appropriate statistics are Mann-whitney U test and Chi sqaure test.

sometime people use  the t-test to compare responses on likert scale but it is not appropratie

Ordinal logistic regression.

Sounds like standard Chi-square test to me for each statement - just compare the proportions in each group who choose each response on the Likert scale. (If some responses are not chosen very much then you will need to combine responses to perform the test as you need E(count) > 5 in each cell for chi-square, although > 1 is actuallly also OK depending which textbook you read.)

The advantage of chi-square as a measure of association is you don't have to score the Likert scale i.e. make unjustified assumptions about the distance between each item being on a scale of 1 to 5 etc. like most researchers seem to.

If you divide your participants into more than 2 groups eg low, medium, high or try to model time spent as a continuous variable then I guess you might what to explore the more complex stats on offer.

Chi-squared is not sensible as it ignores the ordinal scale of the Likert items. Some of the other suggestions seem a bit complicated. Since it is unlikely that the response distribution for each item is Normally distributed, you would be better of undertaking a series of Mann-Whitney U tests.

There is no straightforward answer to this. Technically, virtually all analyses of likert-type data in the sciences that use such scales violate the assumptions underlying the tests (the generalized linear model assumes continuity). However, depending upon the design of the questionnaire, among other things, this need not invalidate the use of such statistical tests. Fuzzy probability was designed from the ground up for this kind of application, but after Zadeh's original work the subsequent decades have shown that 1) often fuzzy set theory offers no improvements over standard tests and 2) there are disagreements among proponents of fuzzy probability measures as to best practices. Item response theory was big for some time but seems to be somewhat a faded fad, and the plethora of statistical measures/metrics/tests designed for these kinds of data, from ordinal data modelling to multidimensional nonlinear descriptive analysis, cannot be readily generalized. So there are several questions that can narrow down the possible answers:

1) How many questions did you ask in your questionnaire?

2) How many participants subjects were in your groups and how were they obtained?

3) If you plot the data for either group, do they appear to approximate linearity?

4) Do the responses seem to indicate either extreme response bias or middle/median response bias?

5) How different do standard tests (e.g., a t-test) yield different answers if you map/scale your data from a 5-point set to a three point (grouping responses into disagree, middle, and agree)? This is a simplistic approximation of fuzzy set theory, but can potentially give you results that, while not in and of themselves useful, can inform you as to what further type(s) of measures are best.

6) What do permutation methods reveal?

Hi Katrin,

Two main considerations: the way that your groups were formed, and, whether you are examining individual Likert-scale items or summing groups of items. You also mention group differences and associations which imply different statistical approaches. So...if you are analyzing individual items you are looking at non-parametric statistics. If items are summed you need to examine the underlying distributions for normality. If the distributions look good you can explore parametric analyses like the t-test that Olga noted (although if you formulated hypotheses about group differences you'd have more statistical power with a one-tailed test). I have always taken Tukey's suggestion to look at my data in multiple ways. Further, I recommend that you consider the comments of the following links regarding Likert items and scales of measurement:

http://mail.asq.org/quality-progress/2007/07/statistics/likert-scales-and-data-analyses.html

http://jalt.org/test/PDF/Brown34.pdf

Good luck with your research! Best wishes,

Nick

Hi Katrin,

Do you want to try only association? or the impact as well?. And what is your criteria variable?. You should think in this issues and maybe try a logistic regression model or propensity score.

best wishes

Enrique

There isn't a fixed answer without further information about the scale and the objectives. For instance, is it a proper Likert scale, a Likert-type scale or a single rating scale item.

For single rating scale items, ordinal logistic regression or a similar ordinal approach may be ideal, but you can often get away with a simpler analysis that treats the response as continuous (e.g., a t test or regression) - particularly if the distribution of observations is unimodal and vaguely symmetrical.

If you are summing items to form a proper scale then most people will treat that as continuous, but again there are more complex models that might be appropriate in some situations (e.g., certain kinds of structural equation model).

T test is best option and you can help from previous research article.

Chi square, as suggested. Often the Likert scale is even used as an interval scale (i.e., the distance from "very bad" to "bad" is equal to the distance from "good to very good"). in that case you could calculate means and compare those means using a t-test.

