Thank you very much for your reply.

It should be mentioned that in this study, SPSS will be utilized for descriptive statistics and t-test analysis. Meanwhile, SEM-AMOS will be applied to analyze the relationships and predictions.

In some cases e.g. incidne of symptom you may omit different levels (Likert points other than 0) an analyse 0 vs non-0. This helps also some logistic regression where 0-1 is welcomed. Additionally maximum level (last point in every scale) may be analysed. All other modes are somehow doubtful because people filled in different scales. Standardization, z-scores are accceptable but are in that case yhmm ...an approximating approach, more coherent when different populations use exactly same scale and we are in doubts whether males vs females see and report things differently. Best regards.

I mean incidence (or occurence) of symptom

sorry for typing error

Jerzy

Thank you so much for your replies. I am studying immigrant couples. I believe that converting the points in the Likert scale for all questionnaires in a survey so that they are the same not only facilitate the analysis procedure, but also makes it easier to be understood and answered by respondents. Imagine, if for example they have to answer to some questions on 7-point Likert scale and some on 4-point Likert scale, they will be confused. I have 180 quetstions in my survey and as you know it is too much and it cannot be summerized. I should find a way to decrease the time of responding to the questions, data analysis,...

So, the problem is that: I do not have any scientific justification for it!

Indeed, I want to know if I do these changes, I will face any problem in my research procedure and my viva session or not.

Thank you very much for your valuable times.

All the best

If you are using published scales it is not a good idea to deviate from the original presentation (including response options) as this throws some doubt on the psychometric properties. If you have constructed your own scales there is value to harmonizing the response options before assessing its psychometric properties.

In terms of analysis there are numerous options - but one that is often overlooked is percentage of maximum performance (POMP) scaling - proposed by Cohen et al.

Thank you very much for your reply.

If you want to rely on the claims of reliability and validity for published scales, then you do indeed need to use them as originally written.

As for the 180 questions, I agree with you that this poses a serious issue of "respondent burden" -- especially if these respondents are not familiar with participating in survey interviews. I would recommend two things. First, go over your intended analysis and ask where every set of items fits into your analysis plan. Does each set of items serve a unique and absolutely necessary purpose? If not, you should drop sets of items so that you have usable data rather than perfect measurement of everything that might conceivably matter.

My second recommendation would be to look at survey scales that originate in either sociology or applied research. There is a strong tendency in both those fields to work with shorter scalers that will fit into briefer interviews and still show high levels of reliability and validity. In particular, a scale with as many as 15 items would be considered to be long in that school of thought. (A different set of assumptions comes fro clinicians who often prefer long "batteries" of items, without evidence that the increased length of the scale is truly necessary for adequate reliability and validity.)

I also understand your concern that respondents who are less familiar with surveys could be confused by using two different response scales. Assuming that the respondents are relatively literate and that this is an in-person interview, then a common practice is to write the the different response scales on cards and show those cards to the respondent for each corresponding scale.

In other words, you inform the respondent that you will using a different set options to answer the next set of questions, then hand the respondent the card that shows those categories, and verbally go over the the available responses with the respondent.

Thank you very much for your valuable time dear professor.

Hello Farimah,

I have been facing the same problems with my PhD survey in recent weeks, so I am grateful to you for posting your question, and to the respondents for their valuable advice. It is important to point out that I am a beginner at this, and the following is just to let you know you're not alone: It is not a recommendation - what I did may not be right.

In addition to my own questions, I used three existing sub-tests with different scale systems, which I adapted to fit a 5-point likert scale. With pilot data, I ran Cronbach Alpha tests on the sub-tests before and after the scale change, and as the results based on standardized items were 0.741 before and 0.736 after, I gathered that I had not significantly damaged reliability of the sub-scales.

I don't have any further information yet though, because I'm still gathering data.

A book that's been very helpful to me is de Vaus, 2002, Surveys in Social Research, Allen & Unwin, Sydney - Especially chapter 11: Building Scales.

