It is ordinal, because the responses correspond to a set of ranked (i.e., ordered) categories.

Yes this is ordinal. In my opinion I don't think recording into the same way is necessary. I doubt how possible is it. For example one set of questions may be about satisfaction while other is about agreement. But yes. You can have sets together under same Likert scale based on your purpose. These all depend on your research question and objectives.

Hello Marnie,

I think you've received good advice above about your individual variables being ordinal. With regard to your second issue, I think there are two problems. First, if you swap the direction of your response options mid-way through your survey, participants might be confused or even annoyed, which could have ramifications for the accuracy of their responses and even their commitment to responding thoughtfully. Second, you would need to keep an eye on which way the variables "bounce" when you come to analyse them.

In essence, I recommend using the same response options across your whole survey if at all possible.

But I have just looked at your question closely and I'm not sure exactly what you're getting at and therefore whether I've addressed it appropriately. Pls feel free to get back.

Thank you everyone that is very helpful. Robert Trevethan basically I am using the British election study data and so it is already recorded. I wasn't sure if when I went to analyse my Likert data that because some are recorded with the positive options starting from 1, and some recorded with the negative options from 1, that this would effect my analysis? For example one Likert scale is recorded as strongly agree at 1, and another Likert scale is recorded as strongly disagree at 1. Not sure how to explain it any better, sorry about that, but from the other answers im hoping it won't affect anything.

I think the bigger question is does it matter? Do people use Stevens' levels to guide, to restrict their analyses? Why have statisticians not used these as much as say psychologists? Worth reading Velleman, P. F., & Wilkinson, L. (1993). Nominal, ordinal, interval, and ratio typologies are

misleading. The American Statistician, 47, 65–72. doi: 10.1080/00031305.1993.10475938.

Marnie Ridley, thanks for getting back with clarification. First, however, Daniel Wright's post is worth heeding, and, ultimately, when you presumably form totals from individual items (I'm not sure how you plan to do that, but it needs to be done with some care), you can regard those totals as being at a "higher" level of measurement than ordinal, and therefore appropriate for analysis with parametric statistics.

Second, it seems you're saddled with the way that your data had been collected by others. That's no great problem. When you conduct your analyses, you simply, need to ensure that all your items are swimming in the same direction if you plan to combine them to create composite scores. That can be accomplished easily in SPSS if necessary. There are some helpful YouTube presentations about that. Just google something like "SPSS recode variables YouTube" and you should be able to find them.

Oh, and your friend is a bit off beam in thinking that your variables are nominal.

Enjoy your research!

Daniel Wright. Thank you for mentioning the Velleman and Wilkinson article. I had not seen it before, but I regard it as a delight to read. The authors come across as intelligent, respectful, and knowledgeable about the nature of enquiry. I even think their article should be placed on lists of compulsory reading for students of research methods.

Robert Trevethan the Velleman and Wilkinson should be part of compulsory reading for all students in the social sciences. I could also advice to read Narens and Duncan Luce (1986) Measurement: The Theory of Numerical Assignments, Psychological Bulletin. This article gives references to other literature, but some are hard to grasp, like Krantz, D. H., Luce, R. D., Suppes, P., & Tversky, A. (1971). Foundations of Measurement (Vol. 1). New York: Academic Press.

Measurement relates to the transformations that are or are not allowed. In a recent reply I mentioned the axiom: A+B=B+A. Relating this to scale analysis: is it true that a score of 3 on item A and 1 on item B is identical to a score of 1 on item A and 3 on item B. With 10 4-category items it means that 286 patterns have all the information that the approx 1.000.000 original patterns (4**10) have. With 10 2-category items it means 11 patterns have the same information as approx 1000 patterns (2**10). It may the reason why 4 category items do not fit IRT models.