Is this correct yes or no? I used to say no, the Likert scale is ordinal. However, the same thing is true for numbers. If we ask respondents 'rate this item with a number between 1 and 10 (1 being very bad and 10 being perfect), we interpret the results as a ratio scale. But - is this correct? In most countries respondents prefer the safe middle, which means that the distance from 5-6 or from 6-7 is small, but the distance from 9-10 is huge. If we use these data a ratio data, we might as well use recalculated Likert scales as ratio data. And thus perform a t-test on the means.

Means and variances are arbitrary with ordinal data, and hence the t statistic is arbitrary. With Likert data, the t test is inappropriate and uninterpretable.

If you go through from the literature then you will find that both test ( t test and chi square ) can be used for likert scale data. So if you use t test then you can also justify it and if you use chi sqaure test, it can also be justify.

I am aware that some people in the literature *claim* that the t test can be used for Likert scale data. Just because people claim something in the literature does not make it true. There's plenty of bad methods advice that gets published.

Richard: I broadly agree. Nevertheless, you can certainly use a t test with rating scale data (true Likert scales are something different). Sometimes this is a bad idea, but at other times it will give you similar results (in terms of inference) as ordinal logistic regression. For example, comparing two groups on a 7 point scale with a mean of 3 in one group and a mean of 5 in other group and SDs of say 1.5 in each group and n of - say - 20 per group. For a hypothesis signficance test the ordinal logistic regression will give broadly similar answers.

For prediction the ordinal logistic regression is a superior model (e.g., avoiding silly boundary issues) and if the assumptions of the t test are badly violated it is the better model.

My view is that the models we use are always approximations and sometimes it is OK to go with an approximate model that has good properties in the current situation (e.g., a t test for rating scale data). However, this requires awareness of the limitations of the model and the willingness to check assumptions.

When you are trying to build a principled argument, the fact that one method *sometimes* gives the same conclusion as another, more principled method does not mean that an argument built on the first method is a good one. Science does not rest on conclusions, but rather forming good arguments. An argument based on a t test with ordinal data is deficient due to the arbitrary assumption of a transformation, regardless of whether it would sometimes agree with an ordinal regression analysis.

Or maybe we can put it another way. If the two analyses disagree, we would go with the ordinal regression analysis because it is more principled. To know whether they disagree, you need to do the ordinal regression analysis. But then what was the point of doing the t test at all? Your conclusions don't actually depend on it, because you'd go with the ordinal regression results regardless. The only reason why you'd ever go with the t test is if you *couldn't* do an ordinal regression analysis. But I think we can all agree that someone who is tasked with analysis of ordinal data should at least know how to perform an ordinal regression analysis. There is no cost of going with the better analysis, and plenty of benefits.

I think this is a strong assumption: "There is no cost of going with the better analysis, and plenty of benefits." There is a cost - which could be time, training/skill, comprehension, access to software, ease of communication. If these are always zero then the choice of procedure is trivial. In the present example, presumably the student would have to learn a new method from scratch, acquire software, learn how to use it etc. - all in a few days or weeks in order to meet a deadline.

It isn't necessary to do both tests to know if they disagree (though sometimes that is sensible if you wish to report a simpler test to a particular audience - with the proviso that it shows the same pattern as the better model). For instance, if the assumptions of the t test are not badly violated (e.g., approximately equal variances; approximately symmetrical unimodal errors) the two tests will give similar outcomes.

I also think the same argument applies to the ordinal logistic regression - this makes assumptions that are rarely likely to be true except approximately (e.g., proportional odds). One might also argue that no t test should ever be performed - I don't know of any situation in which the model implied by the t test is the best possible one.

This isn't really about the *assumptions* of the t test as much as it is about the meaning of the question the test is supposed to answer. For ordinal data, any monotone transformation of the response distribution is equally valid as a "population", and hence questions about the population means are ill-posed. Before we use any test, we have to step back and say "Is this test answering a meaningful question?" We have to answer this question even before we start making statistical assumptions. Ordinal regression is designed to answer the right question. The assumptions may be violated, and that's something that should be checked, of course, but that's not really the issue here.

