@Dung Chau

You need to form latent variables using the following function in SPSS

Transform>Compute Variable> Set on Statistical formula; Mean

Then create new variable (Construct1) giving a name and averaging the sum of responses for Q1 to Q8. Similarly, create Latent variables 2, 3 and 4. Now you can run Man-Whitney U test taking newly created latent variables through any sub-samples/sub-groups/demographic categories.

Thanks Imran Anwar. I normally follow this way if I compare means between or within groups (Likert scales are treated as interval/ ratio) by using t-tests. However, in the current situation, the mean calculation is invalid if Likert scales are set as ordinal. Is this correct?

Hello Dung Chau,

At first, it is important to note that theoretical constructs (e.g. intelligence, anxiety, depression) are not observed variables but latent. Therefore, treating them as direct characteristics (e.g. temperature, speed, length, height) may lead to important errors and misleading conclusions. A better approximation for comparing latent means is to use structural equation modelling (SEM). Such a technique permits to estimate the scores as a function of intercepts, latent variable effects times the factor loading, and residuals. This is not possible when you use any generalized linear models (GLM) or any equivalent nonparametric method. Note: before apply SEM to compare latent means, you have to verify at least parcial strong invariance across groups.

Having said that, if you still have to use nonparametric approaches, the procedure in SPSS involve to place the dependent variable (i.e. ratings) in one column and the independent variable (i.e. group) in other column. To obtain the ratings, you have to sum all items across any dimensions or factors, just like Imran Anwar explained. After that, you can run the Mann-Whitney U test in SPSS. Also, take care about the assumptions of this procedure:

At last but not least, to compare within groups you should not use Mann-Whitney U test but Wilcoxon signed-rank test.

Best regards.

Hi Juan Hernández-Lalinde ,

Thank you for your answer. In my study, the 5-point ratings (1 "Definitely unacceptable, 2 "Unacceptable", 3 "Neither unacceptable nor acceptable", 4 "Acceptable", and 5 "Definitely acceptable" were used to judge the grammatically of various constructions. Therefore, are these considered as latent variables and I still need to apply SEM? I have never thought of SEM before. This is quite complicated for me.

I understand that the Mann-Whitney U test is a replacement for the Independent t-test and Wilcoxon signed-rank test is a replacement for the paired t-test because of some different assumptions between them. My main concern is that in case I use the nonparametric tests (i.e., the Mann-Whitney U test and Wilcoxon test), do I need to compute the mean values, as Imran Anwar recommended, for each type of construction like t-tests? For the nonparametric tests, I want to treat the ratings as ordinal (not interval) and it is said that the mean calculation is not valid when ratings are ordinal.

Regards,

Hello again Dung,

Q1: Yes, these constructs are latent variables and therefore a better choice is to use SEM over GLM. If you are not familiar with this approach, you can use GLM but be cautios about the conclusions and report your analysis limitations.

Q2: No, don't compute a composite score through the mean of the items. Instead, I recommend to obtain the composite score throught the sum of the items. Once you do that, you can compare these resulting variables with UMW or WSR tests.

Hi Juan Hernández-Lalinde ,

Thank you so much for your comprehensive response. Is AMOS the correct estimator for my SEM analysis in SPSS?

Regards,

Hello Dung,

Yes, AMOS is a great software (under SPSS enviroment) to run a SEM analysis. I also suggest you to study very carefully how to do this analysis. Be cautious when selecting the estimation methods for the Confirmatory Factor Analysis (CFA) and check for Wu & Estabrook (2016) recommendations when evaluating measurement invariance with ordered categorical indicators (ordinal items). These backgrounds are neccesary in order to perform a correct estimation and comparison of latent variables.

Perhaps , there are plenty of videos on this in Youtube

Thank you Juan Hernández-Lalinde and Ahmed Al Asheq !

Please note, that all types of data from assessments on rating scales - no matter numeric, Likert, verbal or Analogue line (VAS) only rank invariant non-parametric statistical methods are appropriate to use. Dependent on the research question you can find powerful correct methods. Do not follow the easy-but wrong way- and pretend that you have quantitative normally distributed data- then you run the risk of invalidating your study - and that is not good research!

Thank you Elisabeth Svensson . In the case of rating scales, is the linear mixed model (multilevel model) a correct method when my datasets are hierarchical? I am going to investigate an effect on the outcome variable (i.e., the ratings).

Dung Chau, that depends on the research question, and also on the type of scale; the concept Likert is mis-used to refer to numeric ordered categorical scales, and not only to ordered levels of agreement to statements.

Hi Juan Hernández-Lalinde ,

As discussed above, you have suggested using sum of items when conducting the non-parametric tests. However, I have just realized that adding or subtracting ordinal data are not appropriate as well. What could I do if I still want to use the non-parametric tests? Thank you.

Hello Dung Chau,

Sorry for the delay, but I've been quite busy with class and research matters. Your question is very interesting; I will answer it as soon as possible.

Best regards