It's not clear why "ANCOVA has failed", but I assume this is perhaps because your data is non-normally distributed given the emphasis on a non-parametric version like the Kruskal-Wallis. Non-normal data is not necessarily a problem depending on how you model it, but again there is a lot of missing information here which would help elicit a proper answer.

The better option here in my opinion is to just use regression because 1) you can include any main effects or controls that you want 2) you can more flexibly model whatever you want anyway. If for example your response is nonlinear or binomially distributed, then these can be easily handled with regression, whereas even a non-parametric ANOVA serves as a statistical fire blanket that doesn't allow any real specification in modeling.

REFERENCES:

Nelson, L. R., & Zaichkowsky, L. D. (1979). A case for using multiple regression instead of ANOVA in educational research. The Journal of Experimental Education, 47(4), 324–330. https://doi.org/10.1080/00220973.1979.11011701

Plonsky, L., & Oswald, F. L. (2017). Multiple regression as a flexible alternative to ANOVA in L2 research. Studies in Second Language Acquisition, 39(3), 579–592. https://doi.org/10.1017/S0272263116000231

ANCOVA is failed because conditions were not satsified such as leneves test of nornality. How to control the covariates in regression model and how to interpret findings in spss.

Ibappreciate your references.

How to control the covariates in regression model and how to interpret findings in SPSS?

A common misnomer is that ANCOVA can include control variables but regression cannot, but ANOVA and ANCOVA are just special cases of the regression and the general linear model (along with the articles provided, see Cohen et al., 2003, p.4). Any time you enter a predictor into the model, you are controlling for the effect of the predictor after the inclusion of other predictors. This is what is meant by typical slope coefficients when one says "this is how much x increases y when all other predictors are set to zero." ANOVA and ANCOVA are not special in this regard.

ANCOVA is failed because conditions were not satisfied such as Levene's test of normality.

The Levene test is not a test of normality, but rather a test of equality of variance. This is not necessarily a problem in the regression context. Because the residuals are conditional upon all the terms entered into the model, this can actually completely disappear depending on how the regression is modeled. Even if the assumption of heterogeneity of variance is not met, it may not even matter anyway. From Gelman et al. (2022, p.154):

Unequal error variance (also called heteroscedasticity, in contrast to equal variances, or homoscedasticity) can be an issue when a regression is used for probabilistic prediction, but it does not affect what is typically the most important aspect of a regression model, which is the information that goes into the predictors and how they are combined. If the variance of the regression errors are unequal, estimation is more efficiently performed by accounting for this in the model, as with weighted least squares discussed in Section 10.8. In most cases, however, this issue is minor.

If one is deeply concerned about this assumption, there exist robust methods such as location-scale models which can overcome that issue.

Reference:

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed). L. Erlbaum Associates.

Gelman, A., Hill, J., & Vehtari, A. (2022). Regression and other stories. Cambridge University Press.

Thanks for the the answer but my concern is that I dont want see the effect of X on Y infact I want to see the difference in the outcome variable when comapring three groups while controlling for covariate. So did I miss something basic? I am not sure.

The regression does both (group comparisons and control for the influence of the additional covariate). Typically this is achieved via dummy coding, where the contrasts are used against the reference group (to see the differences in their conditional means) or some kind of estimated marginal means (EMMs).

Thanks Dr. Shawn for your prompt and quick reply. I really appreciate if you could suggest a video or a document for showing how to do this analysis and reporting in the manuscript.

The above references should provide a lot more insight than any single video could. But to simplify by a lot: you can just dummy code your categorical predictor, fit the model to the categorical predictor along with your continuous predictor, and make sure you fit the regression to the proper residuals.

Thanks shawn. I will look into it. I really appreciate your time for responding.

Shawn I have a quick question. how can I dummy code my continuous predictor as it is on continuous scale.

You should only dummy code categorical variables. You should never dichotomize continuous variables. Primarily because it comes at a severe loss of information. Simply enter the continuous variable into the model instead. See reference below.

Royston, P., Altman, D. G., & Sauerbrei, W. (2006). Dichotomizing continuous predictors in multiple regression: A bad idea. Statistics in Medicine, 25, 127–141. https://doi.org/10.1002/sim.2331

thanks Shawn for the response but it is shame for me that I don't have access for this article as it asking for payment. I would really appreciate if you could share the copy of this reference.

No problem. I will send that specific article by DM, but I will also note that p.19 of this book is also very informative:

https://warin.ca/ressources/books/2015_Book_RegressionModelingStrategies.pdf