OK, that makes sense. I don't see such a sharp distinction between assumptions and the representation of the problem - but I accept that I'm possibly being sloppy. My point about assumptions was more about the conditions under which a bad model approximates a better one. As I said, I prefer the ordinal model here and would generally use it.

However, the pragmatics in context are important. A student comes to me and shows me an analysis using a t test (the she has been taught) that will give approximately the same results as the ordinal regression. Do I tell her to re-run the analysis - using a method she has not been taught and does not understand - to get (to her) the same answer. What I would normally do is to explain that there is a better approach and explain that _in this case_ it produces approximately the same result, but that it won't in general (and ideally explain why). Although this is a hypothetical scenario - it happens (in various forms) fairly regularly. It is also close to the pragmatics of the present discussion - that of advice to an undergraduate researcher with presumably no training in ordinal logistic regression and a tight deadline (I'm making assumptions here - but fairly reasonable ones).

More generally I find researchers very reluctant to abandon a bad approach unless it actually fails in their particular case*.

* Generally I have worked with researchers who will not simply publish the wrong model if it gives the desired answer (but I know that may also happen).

Another approach to analyzing likert-scale variable is the cumulative logit model, see Allison 1999 "Logistic Regression Using SAS" or numerous other references - just search "likert cumulative logit". This model assumes that the effect (usage level) affects all but one category roughly equally (i.e. pushes all higher or all lower by some amount), and that assumption is usually tested.

I believe the cumulative logit model is probably another name for the ordinal logistic regression. One generally models the cumulative logit through thresholds or cut-offs and assume that the predictors have the same effect on the outcome on the log odds scale (and hence the this is a proportional odds model - the effects aren't equal on the odds or probability scale).

i haven't seen this one being mentioned in any replies so:

generally, i think your question is more of a regression-type problem (low/high predicting reported problems, if i got that right). this would ideally be an ordinal logistic regression with a (dummy-)coded predictor.

however, if you are interested in association and can't or don't want to have this regression-like "if -> then" setting, you could try a log-linear model. technically it's a GLM, usually with a log-link and a poisson distribution for the dependent data which would, in your case, be the observed frequencies of the contingency table of both variables.

the major advantage over a chi-squared test is that you don't just get a result telling you it's significant/non-significant, but you get parameter estimates that tell you the strength of association between groups and the likert-categories. the "saturated" model would be y = group + problems + group:problems. (y is the count variable resulting from your 2-way contingency table and the variables group and problems would be coded predictors.)

so first, you can test whether the interaction between group and problems is significant (association). that'd be a likelihood-ratio-test comparing the full model (2 main effects + 1 interaction, as above) against a model with only 2 main effects. if it's not significantly worse, there is no association (so you can drop the interaction term). if it's significant, you can look at all parameter estimates and also interpret exp(beta) as odds-ratios in this case.

a thing i'd suggest here is to think about the coding for your variables. dummy coding is fine for the binary variable (low/high), but for an ordinal variable, you might want to use some sort of (backward-)difference coding (aka backward-adjacent) - this means that you don't single out a level that serves as a reference for the other levels of the variable (dummy coding), but you test the "gaps" between adjacent categories.

there's a lot of good info about coding and interpretation of categorical predictors at the UCLA's site (spss, stata and r, probably sas as well):

http://www.ats.ucla.edu/stat/spss/webbooks/reg/chapter5/spssreg5.htm

depending on the software you use, estimating this model and doing all the coding, etc. can be quite easy (r/stata) or terrible (SPSS) ... ;)

hth,

marco

I agree with the body of responses here. Chi Square should work just fine. The problem with using the t test is it requires ratio data and that's not what you have with the Likert Scale. The t test is what's called a more powerful statistic but if you wanted to use it here you'd be better off re-running your questionnaire but without using the Likert response format. Instead use one that produces ratio data.

Use t-test for independent samples for the total score and for sub-dimensions scores of the questionnaire, if any.

Please read the article in the following link

http://pareonline.net/pdf/v15n11.pdf

Use inference techniques that test the hypotheses proposed by researchers. There are many methods available, and the best depends on the nature of the study and the questions they are trying to answer. A popular method is to analyze the responses using analysis of variance techniques, such as the Mann Whitney or Kruskal Wallis.

