most often across participants with varying degrees of self-awareness, attention to detail, or "psychological mindedness". Some amount of learning occurs over the course of filling out a long questionnaire. IIRC, this leads to more consistent (maybe biased) answers as items begin to blur together. </ wild speculation and conjecture> –  Nick Stauner May 8 at 15:53
That all sounds very plausible - I'll admit I was angling for another study addressing the question. (I recall one purporting to show the existence of a "fence-sitting" effect in which the middle level of an item with an odd no. levels was over-represented compared to the two middle levels of an item with an even no. levels. - I'll post the ref. when I find it.) –  Scortchi May 9 at 8:35

To do analysis with ordinal scales like the Likert you would use nonparametric methods based on ranks. What matters with ordinal scales is the order if 5 is best, 0 is worst, 1 is better than 0, 2 is better than 1 etc. Both ratios and intervals are meaningless for ordinal data. So a scale of 1-6 versus 0-5 doesn't matter and won't affect the analysis. Starting with 1 is due to tradition rather than necessity.

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"Both ratios and intervals are meaningless for ordinal data" depends on the underlying measurement model you are willing to assume. –  chl Jul 16 '12 at 22:00
@Chl What is your point? –  Michael Chernick Jul 16 '12 at 22:10
My point is that certain psychometric models explicitly consider discrete response as a proxy reflecting one's location (or liability) on a latent trait, as detailed in an answer of mine. I'm ok with the rest of your answer, which is basically founded on the idea of treating sum (not in this case, but you'll get the idea) scores as mean to rank individuals on a given construct (under the CTT framework). –  chl Jul 16 '12 at 22:23
But variables are usually not strictly ordinal or interval. The blind application of Stevens' taxonomy is just as bad as the blind application of any other rule. For strictly ordinal, you could recode it a 0, 2, 2.1, 2.2, 2.3, 19288191. But would you? And, other than physical measurements, what is really interval? –  Peter Flom Jul 17 '12 at 21:47
@Peter This reminds me of this older thread: Does it ever make sense to treat categorical data as continuous? –  chl Jul 18 '12 at 16:44