I'd add Hand's work on measurement to the foundations books (which as Peter Moorer says are NOT introductory). His Measurement textbook ( https://www.amazon.com/Measurement-Theory-Practice-Through-Quantification/dp/0470685670/ref=sr_1_11?keywords=David+J.+Hand&qid=1585498128&sr=8-11 , he also has one which is labelled something like a very small book on measurement that is physically small, so I bought it not realizing this, too small for me to read, so gave to a grad student with better vision). Also there is this paper with discussion ( Hand DJ, 1996, Statistics and the theory of measurement (with discussion), Journal of the Royal Statistical Society Series A-Statistics in Society, Vol: 159, Pages: 445-492, ISSN: 0035-9238 ). I like Hand's writing style. There are other papers too.

Here are ten types of data (not nested levels as in Stevens), five from Mosteller and Tukey, and then I add 5 more when teaching. This is from a draft of book I am working on.

\noindent Mosteller and Tukey's Five Types

\begin{enumerate}[noitemsep]

\item \textbf{Balances}. These are values that range from large in magnitude negative numbers to large in magnitude positive numbers. These are often not transformed. Many of the statistical procedures in this book assume the data are like this.

\item \textbf{Amounts (continuous) and Counts (discrete)}. These are not negative values. The common transformation is to take the natural log (ln) of these values (see Box~\ref{box:ln}), sometimes after adding a small constant (sometimes called a starting value). The transformation is: $x' \leftarrow \mathit{ln} (\mathit{x + c})$ where $c$ is the constant and $x$ is the original variable (.5 is a popular value for $c$). The $c$ prevents amounts and counts of 0 being transformed to $-\infty$, which can be problematic for many statistical procedures. After logging these data are often treated like balances (see also \S~\ref{sec:poisson}).

\item \textbf{Counted fractions (proportions)}. \citet{MostellerTukey1977} use the example of 4 of 37, or $4/37$, magpies having yellow bills. Proportions will be between 0 and 1, and may be 0 or 1 if none or all of, in this case the magpies bills are yellow. A common transformation is the log-odds, or \emph{logit} transformation: $x' = \mathit{ln} \left( \frac{x}{1-x} \right )$. Since the \emph{logit} of proportions of 0 and 1 are $-\infty$ and $\infty$, sometimes a small value (usually $\frac{1}{2}$) is added to the numerator and twice this to the denominator, so that there would be $\frac{4 \frac{1}{2}}{38}$ of the magpies with yellow bills. see \S~\ref{sec:oddsratio} and \S~\ref{sec:logistic}.

\item \textbf{Grades}. Like the A, B, C, \dots{} used in academic assessments. The transformations they discuss are the proportion at each grade (24/78 got a B) or the proportion at that grade or higher (36/78 got a B or higher). Transformations can then be done on these proportions. An alternative is described in \S~\ref{sec:graded}.

\item \textbf{Ranks}. Suppose a physical education class of 20 students run a mile. The times are not recorded, but the finishing order is. These are the ranks. The fastest student is rank \#1 and the slowest rank \#20. \citet{MostellerTukey1977} discuss dividing the rank by the number of students, so the values for this example are from .05 to 1, and treating these like proportions. There are several rank based statistics. These are discussed in \S~\ref{sec:spear} and \ref{sec:ttestrankalt}.

\end{enumerate}

\hspace{-2.5em} Five additional types:

\begin{enumerate}[noitemsep]

\setcounter{enumi}{5}

\item \textbf{Binary}. Binary data are common in education (does a student correctly answer a question). They can be viewed as a type of proportion, but that can only take on two values. The \emph{logit} is often used in statistical models with binary data. See \S~\ref{sec:logistic} and Chapter~\ref{chap:IRT}.

\item \textbf{Text}. This can range from single word responses to books. Analysts look for various characteristics in the text, and this determines how these are re-expressed so that they can be used to explore your research questions. This is the focus of Chapter~\ref{chap:textasdata}.

\item \textbf{Cyclical}. This includes data like days of week. Data like which day of the week students tend to be absent is of interest to educators. Cyclical data can be used in a set of techniques called time series analyses (\S~\ref{sec:timeseries}). These are popular in economics.