Simplify your survey data by combining the four response categories (eg, strongly agree, agree, disagree, strongly disagree) in two nominal categories such as agreement / disagreement, accept or reject, etc.. ). This offers possibilities of analysis. The chi-square test is an approach to the analysis of the data in this way.

What about converting the ordinal data to interval data using Rasch

analysis before conducting inferential statistics? Would it be appropriate to do so ?

You could also use nonparametric analyses. An aligned Friedman rans test or one of Brunner's macros.

See:

http://digitalcommons.wayne.edu/cgi/viewcontent.cgi?article=1480&context=jmasm

http://www.deepdyve.com/lp/association-for-computing-machinery/powerful-and-consistent-analysis-of-likert-type-ratingscales-mV8oHUc4Yn

If you can avoid treating ordinal data as nominal (with chi-sq in mind) you should, because you waste information regarding ordinality. Ordinal logistic regression is probably the best approach, although the "parallel lines test" that one must consider with OLR sometimes indicates that the effects of the variable are not uniform across the groups, in which case it is suggested that you resort to multinomial logistic regression, which puts you back in the "information wasting" dilemma.

What's interesting about this discussion is the fact that 20 years or so ago, when there were no OLR programs, analysts convinced themselves that treating Likert-like data as interval was okay. The number of factor analyses based on Pearson type correlataions and covriance matrices conducted over the past 20-30 years must number in the thousands! This is sort like what anthropologists term a "technoogical imperative" -- when a tool is developed, it's use will be justified.

Thank you for all the input, I really appreciate it. I decided to analyse it using the Mann Whitney test. Seemed to be the most appropriate approach for the sake of my research, and my supervisor was pleased with the results. Chi-square wasn't possible as it expects a minimum count of 5 for each cell, which my data didn't have.

Right -- if it's just a bivariate analysis that should be just fine. That's what the M-U is for!

Data matrix should be of order nxm (n the total number of participants, m the number of items for your questionnaire). Put 5 scores for strongly agree, 4 for agree, ...1 for strongly disagree . Compute total score for each participant and then using t-test for two independent samples to test whether the difference between the two groups significant or not.

I prefer dividing the questionnaire into two fields, first one includes a questions about time and a second field includes questions about problems. After that compute the total score for each field, then estimate a Pearson correlation between the two fields and apply the t-test to test the significance of the correlation .

I suggest Mann-Whitney U test if you are going to compare 2 groups , or Kruskal-Wallis test for 3 groups or more.

Hi Katrin,

is a good option test the normality before. Then choose between T or U.

Article Five-Point Likert Items: t Test Versus Mann–Whitney–Wilcoxon

appropriate statistics are Mann-whitney U test and Chi sqaure test.

sometime people use  the t-test to compare responses on likert scale but it is not appropratie

Yes ....

We can use the chisquare test and Non-Parametric test for comparison of gp..

[email protected]

Chi Square will be useful 

Both the t-test and the MWW can be used.  See: https://www.researchgate.net/publication/266212127_Five-Point_Likert_Items_t_test_versus_Mann-Whitney-Wilcoxon

In conclusion, for five-point Likert items, the t test and MWW generally have similar power, and researchers do not have to worry about finding a difference whilst there is none in the population.

Article Five-Point Likert Items: t Test Versus Mann–Whitney–Wilcoxon

 I suggest you use the chi-square test. It is easy and quite simple. but you need to factor it into your questionnaire in order to test for the significance.

Hi Katrin,

I am suggesting you a publication which may answer your question about analyzing Likert responses.

Article Parametric Tests for Likert Scale: For and Against

Mann whitney U test will be the best to apply in this case as t test assumption will not be valis so, you have to move for non-parametric test only.

Can anyone help me in data analysis regarding my reserach people perception and conservation

You could convert ordinal categorical data into interval level level data using Item response theory models such as Rasch analysis.

Hello Katrin

Almost all kinds of analyses you can think that are applicable on categorical or scaling based data.

For example-

Chi-Square, Median test etc....

Since, it's wrong to take mean of categorical or scaling based data.Median is a suitable measure of central tendency for categorical or Likert scale based data.

