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I want to check if the mean value of a certain personality trait differs between young adults in organization X and young adults outside of the organization, who are identical in terms of education and other demographic variables. My plan is to weigh cases in each group and to establish a balance in regards to education and other control variables. Because my group samples differ somewhat in terms of their demographic background (persons in the organization are a bit less educated, younger...).

I tried weighting with R, but the packages to calculate weights (WeightIt) or even just to check for balance after I calculate them manually (cobalt) require me to specify an estimand like ATT or ATE. However, I don’t want to compare the groups in respect to an outcome or treatment, just their initial personality. Does it matter which estimand I choose for this purpose? Or is this whole approach not suitable at all to answer my question?

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The outcome variable is not necessary in either cobalt or WeightIt. However, the estimand is. The estimand refers to which group you want your sample to ultimately resemble: the treated units (young adults in organization X), the control units (young adults outside of the organization), or the full sample. These correspond to the ATT, ATC, and ATE. Other estimands are available, too. You have to make this choice because there are many ways to weights groups to resemble each other; this choice determines what the combined group resembles after weighting.

For example, let's say your treated units have a mean education of 12 years, your control units have a mean education of 16 years, and the overall sample has a mean education of 13 years. Do you want your final weighted groups to have a mean education of 12, 16, or 13 years? Or perhaps some other distribution?

See my paper here (Greifer & Stuart, 2021) for some guidance on choosing the estimand for the problem you are studying. Just because the variables you are studying don't have the same meaning as variables traditional used in propensity score analysis doesn't mean the same constraints and choices don't apply to your problem.

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