Reference formulas for four main types of comparisons, in particular "comparison of two groups from the same sample"?

[msulwa]

Hi @MamadouSDiallo

I hope this finds you well.

Please may you share the technical formulas for the t-tests implemented by Samplics? I have reviewed the available supporting docs [i, ii, iii] and several stats textbooks, but unfortunately came up short; and I was hoping you could point me towards the textbook with the relevant formulas for the following:

1. • Comparison of one-sample mean to a known mean
2. • Comparison of two groups from the same sample (I'm looking looking for this one)
3. • Comparison of two means from two different samples
4. • Comparison of two paired means

For context, I would like to compare two groups drawn from the same household survey dataset (unpaired), while leveraging the complex survey design (i.e. weights, strata, etc.). I initially thought of using (3) but ran into issues with psus that have 1 observation (and potentially zero observations when splitting into groups). I was not able to overcome the issues despite following the guidance in #33 . I don't experience any zero-division issues when using (2), but I would like to validate my understanding to ensure I can use (2) in place of (3) for my particular use-case.

Sub-sample of psus with 0 or 1 observation

One-sample, two-groups implementation

Two-samples, unpaired implementation

Any guidance would be greatly appreciated.

Best regards,
Baraka

[i] https://samplics-org.github.io/samplics/pages/categorical_ttest.html
[ii] https://joss.theoj.org/papers/10.21105/joss.03376
[iii] http://isi-iass.org/home/wp-content/uploads/Survey_Statistician_2022_July_N86.pdf