Good luck!

Dear Kerri,

Thank you so much for your kind words and thank you for sharing your valuable experience with me.

Wish you all the best dear,

Farimah

If these are your own scales and you have not already accumulated some of the data, you can simply switch out the scales so they are all the same. If they are previously published scales, switching may be a problem because you will not be able to compare your results to results that others have obtained using different scales. If you have already collected some data using one kind of scale, it may be a problem to combine it with data using a different scale even if you convert to standard scores such as Z-scores. In addition, there is a conceptual difference between Likert scales with even numbers of choices and odd numbers since there is no neutral middle choice with the even numbers.

Thank you for you reply dear professor. I have not collected data yet. Further, I will use the standard scales. You mean, I will face difficulties if I use different point Likert scales?

Hi Farimah,

Suggesting you to standardize them into higher point Likert Scale e.g. 7-pooint Likert Scale due to some advantages derived by higher point Likert Scale.  At the same time needs to take note the disadvantages of higher point Likert scale.  For both advantages & disadvantages, you might want to refer to my post in this link:

https://www.researchgate.net/post/When_should_one_switch_to_the_10-item_Likert_scale

Regards,

Fung

Thank you very much for your reply.

I assume you want to add together all of the items to create a single scale. If so, then they all need to be on the same scoring system, and the most common solution is to convert each item to a Z-score. That way they will all have a mean of 0 and a standard deviation of 1.

Thank you very much for your valuable time dear Professor. I have already collected my data and now I am preparing them to start analysis process via AMOS. 

Sorry Prof, so, I should calculate Z-scores for all variables before running SEM. Am I right?

Regards,

If you are doing SEM, there is no need to standardize the data.

Thank you very much dear professor.

Regards,

Dear Farimah,

I find this link helpful.

http://www-01.ibm.com/support/docview.wss?uid=swg21482329

All the best on your research.

Regards.

http://www-01.ibm.com/support/docview.wss?uid=swg21482329

Thank you sir,

Regards,

Hi, by any chance could you manage to convert different point scales into one?Can you please suggest me the process please? Regards,

Dear Payal

According to the consultations done with some expert people that some of them are available here, I did no change in regard of converting the scales to a common one. I analyzed my data and I did not face any problem.

Hope it helps, 

Good luck! 

Thanks a lot Mr. Kamal Asasifor sharing the link 

It's very helpful for me.

I have a question . In my study i am using 5 questionnaires 4 of them are in 5 point likert scale and one is in 7 point likert scale. All my questionnaires are pre determined questionnaires. I am interested to do SEM analysis. Kindly guide me whether I need to standardise the 7 point likert scale to 5 point scale ? Or can i use the scales as it ?

Dear Suchandra,

Based on my understanding, you can use them as they are. No change is needed.

Good luck with your study,

Farimah

Thanks a ton Farimah.

Thank you Farimah, for raising this question. I was having the same confusion for my study on response scale. However, I would like to ask if we have neo-literates respondents how can we modify the response scales on cards?? I read somewhere that they used different smilies for responses. Is it possible to use the same??

Thanks 

I am sorry Arunima. I am not sure.

Hope the expert people following this post see your question and help you.

Best,

I believe you could use the maximum scale percentage. See COMPREHENSIVE QUALITY OF LIFE SCALE – ADULT, by Robert A. Cummins, School of Psychology, Deakin University. Here is the link to the open access document: http://www.acqol.com.au/instruments/comqol-scale/comqol-a5.pdf

If you want to have a first glance at the formula, go to page 28 of such document.

I see though that this is the method suggested by Kamal already; Cummins' document provides additional details though.

Thank you for your suggestion dear Dr. Fumarco 

All the best,

Hi Darren

Yes, they were different but there was no need to standardize them. 

Hope it helps,

This may be overly simple (maths dullard):

If you have mean values for both 5 & 7 point scales, could you not multiply them up to a common # (e.g. 35), then view them as a % of this number? This would indicate if one mean was greater than another mean, and proportionally by how much.

e.g.