I agree with Mishra. However, the most missed part in the discussion is that there are two types of Likert data as classified in literature. 1) Likert-type and Likert Scale. So, before deciding which methods to use we have to know what kind of Likert data it is. According to that we have to decide what kind of statistical method to be used.

See

"Analyzing Data Measured by Individual Likert-Type Items"

and

"Analyzing Likert Data"

for better understanding.

All the best.

Article Analyzing and Interpreting Data From Likert-Type Scales

HI Katrin,

I suggest some type of regression.

Have a great day!

--Adrian

Dear Prof. Katrin Bruce,

"If there is a difference between the two groups" , I think an Independent T-test will be appropriate.

Katrin Bruce you can use independent sample t-test.

Article Customer-based brand equity and firms' performance in the te...

For details, you can study this article. In this paper, I have used independent sample t-test to explain the difference between two groups. Good luck.

Katrin Bruce Muhammad Farrukh

Article Applying Multigroup Confirmatory Factor Models for Continuou...

The statistical analysis techniques mainly depend on the type of outcome, here it appears you converted time into binary, so Chi square test or Fisher's were appropriate to test presence of an association. If you also needed to measure the magnitude of the association, you could have used logistic regression to get odds ratios or a technique that gives prevalence ratios if the outcome is "not rare".

The t-test is only suitable for variables that are quantitative; t-test is most commonly applied when the test statistic follows a normal distribution.The Likert scale is not quantitative. There is no "significant difference" with this scale. The difference between 5 and 3 is not the same as 7 and 5 for example

Likert scales are ordinal and mostly require non-parametric tests like Chi square test. If however, one is in doubt, it is recommended to 'exploratively' analyze the data to see if it satisfies the conditions of a parametric test which include normal distribution, homogeneity of variances etc. Based on the outcome of this analysis, if not normally distributed then one may transform the data to get it normal. If after such transformation it still not normal, then there is no other option than to run the analysis using a non-parametric test.

It is generally agreed that parametric tests can be used to analyze Likert scale responses. This will be more likely useful if the data are normally distributed.

You have two ordinal variables (users group and level of agreement). To study the association between two ordinal groups, you may use chi square test for independence a.k.a contingency test. So at the end, you may find whether the level of agreement associated with whether the users are low online user or high online users (when the p-value < alpha).

Unless you have many items measured by Likert scale and you are able to compute a total score or mean score for the "agreement". Then you can go further by comparing the difference in mean score regarding the subject matter ("the agreement") between the two groups.

Following....Important discussion

rasch analysis

It's dependent on your hypotheses.

I agree that parametric statistics should be utilized, Chi Square or Mann-Whitney, but the article that Hershey S Bell posted about comparison of t-test to Mann-Whitney for type I and II errors is intriguing and can show evidence for the use of a t-test.

As per some of the researchers if your data is Likert-type data u have to use non-parametric statistic and for a Likert scale data one can use parametric statistic. I got one paper concluding that one can use parametric statistic to the ordinal data set that violates the assumptions of normal distribution, sample size. etc. There is lot of confusion on this issue.

Hello,

If there is a Likert scale (even for only one variable), only non-parametric methods should be used. Here are useful tips for doing so.

https://www.st-andrews.ac.uk/media/capod/students/mathssupport/Likert.pdf

discussion of the same topic here: https://www.researchgate.net/post/What_statistical_analysis_should_I_use_for_Likert-Scale_data

https://rcompanion.org/handbook/E_01.html

https://en.wikipedia.org/wiki/Likert_scale

Success!

Greetings

I recommend the use of Mann-Whitney U tests. A free program to consider is jamovi due to the TOSTER option that can be downloaded from the JAMOVI library to assess whether there is equivalence between groups or there is a difference in effect.

I recommend reading: Equivalence Testing for Psychological Research: A Tutorial by Daniel Lakens, Anne M. Scheel, & Peder M. Isager

Independent samples T test is appropriate for your research

likert -scale - data based on the rank, median or range—are appropriate for analyzing these data, as are distribution free methods such as tabulations, frequencies, contingency tables and chi-squared statistics.

