The standard approach is to test the covariate before testing the independent variable of interest (IV). If the covariate is not significant, it suggests that the covariate had no significant influence on the IV. Thus, the use of the covariate was not needed. In fact, applying the covariate used a degree of freedom that otherwise would have gone to reducing the size of the error term. This would have reduced the significance of the IV slightly. To answer your first question, if the covariate is non-significant, the significance of the IV should be about the same with or without the covariate. To answer your second question, the type of relationships between your covariate or IV and your dependent variable is best determined using linear regression. I hope this was helpful!

Thank you very much! That makes sense. I was under the impression that the covariate had to be non-significant for you to even use it as a covariate. Like in order to meet the two assumptions before performing the ANCOVA, the covariate should be uniform amongst all groups of the fixed variable, and thus non-significant. As well as the product of the covariate and fixed variable should also be a non significant value to prove homogeneity of regression.

James E. McLean, what you have described as the standard approach sounds to me like pre-screening with univariable tests to determine which variables to include in a multivariable model. And many folks nowadays consider that a bad practice that leads to overfitted models. See, for example:

• https://discourse.datamethods.org/t/author-checklist/3407#arrow_rightuse-of-stepwise-variable-selection-24
• https://discourse.datamethods.org/t/author-checklist/3407#arrow_rightlack-of-insignificant-variables-in-the-final-model-25
• https://discourse.datamethods.org/t/reference-collection-to-push-back-against-common-statistical-myths/1787#screening-covariates-to-include-in-multivariable-models-with-bivariable-tests-8
• https://people.duke.edu/~mababyak/papers/babyakregression.pdf

Bhavika Gupta, as you are using SPSS, I assume you used the UNIANOVA command to estimate your model. If so, and if you want to see a table of coefficients, you can get it by including PARAMETER on the /PRINT sub-command.

• https://www.ibm.com/docs/en/spss-statistics/28.0.0?topic=unianova-print-subcommand-command

It will show the same coefficients you would get if you estimated the model with the REGRESSION command, although they will be called parameter estimates rather than coefficients. So in answer to your question, you do not need to use "linear regression", because UNIANOVA and REGRESSION estimate exactly the same model. Of course, if one command has options you want that the other one lacks, that would affect your choice of which procedure to use.

Oh, one other thing: Is your study experimental or observational? If experimental, were subjects randomly allocated to groups? Thanks for clarifying.

HTH.

Bruce Weaver Thank you so much for the valuable info. My study is observational so there was no random allocation. And just to clarify again, my study is still relevant if my IV is significant, even tho my covariate is not? Like i can still say the model predicted significant correlation for the variables while adjusting for the covariate?

Hello Bhavika Gupta. If you have not already done so, I suggest that you make a scatterplot with X = your covariate, Y = the dependent variable, and separate lines by Group (i.e., your IV). It would help members here to better advise you if you showed us that plot. See the attached PDF if you do not know how to add regression lines by group. HTH.