5 point L = barX2,   7 point L = barX3     Common # = 35

2x7 = 14  ÷ 35  x  100  =  40(%)

3x5 = 15  ÷ 35  x  100  =  42.86 (%)

Doesn't the number show that the 7 point scale value was 2.86% greater than the response for the 5 point scale?  What this means in context is open to interpretation (and not very mathematical), but if you simply want to say that 'respondents in survey Y were slightly more in agreement than the respondents in survey X' (equivalent Likert mean 3L7:2L5), then perhaps this gives you the supporting evidence?

For producing a formally common scale you can't avoid complex maths, but if you are just looking for a way of seeing proportional difference to support a qualitative observation or idea, then would this not work?  The original scales are preserved in the text, so you have not changed or misrepresented any data.

 Hi, 

I would like to conduct factor analysis and then run regression. I have data measured on scale 0=strongly disagree to 10 strongly agree. Respondents evaluated 24 statements for 5 different brands. So, I have in my data set 5*24=120 variables. Now, my goal is to combine these variables into one set of variables so they represent valuations of all brands together. So I want to get 24 items which includes valuations of all brands.  I need to combine this statements. Also one item is negatively formulated. Do I have to reverse the codes?  

What would you suggest? How should I transform and combine these variables, so that I get one set of variables to conduct factor analysis (which takes into account all scores for all brands)

I would much appreciate your quick response

Best regards,

Davit

hello,

I have selected an instrument for data collection which has been developed using 5 factors of a model but the author has combined these 5 factors into 3 new factors and defined them. I want to use 5 factors of the original model by distributing the items accordingly. will this effect the validation of original tool?

Dear Noora

In my opinion and based on my experience, there is no need for standardizing the data.. 

BTW, sorry for late response dear..

Best,

Farimah 

 Dear Davit

If I m correct, you have 120 items that every 24 of them measure (for example) the level of satisfaction about one brand.. So, you measured 5 different things that cannot be combined! 

Regarding the negative item, yes, you should reverse its score.. 

Hope it helps..

Sorry for late response.

Best,

Farimah

Dear Farimah and all interested in this subject.

There is a quite misunderstanding of what you want to do and how to do it. This subject was treated with experts in psychometric and statistics in a rigorous manner.

I do believe that, depending on how you want to combine your scores, you need to bring them to the same scal either by normalization, or using equating methodologies such as equipercentile equating method(s). The R software has interesting and easy packages for this issue. The most easy and simple way is to normalize to zero-one interval and the formula is easy, since it uses only the min-max values (like z -stat, but in the denominator it uses difference between max and min values). I hope this will solve the problem for all.

Dear Dr. Boudribila 

Thank you for your response. However, when we are applying AMOS, it normalizes our data automatically; hence, there is no need to normalize it before running the model. 

Moreover, I compared the results of analyzing the normalized data and non-normalized data. They were the same!

Best,

Farimah

Dear Farimah, I agree with David L Morgan, and I would like to add that the questionnaire form should be coordinated, disaggregated, similar and far from complex in terms of design

From the outset in order to shorten time, effort and costs

I'm happy to come across this issue of standardizing scales because I have a related problem. Pls, I need your suggestions.

In my case, I'm using PLS-SEM for my survey data analysis. I have one variable that is not latent.The variable has a single (proxy) amount in each questionnaire (range in all questionnaires: 30,000 to 400,00). It is in ratio scale. All other variables are on 5-point Likert scale.

Pls refer me to the process and justification for converting the ratio data to interval scale (5-point).

Thank you

Dear Sulaiman

As far as I know, it is okay to run your model with both observed and latent variables. SEM needs at least one latent variable and all other variables can be observed. There is no need to convert your ratio scale to interval one!

Hope it helps,

Farimah

Hello, my name is Dela. Now, I'm doing data processing for my thesis.