\item \textbf{Images (and other messy data)}. In this era of big data, what constitutes ``data'' is expanding. For example, the machine learning program $H_2O$ allows you to input any images, videos, sounds, texts, and numbers and it searches for patterns (see \url{https://www.h2o.ai/}). Messy data for most education examples will be different amounts of data, including text, for different students. Useful transformations will depend on the research questions and aspects of the data. For example, the Baum Test requires people draw a tree. This image could be scanned and various aspects of it that are supposed to be associated with different personality types (e.g., the width of the trunk, the length of the roots, the size of the branches and leaves) could be extracted (or more complex aspects, like those common in machine learning).

\item \textbf{Mixed}. Mixed data data may be a count, how many ham sandwiches did each student eat that year, but also be binary (did the student eat any?). As with the messy data, useful transformations will depend on the research question. For the ham sandwich example, there are statistical procedures appropriate when the number of zeroes in the data set is high and follows a pattern (e.g., zero-inflated models, see \S~\ref{sec:zeroinfl}). Things that would likely predict the zero-component of this model include being vegan and not eating pork for religious reasons. Other mixtures of data types may also have well-suited statistical procedures, but need to be considered individually.

\end{enumerate}

Dear Marnie Ridley

For every item in you scale the data is ordinal data. But when you collect the scores on the total scores for questionnaire or on the sub-dimension, in this case your data will be scale not ordinal. All your items should be recorded in the same way. But, for total scores the issue is different. When make your statistical analysis for the total scores or for the sub-dimensions, you should firstly test the normality distribution of the data. If it is normally distributes then you can use parametric statistical methods.

With my best wishes

Nasser Said Gomaa Abdelrasheed , I do not agree with your message.

Computing a sum score with ordinal data and look if it is normally distributed does not give a scale. You have to proof or show taking a sum score is an admissible mathematical operation. My mentor would you answer 'measurement by fiat', but it is not a 'measurement'. In IRT models, this assumption can be checked. With Rasch and Mokken scaling, one can investigate the admissibility of the summation. With these models the sum score should be necessary and above all sufficient statistics.

When people give me a sum score as you want them to give me, I am calculating the amount of error that can be added to the scale, but also try to see if the sum score is a wrong measure. Sometimes I can see it when I check the questions: some formulations will make a sum score unbelievable. In factoranalyses and IRT modelling the items might have a stronger relationship then implied by the model.

A few years ago at a conference CITO showed how this might work with drivers licenses testing in the Netherlands. They looked at the complexity of the questions: how many objects, how many streets, how many signs. With questions, I look at the objects and the subjects involved. Are the questions in "I", "We (I and them"), "them" form. It can show up as violations for sum scores. In factoranalysis this might show up as residuals >.05 and in IRT models as large chi-squares for two and three way interactions.

Item Response Theory (IRT) has been offered as an alternative way to deal with the scaling of ordinal data for several decades. If it were going to become popular enough to replace traditional methods, that would have happened long ago.

A major part of the problem is that IRT requires at least as many assumptions ("by fiat") to make the actual properties of the observed measures match the underlying models. Plus, the procedures involved are much more complicated than traditional approaches to reliability. If it were somehow proven that IRT produced truly superior performance, then those problems would not matter. In absence of such evidence, the basic response from the world of measurement has been to treat IRT as an interesting niche field.

David L Morgan, IRT does have assumptions, but so do have traditional methods. Reliability and normal factoranalysis require interval level of the data. Both require showing unidimensionality. Ordinal factoranalysis is related to IRT models and shares some of its problems. In IRT models, the assumptions can be tested. I also have some reservations with some of the assumptions and ideas. 'The' dichotomous Rasch model does not exist. It is a class of models. If you set the difficulty to 25 or higher, it becomes close to a Guttman model.

More difficult is the assumption of the scale having a mean of 0 and sd of 1. Across all scales this seems very odd. Some (many?) scales will have an absolute lowest score. In mathematics, maybe the sum 1+1=2 may be the absolute low anchor of a mathematics scale.

Nowadays, I use a host of methods to study scales (including factor analysis, IRT models, network analysis, regression tree analysis). I worked at the teacher education of the university of Groningen and was performing analyses on 15 datasets with 2000+ cases each (see De ICALT leerling-vragenlijst: BIG-data meervoudige schaalanalyses Part 1: voorbereidende analyses) . I have one R/SPSS syntax that performs 7 types of analyses to get a detailed insight.