Since you have two dependent variables (time spent online and reported problems) and both constructs measured on a likert scale...compute a composite score from the total number of items in each construct giving each individual an overall construct score, then check differences between the two group on the composite score of two dependent variables using multivariate analysis of variance (MANOVA)

You may possibly focus on Chi Square or Mann-Whitney. In fact all depends upon your hypothesis.

hello? what would be an appropriate tool to analyze responses from a 9 point hedonic scale? Thanks a lot!

Parametric methods are wrong, unless a "distance" between the elements of the item are defined. Otherwise you're likely to get nonsense.

Same about non-parametric methods for paired (dependent) data - it involves subtraction, which isn't defined here - for the same reason as above.

Let me show you why.

Let's assume it's: 1=very bad, 2=bad, 3=neutral, 4=good, 5=very good

1. is 2 - 1 = 4 - 3? Or is 5 - 4 = 3 - 2? Can you justify that? If so - no problem.

2. what does it mean to subtract 5 - 2? What is "very good" minus "bad"? a "neutral"?

3. what does it mean to calculate arithmetic mean of, say, {neutral, good}? Let's try: (3+4)/2 = 3.5. To which value the 3.5 maps? Is this "neutral and a half"? Or "almost good"? Or "above neutral"?

4. if you have 2 means to compare, say, 4.1 and 4.23, and the difference is statistically significant (just assume it is), what does it mean? Significant difference would suggest different answers. But both seem to point to "good". Yes, it may suggest, that in one group the answers "are generally lower than in the second" - and that's all. Nothing more.

There are basically 2 methods you can use: ordinal logistic regression (proportional odds model) and multinomial logistic regression (if the proportionality don't hold). There's also non-proportional odds model, called "Generalized ordered logit").

Some Likert items have more points, say 0-10. This might be, potentially, mapped to percentages and analysed using the beta regression. But I'm not very convinced, unless the labels are truly "0%, 10%, ....100%).

Likert scales, however, usually combine Likert items, and this is often treated as interval or ratio scale.

Here you could try first, permutation and bootstrap methods (allows you to use parametric tests), if only you have more than, say, 10-15 observations and you don't care much about the asymptotic average coverage probability (in layman's term: the 95% level of confidence may not be actually 95%, but, say, 70%). But you still can speak about means and confidence intervals (I suggest using the BCa ones).

Alternatively, you can use non-parametric tests, but you're likely to loose the interpretation. Remember, don't interpret the output of the Mann-Whitney or Kruskal-Wallis in terms of medians, *unless* the distribution is symmetric (not necessarily normal; use histogram or QQ plot or boxplots) and dispersions (variances) are equal (Ansari-Bradley test). If not, the null hypothesis of these tests if about "stochastic dominance" and by no means about medians (easy to show even by simulations).

Hope this helps a bit.

Chris William Callaghan, the problem is that it's possible to do it wrong by repeating the procedures that are published commonly without a convincing justification in our own case. A lot of publications contains parametric analyses of Likert items, even as small as 5-items, without any justification or justified like "because it's common approach", which doesn't make it automatically valid. Of course, some of them may justify their choice convincingly. This should be verified every time. Similarly, in many publications authors incorrectly interpret, Mann-Whitney (Wilcoxon) or Kruskal-Wallis in terms of medians, which is incorrect without certain assumptions about the data distribution met (and it's easy to run a simulation and show how nonsensical outcomes it may produce). Same about certain fundamentally wrong interpretations of p-values and confidence intervals, "because everyone else does", which only supports promulgating and spreading it, which only confuses the readers. Even here, on ResearchGate, I was told by some Professor "I use this, because the famous professor XYZ told me he always does it". When I pointed out why this may be incorrect, I got no answer, just ignored (I suppose why). It's very bad for the science, if scientists (people we'd like to trust) do that only because "it may not be published otherwise". I work in clinical research and also can see this approach common, on what I cannot agree, and I refuse to use methods that are formally and sensibly incorrect. Instead I often hear "Adrian, kindly please, more - I insists, do what they ask, because we won't be published otherwise". It's not surprising then to see prof. Ioannidis writing an article " Why most published research findings are false". 

To the point - I would also recommend reading this: https://bookdown.org/Rmadillo/likert/

The author highlights similar issues. After doing that, if the asking person decides that "it's OK in my case, because I can justify it" - no problem. Otherwise, I'd be very careful to not fall into interpretational traps and get rejected or criticized later.