My research is about the quality of marriage by Norton (1983). In this questionnaire, there are 5 items with 7-likert scale and 1 item with 10-likert scale

In this case, Im confused, how to process data with different likert scale in one questionnaire? Can I directly score in total score? Or should be standardized first?

Because, in the manual book that I found, it is not explained further how this statistical processing. However, it is only explained that the total score gained from this questionnaire will illustrate how the quality of the marriage is perceived by the individual.

I ask for an explanation of how to convert data into standardized data, especially in SPSS. Thankyou for your help and information, it means a lot for me..

@ Dela Aghnia Maraya : There are two ways to do it systematically: either you take the time and trouble of learning about statistical Rasch modeling or its generalization called Item Response Theory or you apply the non-statistical but more straightforward approach I have worked out under the assumption that your respondents give roughly reliable and stable responses, i.e. without too much noise.

In the latter case, and if you opt for that approach, I can give you the simple formula to standardize your k-point Likert scales (for any integer k) into standard bipolar Likert scores ranging between -1 and +1. Once you have standardized, there is another simple formula to calculate weighted averages or means, either for a single person (over all scales) or over all persons (per scale or using all scales simultaneously). You don't need SPSS for that, an Excel-sheet is all you need. Depending upon the number of data you have, it will take just a few days to get the answers you need.

Of course, if your supervisors insist on a statistical approach, there is currently no way around some sort of Rasch modelling, but that will take some months to understand and apply.

• I am no fan of Rasch and IRT, because they tacitly assume that your user's responses may be thought of as lying on the real line, i.e. neither bounded below nor bounded above, because only then you can add scores in the usual way. But bounded scores behave diffrently, they have to be added in a completely different way. If not, the results will be inflated or biased conclusions, although they won't tell you this when using SPSS or similar statistical packages (unless you read the "small letters", of course).

Sample-Likert-Scales.pdf

[last update: 2018-03-12]

Thanks Noor Atikah Zainal Abidin for sharing with us these 5-point and 7-point Likert scales. Some remarks for those not so much acquainted with the meaning and use of Likert scales:

• A Likert scale is a qualitative (ordinal) scale. The symbols "1", "2", ... attached to the points are not numbers, they are just anchors ("points") chosen in the same way that rulers do: they indicate some points ("anchors") on the underlying scale usually assumed to be spread out more or less evenly.
• There is no intrinsic restriction to 5 or 7 points. In fact, you may set up your own n-point Likert scales where n is different from 5 or 7. For obvious pragmatic reasons, however, Likert scale experts favor scales with not too many points, i.e. anchors, and to use *only* the anchors when rating, but obviously this is just a convention.
• Mostly, a Likert scale will have an uneven number of points: (3), 5, 7, 9, (...). The argument is, that there should be a "neutral" point in between, so that people get the option of not deciding between negative or positive scores. Some Likert scale in use, however, force people to decide between a positive or a negative score: these scales have an even number of "points" or anchors.
• From the foregoing it follows that there are two different types of Likert scales: either the underlying numeric scale is the bounded interval between -1 and +1 (with neutral anchor) or the underlying numeric scale is the bounded interval between 0 and +1 (without neutral anchor).
• It is best to think of the leftmost anchor (i.e., mostly "1") as the lowest possible score and the rightmost anchor (e.g., "5" on a 5-point scale) as the highest possible score. Thus it makes no sense at all to assign a rating below the leftmost anchor or a rating above the rightmost anchor. In fact, they should be treated as -infinity and +infinity, respectively. Mathematically there is a simple way to transform Likert scale ratings to real (decimal) numbers such that the above remarks get a "real" sense.
• Where the rest of the anchors will be positioned on this numeric Likert scale depends upon your assumptions: if you assume (without verifying) that the anchors are evenly spread out, the anchor positions are fixed once you fix the number of anchors; if you don't assume the principle of even-spread, you have to do some empirical research (see the literature) to find out where the anchor positions are best located. In the last case you will plausibly find that indeed the anchors are not evenly spread out, but cluster more and more to both endpoints of the scale.
• Once you have the scale points of the anchors (Likert-points), you can apply the Likert algebra (see my previous contribution) to calculate sums, differences, means or whatever you need to get aggregated scores over test items and/or respondents.