The results will probably never be published, but I performed Mokken analyses and found two scales without Differential Scale Functioning. For one scale, I performed a psychotree analyses and found that DSF holds for the Mokken scale. The parameters for a GRM were not identical, but lay almost on a straight line.

I begin to think that DIF and DSF are closely related to the observer problem in physics. I start to have some ideas how that can be, but only at a university I could continue my work.

If and when IRT becomes both a) as easy to perform of traditional reliability analyses and b) as widely accepted, then I will pay more attention to it.

David L Morgan, the acceptability of IRT Modelling is growing -fast. In the '90, no dif analyses could be found, since 2000 there are plenty, because of IRT modelling. These types of analysis cannot be done with standard reliability analysis and are harder to perform using factor analysis.

If you have SPSS and add the R functionality, you will get several IRT models in your menu for scales analysis (alongside 'reliability analysis'). That makes it easy to perform, but no less you have to understand what you are doing.

I object to the use of 'easy to perform'. Statistics has become increasingly more complex. Structural Equation Modelling and Multilevel analyses are not more complex then IRT modelling, but if you would say 'leave them out as they are complex', I do not know were you want statistics to go. SPSS has not included IRT modelling in their menu's and that is one of the reasons people do not use it. Most people want drop-down-boxes because it is 'easy to perform' an analysis.

In R, IRT modelling it is not more difficult then an multilevel or sem analysis. Maybe someone will create a Rcmdr to perform a wide range of scale analytic methods.

COnferences like NCME (measurement folks in education) are almost all about IRT, and certainly all the measurement folks in the testing organizations use it regularly. So it is accepted. David L Morgan , you might know it as latent trait modeling, and this makes clear both it and factor analysis are part of the same family.

I think the dislike of both IRT and factor analysis among stats folks is less than it was. As far as "traditional reliability analysis", do you mean Cronbach's alpha?

I have seen a many things written about latent trait modeling over the past 30 years and it, like IRT, remains a niche industry.

By traditional reliability analyses, I mean things that begin with alpha and exploratory factor analysis, and extend from there to confirmatory factor analysis and structural equation modeling.

Given how widespread the use of those methods is, I don't see how anyone can claim that IRT and kindred are competitive. Certainly this could change in the future, but I haven't perceived any trend in that direction.

Well, David L Morgan , I guess we work in different fields. In education and statistics/psychometrics--and those who use multiple choice test--there is much interest in binary observed variables, and it is used more in those niche industries than others.

Yes it is ordinal as you have worded it. On this scale and the agreement scale to which you also refer, I tend to follow the rule highest rating is best/most positive (it therefore follows higher the mean is better outcome), whether perception or attitude. I also apply this to ordinal scales (therefore my rank 4 would be very interested). However why not use a 5 point interest scale where the middle is neutral, this could then be considered as an interval scale?

Your question sparked an interesting discussion which ventured beyond the simplicity of your question. Both arguments/positions have merit and I welcomed the debate

Robert James McClelland , please do not use 'neutral' as middle category. It might be 'as much agree as disagree', but not 'neither agree nor disagree'. The last wording might indicate I am indifferent or unable to provide an answer. Neutral or middle category might (should?) mean: 'i can not decide if it is closer to agree or disagree', but respondents should not see it as being indifferent. If they are, they do not follow the latent structure below the item. I have added a picture to explain. In this interpretation, the range for neutral should be very small (between 48 and 52% in either direction in the graph.

Peter Moore I agree - never use the word neutral. It is the concept of neutral I referred to. If your interpretation of what should be used (semantically) is that sentence i support that as a suitable neutrality.

My suggestions to use such a 5 (or 7) point scale is to move to a position where we can examine possibilities of normal distribution, reliability and employ a wider ranges of statistical measures

Marnie Ridley, in my opinion, the variable is derived from the ordinal scale and can be declared in SPSS in the Scale section (interval/report). Declaring the variable on this scale allows the calculation of parametric statistics (average, standard deviation, etc.) in the case of the ordinal scale, these operations are not allowed.