I anticipate many won't agree with me. OK, I'm not a preacher. I just warn and advise to never ignore statistical assumptions without a solid, reasonable, convincing justification.

https://statisticsbyjim.com/hypothesis-testing/analyze-likert-scale-data/

Kaushik Kumar Panigr with the assumption one doesn't do paired analysis. In this case it involves subtraction, which requires extra assumption about the data to be defined and result in sensible (interpretable) results. See my answer above. One, may, however test paired proportions of answers and concordance (Kendall's w for example)

Chris William Callaghan, I couldn't agree more!

You can use ordinal data analysis. There are measure of association for ordinal data.

therewill be test of significance and Hypothesis to be stated and it signify with 0.05 level of significant .Test also will be depend upon population and sample size not only the measurenet

If sample size and data type is Ratio or Interval the parametric test chai squre can be used

If sample size is low Non parametric test will be used considerably data type should be nominal or ordinal that is Mann-Whitney

i think rasch model is the appropriate analysis for RSA

Good question.I appreciate our RG members for their valuable information about statistical analysis for Likert-Scale data .

Depending on the research question, you can use ordinal measure of association including Goodman & Kruslal gamma, Somer's d.

You can use ordinal logistic regression

I think, the simplest and most precise would me to find mean of scores in two categories and put a t test between two means

@Rachita Gupta,

Please find my answer above on why it's probably not the best approach (same about the paired Mann-Whitney(-Wilcoxon))

Briefly:

1. Subtraction is not defined for ordinal items unless a very strong (and possibly unrealistic) assumption is made, that all levels are equally spanned.

If you have: very good=5, good=4, average=3, bad=2, very bad=1,

then you have to assume that: very good - good =average - bad = bad - very bad.

Can you do that? Can you justify it convincingly? If so - OK.

2. Arithmetic mean (and median) will likely produce outcomes outside the original levels.

What does it mean to have 3.5? Is it "average and a half" ? Or maybe "almost good" ? What does it mean to have 4.73? "Practically very good"? How are you going to interpret two means: 3.12 and 3.67? Almost average and about good?

Of course, it's just numbers, so technically you can do anything you want. But you are then responsible for:

a) making assumptions that have to be convincingly justified; if you take wrong assumptions, your entire analysis will be wrong

b) providing explanation for fractional outcomes, that will be acceptable to your readers. You could agree, for example, on threshold =0.5, so 3.51 is good, while 3.5 is average. And 2.51 is average, while 2.5 is bad. But does it sound sensible?

If so - please go ahead. But If you feel you cannot make so strong assumptions, better stick with more relevant methods, like Multnomah logistic regression or ordinal logistic regression (proportional odds model) - If only the assumption on proportionality holds. Otherwise use partial proportional odds model or dichotomize the output and use separate logistic regression.

All those methods are more difficult to perform and interpret (a matter of training) but are formally correct.

Simple methods work well except the cases when they don't.

T-test (let's forget about the problem with subtraction) may tell you that in average your responses are generally lower or higher in certain group, but that's all.

if i had 0.2 euro for each time this question has been asked here I could have retired in 1980. Here are two recent examples:

https://www.researchgate.net/post/Is_the_likert_scale_ordinal_nominal_discrete_or_continuous_ratio_Is_it_valid_to_use_one_of_them_as_an_approach_of_another

and

https://www.researchgate.net/post/Which_is_better_ML_with_bootstrapping_or_MLR_estimation_with_non-normal_data

Note they don't always look like Likert questions. If the DV is Likert use Ordinal Logistic Regression. That is what it was developed for. If an IV is Likert it is ordinal Please follow the links in the above posts,.in order to begin a long journey frought with peril. Just remember that Ordinal means ordinal not anything else and you will survive. May the force be with you. David Booth

Have a look at https://statisticsbyjim.com/hypothesis-testing/analyze-likert-scale-data/

we can use the measure of association Katrin Bruce

We should prefer to use non-parametric tests on Likert-Scale data. However, different researchers use different ideologies.

I agree with https://www.researchgate.net/profile/Vijaykumar_Mishra2

i am doing content analysis on five point scale. Please suggest the appropriate statistical tool I can use