Interesting, from the previous conversation, gave a slight insight to my current problem. However, it is not clearly for my case. In my study questionnaire, the variables I am interested to run a factor analysis for my new measure 'uncertainty avoidance', are on 6- point likert scale, 9- point scale and a 4 -point scale.

I understand that its advisable for all the variables to be similar in scale length, so they contribute equally in the new scale formation. And I saw in the conversations here, that a z score can be used before performing factor analysis. If so, should all be standardized or just the different one. For eg: most of my variables are in 6 likert, only two are in 4 and 9 likert scale. Any experience or way forward for this?

I would appreciate a timely respond. Thanks in advance!

Thanking for asking Awa.

z-scores are calculated for all the variables to make them standardized, that is having values between -1 to 1. If you calculate z-scores for 4-point and 9 point items only, it will be difficult to interpret results of factor analysis.

Thank you for the timely respond, Ali. In the sense that all have to be standardized. What likert scale should be chosen for all the variables? The 6 likert , since it has the most?? How is the scale determined anyway?

Also, I read a few post that converting the previously used scales ( Switching of scale in general) may create a problem of not been able to compare your results to other results that were obtained with the old scale. How do I go with this? I forget to mention that I will run some regression after my factor analysis ?

Two citable sources are:

Preston, C. C., & Colman, A. M. (2000). Optimal number of response categories in rating scales: Reliability, validity, discriminating power, and respondent preferences. Acta Psychologica, 104, 1–15. https://doi.org/10.1016/S0001-6918(99)00050-5

They used the following formula to match scales with different numbers of response categories: …(rating-1)/(…number of response categories-1)*100

Dawes, J. (2008). Do data characteristics change according to the number of scale points used? An experiment using 5-point, 7-point and 10-point scales. International Journal of Market Research, 50, 61–77. https://doi.org/10.1177/147078530805000106

He described also an alternative way by anchoring the scale end points.

Correlation-based analyses won't differ, but if you have to use mean differences (like in a pairwise t test), you will get biased results if variables aren't rescaled. Of course, both variables should be interval-scaled and measure the same construct (e.g., positive affect with a 5-point or a 7-point Likert-type scale).

@ Youssef Boudribila: "I do believe that, depending on how you want to combine your scores, you need to bring them to the same scal[e] either by normalization, or using equating methodologies such as equipercentile equating method(s)."

• These two options represent the popular wisdom coming from elementary statistics. Unfortunately, this is not enough and may lead to (gross) errors. Indeed, plain normalization and equating are simple to do, but their simplicity is misleading.
• The problem is that those elementary statistical approaches don't respect the inherent structure of (ordinal or interval) n-point scales. Those scales possess a structure of their own (sic!), which can be modelled in a rigorous mathematical way.
• Knowing the rules, it is not difficult to work out the optimal way of merging any number of items on n-point scales, where n may be different for different items/scales. I have done this even for the problem of peer assessment, where you have to merge two completely distinct scales/scores, each based on ten or more n-point items.
• Statistics may be used to figure out how many items to use, which items to use, and how many points on a scale are reasonable. But if you don't take the underlying scale structure into account, your results and conclusions will be false, anyway.

My offer: if you have an example of a questionnaire or test with different anchor points for different items, and want to know how to correctly "equate" them without any statistical hocus-pocus, please send me the data and I will quickly show you the correct solution. Don't forget to tell me how you would like to report the conclusion, i.e. which format of the merged scales you would like to use, e.g. a 5-point scale or a 7-point scale or even a percentage scale (101 points).

