Cramers V with weighted data

[Luis Mijares Castaneda]

Hello, I was wondering if anyone knew how to perform a Cramers V with weighted data? I found some code in this old Statalist post below. Would the code I produced based on the blog post below be an appropriate way to generate the weighted test statistic?

  
svy: tab biosex ai_mh, pearson

local denom = min(e(r)-1, e(c)-1)

display "Weighted Cramer's V = " ///
    sqrt(e(cun_Pear)/(e(N)*`denom'))

https://www.stata.com/statalist/arch.../msg00581.html

[Choonjoo Lee]

I was curious about this too, so I checked the formula and tried your code.
It appears correct for estimating weighted Cramér’s V.
Here, “uncorrected” means that e(cun_Pear) has not been adjusted for the survey design; it is still based on weighted proportions.
For significance testing, use the design-based F test’s p-value, e(p_Pear), and report V as the effect size.

Please double check the code below and anyone let me know if this works.

version 16.0
clear all
set more off

* StataCorp. (2025). Stata 19 survey data reference manual. Stata Press.
* [SVY] svy: tabulate twoway, Methods and formulas, The test statistics.
* Entry PDF p. 24 (full manual printed p. 187):
* https://www.stata.com/manuals/svysvytabulatetwoway.pdf#page=24
*
* X2_P = m * sum_r sum_c ((p_rc - p0_rc)^2 / p0_rc)
* p0_rc = p_r+ * p_+c
* m = unweighted number of observations in the analysis sample.
* p_rc = weighted cell count / sum of weighted cell counts.
* This computes uncorrected Pearson chi2, not the design-based F test.

* 1. Artificial example: replace this section with your data and svyset.
set obs 360
generate long id = _n
generate byte x = mod(id-1, 3) + 1
generate byte y = mod(floor((id-1)/3), 3) + 1
generate double weight = 0.7 + 2.3*(x==y) + 0.13*mod(id,7)
generate int psu = ceil(id/6)
generate byte stratum = ceil(psu/10)
svyset psu [pweight=weight], strata(stratum)

* 2. Stata benchmark; save results before changing the data.
* For your data, replace x, y, and weight throughout the code.
* Scope: ordinary pweights, without subpop(), tab(), standardization,
* or poststratification/calibration that changes the effective weights.
svy: tabulate x y, pearson
scalar m = e(N)
scalar X2_stata = e(cun_Pear)
scalar k = min(e(r)-1, e(c)-1)
scalar p_design = e(p_Pear)
assert k > 0 & k < .

* 3. Direct calculation from the individual-level weighted data.
preserve
keep if e(sample)
keep x y weight

* Nhat_rc: sum of sampling weights within each cell.
collapse (sum) cell_w=weight, by(x y)

* Include unobserved combinations as zero cells in the R x C table.
fillin x y
replace cell_w = 0 if _fillin
drop _fillin

* p_rc and its row/column marginals (manual pp. 22-23).
egen double total_w = total(cell_w)
generate double p_rc = cell_w/total_w
bysort x: egen double p_row = total(p_rc)
bysort y: egen double p_col = total(p_rc)

* Null proportion under independence (manual p. 24).
generate double p0_rc = p_row*p_col
assert p0_rc > 0 & p0_rc < .

* Pearson formula on p. 24, implemented term by term.
generate double term = (p_rc-p0_rc)^2/p0_rc
quietly summarize term, meanonly
scalar X2_manual = m*r(sum)

* Optional: derive weighted Cramer's V from the Pearson statistic.
* This extra step is not itself a formula printed on manual p. 24.
scalar V_weighted = sqrt(X2_manual/(m*k))

sort x y
format cell_w %12.4f
format p_rc p_row p_col p0_rc term %10.6f
list x y cell_w p_rc p_row p_col p0_rc term, noobs sepby(x)
restore

* 4. Numerical verification and results.
assert reldif(X2_manual, X2_stata) < 1e-10
display "m (sample size)       = " %12.0f m
display "Pearson chi2 (manual) = " %12.8f X2_manual
display "Pearson chi2 (Stata)  = " %12.8f X2_stata
display "Weighted Cramer's V  = " %12.8f V_weighted
display "Design-based p-value = " %12.5g p_design
display "PASS: manual p. 24 formula agrees with e(cun_Pear)."