Deborah J Hilton I have used validated questionnaires but I want to compare the effects of age on depression and anxiety, therefore I don't know what effect sizes I need to use.
Which effect size statistic to use usually depends on what analysis you are using. For example, Cohen's d makes sense when you are using a t-test. r-squared makes sense for linear regression. Glass rank biserial coefficient makes sense for Wilcoxon-Mann-Whitney test.
Usually for anova, eta-squared or partial eta-squared is used. eta-squared will be the same as r-squared for a general linear model (including anova).
Other effect size statistics may make sense depending on what you want to know. For example, the simple difference in means (or estimated marginal means) between groups is easy for the reader to understand. (Assuming that the units of the dependent variable are intuitive for the reader.)
It's also possible to calculate Cohen's d -like statistics to compare among groups, although it can be a little complicated in models that have more than two groups to address.