Paul Hubert Vossen : Thank you for sharing your point of view. You may have a good experience in this field from the mathematical point of view. I do respect it and would like to know it. I can give a simple example not from education system but from labour market when the subject is to score skills or abilities required for a given occupation. There two scales from 1 to five and 0 to 7 for the same items. The first interval for the importance of the skill and the second for the level. If you are interested to convert from to the other I will send you the data. Thanks.@

Youssef Boudribila : Yes, I would like to share my knowledge with you. It will also be a good opportunity for me to see whether I have overlooked an important aspect which didn't occur in the educational context (up to now). From what you told me, I infer the following:

• You have two scales each measured by the same number of items N. Let's call them scale A for skills and scale B for skill level. On face value I would say that scale A is the more important one, so I would suggest to take scale A as the primary scale and scale B as the secondary scale. This matches quite well with the inherent structure of Peer Assessment, so we may as well adopt the same approach/method.
• Probably you are using some sort of a 5-point Likert scale for A and a 8-point Likert scale for B. I assume (until you tell me otherwise) that both scales are ordered from low to high. If not, we may reverse the order during analysis, although it is known that there may be small numerical differences in scaling when negatively poled items are used.
• Unclear is still, whether there is a sense of "negative answers" versus "positive answers" for both scales or for one scale, but clearly scale A has a midpoint (anchor 3) and scale B not (somewhere between anchor points 3 and 4).
• Let's assume that the items are just graded from low to high, with an absolute zero at the left end of the scale. Then I suggest to convert all "points" to the standard scale from 0 to 1 (representing percentages, if you like).
• Are the scale points ("anchors") spread out more or less evenly along the scales (case "symmetry") or do you feel (and did the respondents feel too) that distances between the lower anchors are larger (clearer) than distances between the higher anchors (case "non-symmetry")? It may be possible (I have to check that on the basis of your data) to infer which case (symmetry or not) applies for scale A and which for scale B. For the moment, let's assume that we have a case of non-symmetry for both scales, which is the more common case too in an educational context.
• Now we have uniquely defined which model to apply: it is the model with standard scale [0,1] and where it is not true that distances between the anchor points are evenly spread out. This model comes with some fairly simple scoring formulae, i.e. how to calculate averages and how to calculate a single final score for each respondent from his score on scale A and his rating on scale B.

So, my approach not only "equates" the scales (in the sense of mapping both to the same standard scale [0,1]), but - more importantly - gives you a nice standard way of merging the separate scores A and B into a single final score between 0 and 1.

Of course, if you like, you may "translate" those numerical scores back to 5-point, or 7-point scale, or even to a percentage scale with 101 anchor points. That's up to you.

Hi Paul, thanks for all of your input. Can you give me your opinion on whether it is possible to compare 2 sets of items, one with the anchors "strongly disagree," "disagree," "agree," and "strongly agree," and the other with the same anchors, but with a mid-point "neither agree nor disagree" added? It seems that any math I run, from a simple equating, to modeling the spacing of the responses for each item, to using IRT for each item, would ignore that identical anchors exist between the 2. Is this permissible because the anchors themselves are not as important as how they function within the structure of the scale? Or does it make more sense to code the 4-point scale with the 1st, 2nd, 4th, and 5th points of the 5-point scale?

Hi Naomi: This is an interesting situation which I didn't think about before. In fact there are two strongly related issues: (a) how to map the categories (verbal anchor points) onto scale numbers? (b) how to assure that your respondents mentally associated the categories in the same way you did (or intended to do)?

Issue (a)

Can be boiled down to the question: Is the first scale intended to be like the second scale, i.e. with an implicit midpoint in between "disagree" and "agree" such that we get "equally-spaced scale points", BUT with the added restriction not to use that midpoint (i.e., forced choice)?

• If so, then, yes, you should equate all 4 common categories and see to it that distances between numerical scores "respect" this invisible/dropped midpoint.
• If not, don't equate in a numerical sense and accept that both scales have equally spaced anchors so that e.g. the answer category "agree" gets a different score on the first scale as compared with the second scale.

