# What statistics does one use for a Likert scale?

My data was collected by likert scale. Are they ordinal or interval data? and Can I use Factor Analysis to analyze these data?

Question

My data was collected by likert scale. Are they ordinal or interval data? and Can I use Factor Analysis to analyze these data?

- Likert scale data are subjective numbers, used as labels for convenience in place of descriptors such as "strongly agree" or "neutral" or "disagree." The only property they have in common with real numbers on a number line is order. Because, as Winfried points out, the numbers are not equidistant. That property of equidistance between units is the property that makes addition and subtraction meaningful. Since it doesn't exist with numbers on the ordinal scale, arithemtic with those numbers is inappropriate. The mode may be the only useful and meaningful average for ordinal responses.

What's generally best is to get large enough good random samples (and I MEAN random samples) that you can use the proportions meaningfully. What proportion answered 5? What proportion answered 1? You can do a lot with that information. - Great! I thought that item response theory was useful for creating inventory or tools in general. How can we use it to analyze data? Is it possible to do it using spss or we need other software (stata or others)?
- Thanks for the references, Jan. I am familiar with item response theory, and have seen it used well in some studies where careful construction of items and scales, along with good validation, produced reasonable results. I don't think that's the standard when using "Likert scales" for many applications, though. Most of the surveys I've seen done have been done using ordinal labels for opinions and were administered and/or analyzed by people who not only don't know anything about IR methods, they don't know the difference between nominal, ordinal, interval and ratio scales of data. They think that by assigning numbers they render the opinions objective, and they calculate means and standard deviations--they don't understand that these "statistics" have no more meaning than an average phone number. It's especially harmful when they allot too much importance to tiny increments...I have seen someone call the mean of a set of responses an outlier because it was 1/100th of the increment between "Very dissatisfied" "very satisfied" lower than the cut-off for a 95% confidence interval.

So, I'm always skeptical. If you can prove that your scale has the necessary discrimination to allow for factor analysis, then do it. For most applications I see in practice, it's better to just track the proportions. - Yes, likert scale can be considered as ordinal. Also, your are free to develop factorial analysis or other parametric measures. Check Jan Rasmus posts. He is right.
- There is also another solution. You can always make an index (of course remembering about validation) out of variables meassured on ordinal scale (eg Likert scale). Then you are able to count mean and other parameters unattainable on lower levels of meassurement. It actually works - it is described for example in "SPSS Survival Manual".
- When you consider Likert scale as it has been done by the Author himself - you have many sentences with five steps of agreement and disagreement, then you check correlations between them (my statistical English is not that good) and you pick up those that correlate. This gives "the scale" itself. And that is actually a moment to put it into the survey. If it is done properly, you can make an index out of all sentences (variables if you consider the level of agreement/disagreement). One may (should) check eg. Cronbach's alpha (with all its disadvantages). But you receive index that is on higher scale of measurement. Writing "it actually works" I meant that it is quite convenient solution for more sophisticated analysis - giving a new variable on interval scale. I've been using it from time to time.

It is not that advanced as IRT (which I find completely interesting, but I don't know much about it). However, simple but convenient. - If you assume Likert scale data you've collected as interval data (which is reasonable in random sampling), then you can apply analysis of variance technique for analysis.

Besides, Likert data is generally a summative scale.. you can sum some of the items into a group and collectively analyze. - Since Likert scale usually measures a level of agreement or disagreement with the statement you are asking from the respondent's oown opinion, i(usually a 5-point or a 7-point) then, it actually means a more of an interval data .... though the intervals may or may not be equidistant in value .. for example, the 5 point may correspond to the values -10, -7, 0, 7, 10.. or even as -10, -7, 1, 6, 8 ... these are hypothetical cases... so in reality assigning numercial value to them is a difficult task for caluculating variance..
- I agree with Abhishek. Likert scales are mostly summative and sum of scores can be calculated and analysed accordingly.
- Writing about index I meant summing variables ;) (eg. SPSS: summing)
- @Mateusz, I agree, You have written all the procedure. I am also doing the same thing. Cronbach's alpha is always good to identify the internal consistency of the scale before creating an index (sum of score).
- Likert scale is ordinal method, answer type direction is for example: "Not satisfied"(0), "Some Satisfied" (1) "Satisfied"(2) "Very Satisfied"(3) "Extremely Satisfied"(4) and so...frequently use 5 categories, but not always, yes you can use Factorial analysis for identify the "Principal Components (each component is composed by some questions)" method is frequently used and setting SPSS option "Eigenvalue" to 1.0 if you think every factor is independent from others, if not...the researcher can change it to 2.0 or three, I suggest study this theme. You have to know about "rotation solution Technique"(Varimax, Orthogonal, etc.) adequacy, after...have to apply criterions (e.g. Bartlett determinant, KMO, etc.) to qualify the data how good for factorial analysis or not, and THEN...you can configure in SPSS the database...of course I have the belief you have dependent variable...(Yes/No)
- Yes, I have used SPSS and it is much simpler and nice to use it...better to use it for analysing data ..
- In psychology, we almost always think of Likert scale as interval scale, because we suppose that the intervals between every two successive options are the same size. So, in our research we regularly apply factor analysis due to analysing this kind of data. So, it's ok to use FA in this purpose.
- Hi, In u r data collection is it Interval scale. So we use factor analysis for ur data
- In psychology research, it is ok that data come from Likert scale (e.g. 5-point, 7-point or similar), and we use FA (confirmatory of exploratory type). And, we get fine data and we haven't problems with naking our conclusions about that. I mean that using FA in psychology is justified and proved in a that way. And, you can find lots of scientific papers in a prestigious journals where the authors use it in described way.
- For likert scale normally we took weighted averages if data is quantitative and giving ranking method to interpret it but if data is qualitative then better to use garret ranking test,or krushal walis ,man-Whitney like nonparametric tests to analyze and interpret. it,In many of Ph.D . of management streams it is better to use in this way.better way to use MS Excel or SPSS .
- factor analysis is robust for non normal data. in factor analysis we statndardise the variable and then we use FA. but before go to the FA, it is very important to check sampling adequecy of the data by using KMO method and ur correlation matrix it should be diffrent from identity matrix. if KMO values getting more than 0.5 then u can move for FA and u can check whether correlation matrix deffrent from identity matrix or not by Bartlet test of sphericity. then extract factors by using eign value criterion or scree plot. then rotate factors by varimax rotation( orthogonal rotation) , factors should be independent.

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