Usually on the ordinal scale are included only variables that assume a natural, intrinsic order of values: education level, military rank; etc.

Regarding the inverted items, they are used in the construction of questionnaires to prevent the tendency of answering mainly "positive" or "negative" and to increase the attention of the respondents to the questions.

Although it is a technique appreciated in the construction of questionnaires, it can lead to difficulties in data analysis.

In this case, the solution is to transform the inverted items using the Transform - Compute Variable menu.

Best regards,

Marius Babici, you have provided some good advice above, including the need to reverse code responses on some items.

However, and this could be my ignorance showing badly, I am not sure what you're referring to when you have written about the "Scale section" in SPSS. Could you explain, please.

Regardless of that, I suspect that whether variables are regarded as nominal, ordinal, or at a "higher level" of measurement does not put any constraints on the kinds of analysis that can be produced by SPSS. In other words, SPSS will often do pretty much what it's asked to do, which, of course, means garbage-in, garbage-out - or GIGO - at times.

Robert Trevethan, the Scale section I referred to above is the type of measurement associated with the variable, declared by the user in the Data - Define Variable - Measurement menu. In this case, it is about the interval/report scale.

Even if further processing of the variable is set by the user, it is recommended that the variable has set the measurement scale correctly from the beginning.

Best regards,

Robert Trevethan , in SPSS one can set the measurement level for variables. Just as you can set the format. In a syntax you would specify: VARIABLES LEVEL varX (SCALE) or (ORDINAL) or (NOMINAL). Most procedures in SPSS do not react to this information. Except the CTABLES and data mining procedures/regression trees.

You can play with these levels to see if results are different in data mining procedures. CTABLES may disallow specific statistics to be shown. If data are marked as ORDINAL, one can not ask for mean or standard deviations, it will only give counts and percentages. However, changing the measurement method in SPSS doesn't change the variable level as such. But you can play with it and obtain different insides. I do it when using optimal scaling or non-linear factor analyses (GIFI models).

In the 'ancient' program GLIM, it controlled the analyses to be performed.The program analyzed data as a Generalized Linear Model and the specific analyses would be chosen based on the measurement levels of the independent and dependent variables. This is also implemented in R. Some packages in R do not give results when the measurement levels are inadequate. For instance in Rcmd a factor analysis will not be performed if the data are ordinal. As you indicate, SPSS does not constrain users in this way.

Marius Babici, thank you for getting back. I now realise what you were referring to. If I'm correct, I think that, whatever is entered into those fields, SPSS will do what it is asked to do, so researchers need to be aware about use of appropriate statistics. In essence, SPSS often won't, in essence, say, "You can't do that".

Peter Moorer, thank you for getting back, too. I'll keep your information in mind.

Robert Trevethan a neat trick in SPSS is the command 'ALTER TYPE'. It forces data to become another type. For instance turn a DATE-format into text or vice versa. It can be used to check if data read from other sources are what they supposed to be. It is ALTER TYPE variable (type of data, for example ALTER TYPE vara to varz (A255) makes all text variable of equal length. Useful for merging SPSS files (but there are more advanced alternative in the newer versions of SPSS.

For those interested: Springer Verlag has made 400 books available for free during the corona crises. Just go to: https://www.r-bloggers.com/free-springer-books-during-covid19/ . Enjoy. I have downloaded 4 books already.

Among the books free of charge is 'A course on Rasch Measurement Theory' with a nice introduction on measurement (https://link.springer.com/book/10.1007/978-981-13-7496-8).

Taking into consideration all the advice from previous replies, also look into the semantic differential scale.

Since Likert scales involve conclusive statements to which the respondents give their level of agreement, mixture of positively stated and negatively stated questions to eliminate acquiescence bias is another way.

Semantic differential scale does not give a directional statement, rather the evaluative dimension is explicitly given in the choices.

It seems you have reverse scoring for some of your items and this can be recoded accordingly. There is a whole debate on whether Likert scale scores are to be considered as scaled or not. With scaled option, you can perform more statistical tests for sure. There is no right or wrong way as long as you can justify the statistical tests you use! Wish you the very best!