Yes, you can use ANCOVA (Analysis of Covariance) to compare means of control and experiment groups at pre- and post-test, even if the responses are not paired

Dinesh Kumar , can you give an example of what you mean ?

Reynaldo Senra , what do you mean by not paired ? Do you mean that for an Individual A, you know they were in the pre group and the post group, but that you don't know the scores pre and post associated with Individual A ?

Dear Salvatore Mangiafico. Exactly, but to make it worse, some of the students at pretest, didn't take post test. Indeed, some didn't take pretest, but they took postest.

Reynaldo Senra just to be curious: how can you design a pre-post experiment without assuring that you can match the data from pre and post measurements? Isn't that absolute basic??

Rainer Duesing. Unfortunately, I didn't collect the data.

If you are not able to identify the pairs of pre and post measurements, you cannot use ANCOVA, to incorporate the pre measures as covariable. What you could do is run a simple two-way ANOVA, with pre/post as between factor, BUT this will have much less power to detect differences, since you cannot account for the correlation between pre and post measures.

P.S. and in case you would have had the information of pairs, maybe a multilevel model would be appropriate, since you could have incorporated the participants which only delivered pre or post information.

I agree with Rainer Duesing . I would add that you should note in the results that (at least some) of the same individuals are included in the pre and post test, but that the data were collected such a way that you can't pair the pre score for the post score for each individual.

Yes, you can use ANCOVA (analysis of covariance) to analyze data from a Likert scale at pre and post test if the data is not paired. ANCOVA is a statistical method that can be used to compare the means of two or more groups while controlling for the effects of one or more confounding variables. In this case, the pre-test scores could be considered as the confounding variable and the post-test scores as the outcome variable. However, it is important to ensure that the assumption of homogeneity of slopes (i.e., the relationship between the confounding variable and the outcome variable is the same across groups) is met before using ANCOVA.

Mayur Wanjari please explain how you incorporate the pre measures as covariable, if you cannot match the pre and post measurements? This makes no sense since they are uncorrelated (assuming that they are really randomly assessed). If the CV and DV are not correlated, ANCOVA does not make any sense.

Dear Rainer Duesing, that was my thinking because ANCOVA is very similar to linear regression. However in several websites and in one pdf that now in can't find, I have read that ANCOVA is appropriate when the data is not paired. What I have found is the article "Repeated Measures Correlation" and there is written "While ANCOVA can operate on paired data ...." I may be wrong, but this suggests that ANCOVA can be done with not paired pre and post tests.

Reynaldo Senra you are not explicit here, but there are several models, which could be termed "ANCOVA", since they follow the same principle, but in all cases, you need to know which value of your DV is paired with your CV (and of course to which independent group this subject belongs). But to clarify the term "paired data":

1) In your case (when you would have the paring information) you have a paired repeated measure AND between measure (a split plot design). Here, you have the pairing in your focal DV, which has been measured twice (t1 and t2). In case of a random assigment to the between factor, an ANCOVA with t2 as DV, Group as between factor and t1 as CV is appropriate and should have more power as a Split-Plot ANOVA with t1-t2 as within factor and Group as between factor.

2) Imagine a pure factorial between design, where the possible CV is not the focal variable, e.g. 1. factor sex and 2. factor experimental condition. Possible covariables could be income or any other variable you are interested in "to control for" (the problem here is beyond the scope of this topic but look for directed acyclic graphs DAG, if interested). Here is no paired or repeated measures design itself, but you still need to know the pairing of the DV and the CV of course, they have to be paired to account for the (co-)variance of the CV.

3) It gets more complicated if you have the split plot design mentioned above with a within variable and a between variable, but as in case 2) you want to account for non focal CVs. You could analyse your t1-t2 plus between factor designed with a split plot ANOVA AND incorporate an additional non focal CV. I would not recommend this, since the interpretation may get complicated, but it is possible in princinple. It would be something like a split plot ANCOVA, with a reapeated measurs factor, a between factor and additional, non focal CVs.

Therefore, if you want to incorporate CVs, they always have to be "paired" with the DV, but this is not the same as a "paired" or "repeated measures" design. I hope this clarifys it a bit and is in accordance to what you read so far.

Thank you very much for your response. Everything is clear now