Pre-campaign A/B Testing - T-test / ANAVA

Hi this is my first post.
I have created my campaign selection criteria which produces a subset of my database. I am now attempting to ensure that they are randomly split into equally sized ‘test split’ groups (eg, Test & control populations) ensuring each of the two splits are not skewed for some identifiable ‘key’ variable/s. For example, age - so average age between test and control are equal.

In a past role I used a simple T-test comparing the age means of the two test splits and when the null hypothesis could not be accepted then the splits were scraped and new random splits produced and tested again untill they could be accepted.

  1. Is this process overkill or a sensible way to limit occasional skew in test cells
    that random splits may introduce?

  2. If Gender was a key variable how do I test the gender splits in a similar way? Gender is nominal data and T-tests need to use ordinal data, right?

  3. T-tests are usually used for small sample sizes. In this case, 100% of the identified target audience (a subset of the database) is being selected and split into two smaller test & control groups. Therefore:
    a- is the T-test still appropriate and
    b- at what volume is it no longer a small sample size, 30+ in each split?
    c- should the z-score be used if each split is GT 30 or is T-test still ok?

  4. For a multivariate test, where there are more than just a control and a single test split, (i.e. more than two spits), is it best to use ANOVA to compare the means?

  5. Can I still use T-tests & ANOVA if the splits are not evenly split (same size)?

Thank you.