Issue (b)

Whether you opt for case 1 or case 2 is not enough. Your respondents should be aware of how you intended the categories to be interpreted and used. In particular, they should know that the intended distance between "disagree" and "agree" on the first scale is twice the distance between the answer categories on the second scale. BUT: respondents on the first scale have no way to let you know how strong their opinion on "disagree" versus "agree" was before they made their "forced choice"!

Recommendation

It's a tricky situation. Adopting afterwards one or the other assumption on how your respondents thought about the difference between both scales seems to me to be very risky. In order to find out if you have to worry about the differently framed scales I advise the following. Perform THREE analyses (assuming that it won't take too much time to do and would substantially guard you against objections later on):

Then compare the results of all three analyses. Any unexpected or strange differences, which you can't explain away?

Of course I hope that you will find that all three analyses lead by and large to the same conclusions, which may be taken as proof that the respondents behaved more as less in the way you intended.

Hope this helps.

Thank you *very* much for the thorough response! I will perform all 3 analyses on the data.

I am using two valid and reliable surveys for my data collection; however, I want to make major changes to one item. One survey is a 5-point Likert scale ranging from 1 "Strongly agree" to 5 "Strongly disagree." The other is a 7-point Likert scale ranging from 1 "Strongly DISAGREE" to 7 "Strongly AGREE". Is it possible to create a single survey that uses a 5-point scale that converts the 7-point scale to 1 "Strongly agree" to 5 "Strongly disagree" scale?

Dear Robin

Did you read my suggestions on a similar question some months ago, just a few posts upward?

Paulus

How can I convert different point Likert scales for all questionnaires in a survey so that they are the same?

Before conversion, it also depends on whether you'd collected data from the field already or not. E.g. if you haven't collected data yet, I prefer convert all questionnaire to either 5-pt or 7-pt Likert scale i.e. if not too many questionnaire items per questionnaire, I will use 7-pt because because it offers more variance than 5-pt Likert scale. If there are too many questionnaire items per questionnaire, then 5-pt Likert scale can be considered in order to avoid fatigue experienced by the survey respondents.

In the event data had been collected for various 7-pt, 5-pt & 4-pt questionnaires then you should convert all to 4-pt because you can only convert from longer to shorter scale & not the other way round to avoid fabrication of unnecessary data points.

Paul,

I did. Thank you so much for all the great resources. I did not see anything about the order of the scale. Does it matter that they present the scale in opposite orders? Since participants often selected from the first two options and may not consider all options (not sure if this applies to Likert Scale) would this impact validity? I have to conduct EFA due to other changes I have made, but I want to understand if this will impact participant responses.

Also, thank you Han for clarifying that I can convert the scale before the study to avoid mathetatical conversion later- I hope I interpreted your response correctly. . .

Thank you for your responses!!

If you already have collected items on both 5- and 7- point response formats, you should standardize each of them (z-scores) before adding them. Note that this will not affect procedures such as Cronbach's alpha, which rely on correlations, so they are inherently standardized.

This is a problem of finding equivalent scores. Let scores of the 1st scale be denoted as X and the same for 2nd scale be Y. A score of 📷 in scale 1 is equivalent to 📷 of scale 2 if 📷.

A simpler way to find various combination of (📷 would be to draw less than type ogive of the 1st scale and also the 2nd scale. Choose a particular cumulative frequency and draw a horizontal line till it touches the 1st ogive at 📷 . The X- axis value corresponding to 📷 will be equivalent to the X-axis value of 📷.

Finding of equivalent scores in this fashion will permit further operations.

Transforming different Likert scales to a common scale

Troubleshooting

Problem

I have data from a questionnaire which used a 5-point Likert scale last year. But, although the questions are the same, this year the answers were recorded using a 7-point Likert scale. I want to analyze the combined data from both years. How can I transform the data to a common scale?

Resolving The Problem

Here is how to easily find the right linear transformation to convert one Likert scale to another. This is best done in two stages. Notice that a Likert scale is determined by its minimum, which is usually 1, and its maximum, for example 5. First, find the linear transformation so that in the new scale, the minimum is 0 and the maximum is 1. Second, find the transformation which undoes this. That is, starting with a scale with a minimum of 0 and a maximum of 1, transform it so it has whatever minimum and maximum is required.

It is easy to check that for a scale with minimum a and maximum b, the transformation

X = (x - a) / (b - a)

is the one we want. Just substitute a for x to see that the result is 0, and then substitute b for x to see that the result is 1.

To go in the other direction, let's say we want the new minimum to be A and the new maximum to be B. The transformation we want is

Y = (B - A) * X + A

Substitute 0 for X to see that the result is A, and 1 for X to see that the result is B.

Now to put this all together, substitute the whole first transformation in place of X in the second:

Y = (B - A) * (x - a) / (b - a) + A.

That looks just a little messy, but let's apply it to the example of a 5-point scale to be converted to a 7-point scale. Since the minimum of the 5-point scale is 1, we have a=1, b=5 in the first transformation. Similarly for the second transformation, we have A=1, B=7. Putting them together we get:

(7 - 1) * (x - 1) / (5 - 1) + 1

Of course this looks a lot less scary if we do the subtractions:

6 * (x - 1) / 4 + 1

A little rearrangement gives:

(6/4) * x - (6/4) + 1

A little more rearrangement and we get:

1.5 * x - 0.5

So in SPSS we just need

COMPUTE x2 = 1.5 * x1 - 0.5 . EXECUTE.

You can check the results on a small dataset:

x1 x2 1 1.0 2 2.5 3 4.0 4 5.5 5 7.0

In particular, notice that 1 is sent to 1, and 5 to 7.

You should be able to quickly work through the formula to convert a 4-point into a 5-point scale:

(5 - 1) * (x - 1) / (4 - 1) + 1 = 4 * (x - 1) / 3 + 1 = (4/3) * x - (4/3) + 1 = (4/3) * x - (1/3)

Again, notice that if we substitue x=1 the result is 1, and x=4 results in 5.

To convert a 5-point to a 4-point scale:

(4 - 1) * (x - 1) / (5 - 1) + 1 = 3 * (x - 1) / 4 + 1 = (3/4) * x - (3/4) + 1 = (3/4) * x + (1/4)

As intended, x=1 results in 1, and x=5 results in 4.

Hi,

Please could someone clarify what the 'x' in the equation is referring to in the above answer ^ (from Kdv PRASAD Xxx )

I have worked out the necessary equaition for my scales, but I'm not stuck at the 'COMPUTE' step.

Thanks in advance!

I think the solution described in this answer would still work for your case

https://datascience.stackexchange.com/questions/1240/methods-for-standardizing-normalizing-different-rank-scales

If you are applying psychometrics, you do not need to convert the Likert scale. You can use a multidimensional IRT model properly adapted for the number of response keys for each scale/item. Converting Likert scales using some of the proposed procedures is not the most appropriate approach as Likert scale are ordinal measures and operations such as averaging is not meaningful.

[updated 2020.11.04]

I agree with Víthor Rosa Franco if he means "arithmetic average" but using the appropriate quasi-arithmetic mean (see my numerous contributions here) takes much from the objections away.

After all, IRT uses the same quasi-arithmetic operation on scores ASSUMED to lie on the real line. In IRT, probabilities are just calculated as one-to-one transformations from the real line to the unit interval. However, there is no inherent reason or necessity to regards such transformed numbers as probabilities. IRT does it because it wants to apply probabilistic reasoning to its real-valued scores. But there are equally good, sometimes even better, alternative interpretations and reasoning frameworks, e.g., fuzzy logic and mathematics. Indeed, the IRT transformation is just one of many one-to-one transformations which may be applicable in your domain of research.

Often, the probabilistic/statistical framework followed by IRT is simply not required / useful / possible in the application domain of the user / researcher.