CAPIRE — Stratified randomization

Strata construction and block-randomized assignment to treatment and control

library(tidyverse)
library(here)
library(janitor)
library(randomizr)
library(gt)

# Helper: render a janitor::tabyl as a formatted gt table.
gt_tabyl <- function(x, title = NULL, subtitle = NULL) {
  x |>
    adorn_pct_formatting(digits = 1) |>
    gt() |>
    tab_header(
      title = title,
      subtitle = subtitle
    ) |>
    opt_align_table_header(align = "left") |>
    tab_options(
      table.font.size = px(13),
      heading.title.font.size = px(15),
      heading.subtitle.font.size = px(12),
      data_row.padding = px(4)
    )
}

Info

The file documents the randomization procedure from the raw registration data to the allocation to the two cohorts. Please check each step, in particular the creation of the strata variables!

We could opt for a simple randomization, but using strata - randomizing within blocks of variables - leads to a more balanced randomization, especially with small samples such as in our case and no other baseline information.

The proposal is to create a strata which is the crossproduct of seniority of role (managerial or not) x institution type (teritorial, central or other): - this results in 6 strata, with reasonsable number of participants each. - Within each, we assign roughly half to treatment and half to control. So by construction, our randomization will balance these 2 variables, and their product. - We could add other variables, such as gender, or region (north, center, south-islands), but then our strata become very small which is not ideal. If some participants drop out, we risk not having both treated and controls within a given stratum, which complicates the analysis. Using seniority as a balancing variable also likely balances the sample well in terms of age.

The procedure is as follows:

1. Clean the participant list (remove incomplete and duplicate registrations).
2. Build a role stratum and organization type stratum, classifying also open text answers.
3. Cross the two strata to form randomization blocks.
4. Randomize to treatment and control within each block, at approximately 50/50.

1 Data import and cleaning

The raw file is the registration export.

df_raw <- readxl::read_excel(here("data", "capire_participants.xlsx"))

df <- df_raw |>
  set_names(c(
    "timestamp", "email", "name", "surname", "cf", "email2", "org", "role",
    "privacy1", "privacy2", "privacy3", "org_type", "thanks"
  ))

n_raw <- nrow(df)

df |> 
  select(
    # name, surname, 
    role, org, org_type
    ) |>
      arrange(org_type) |> 
  DT::datatable(filter = "top")

n_dupes <- df |> get_dupes(name, surname, cf) |> pull(cf) |> unique() |> length()

There are 221 entries, but one is an empty raw and there are also 7 sets of duplicates.

df <- df |>
  filter(!is.na(email)) |>
  arrange(name, surname, cf, privacy1, desc(privacy1), privacy2, privacy3) |> 
  distinct(name, surname, cf, .keep_all = TRUE)

n_clean <- nrow(df)

tibble(
  Step = c("Raw registrations", "After dropping empty records and duplicates"),
  N = c(n_raw, n_clean)
) |>
  gt() |>
  tab_header(title = "Participants") |>
  opt_align_table_header(align = "left") |>
  tab_options(table.font.size = px(13), heading.title.font.size = px(15))

Participants
Step	N
Raw registrations	221
After dropping empty records and duplicates	213

2 Seniority role stratum

The role field has many responses with free text, which have to be classified.

2.1 Raw role values

df |>
  tabyl(role) |>
  arrange(desc(n)) |>
  gt_tabyl(
    title = "Raw values"
  )

Raw values
role	n	percent
Dipendente	154	72.3%
Dirigente	32	15.0%
Consulente	6	2.8%
Collaboratore esterno	2	0.9%
Assessore	1	0.5%
CAS	1	0.5%
Capoufficio sviluppo e innovazione organizzativa	1	0.5%
Componente nucleo	1	0.5%
Coordinatrice	1	0.5%
Eletto	1	0.5%
Funzionario Ufficio Cultura - Biblioteca	1	0.5%
PM Esperti PNRR	1	0.5%
Prima Ricercatrice	1	0.5%
Responsabile Amministrativo Scolastico	1	0.5%
Segretario particolare del sindaco di Alghero	1	0.5%
Segreteria di presidenza	1	0.5%
Vice capo ufficio di gabinetto ministero università e ricerca	1	0.5%
direttore	1	0.5%
direttrice	1	0.5%
funzionario con incarico di componente	1	0.5%
personale tecnico amministrativo - subalterno	1	0.5%
posizione organizzativa	1	0.5%
ricercatore	1	0.5%

2.2 Step 1 — three categories

The three categories are:

• apicale (senior / managerial). Roles carrying formal managerial or political responsibility: dirigente, direttore / direttrice, capoufficio, coordinatrice, responsabile, posizione organizzativa, vicecapo gabinetto, assessore, eletto, componente nucleo. Please check!!!
• esterno. Consulente and collaboratore esterno — people who are not employees of the organization they registered under.
• non_apicale (non-managerial staff). Everything else - dipendente, funzionario, technical-administrative staff, ricercatore etc.

df <- df |>
  mutate(
    role_clean = str_squish(str_to_lower(role)),
    org_clean  = str_squish(str_to_lower(org_type))
  )

# ---- Step 1: role -> 3 categories ------------------------------------------
df <- df |>
  mutate(
    role3 = case_when(
      str_detect(
        role_clean,
        "dirigent|direttore|direttrice|capo ?ufficio|vice ?capo|coordinatore|coordinatrice|responsabile|posizione organizzativa|assessore|eletto|componente nucleo"
      ) ~ "apicale",
      str_detect(role_clean, "consulente|collaboratore esterno") ~ "esterno",
      TRUE ~ "non_apicale"
    ),
    role3 = factor(role3, levels = c("apicale", "non_apicale", "esterno"))
  )

2.2.1 Check

Please check if OK

df |>
  tabyl(role, role3) |>
  gt() |>
  tab_header(
    title = "Raw role value to the three-category classification"
  ) |>
  opt_align_table_header(align = "left") |>
  tab_options(
    table.font.size = px(12),
    heading.title.font.size = px(15),
    heading.subtitle.font.size = px(12),
    data_row.padding = px(3)
  )

Raw role value to the three-category classification
role	apicale	non_apicale	esterno
Assessore	1	0	0
Capoufficio sviluppo e innovazione organizzativa	1	0	0
CAS	0	1	0
Collaboratore esterno	0	0	2
Componente nucleo	1	0	0
Consulente	0	0	6
Coordinatrice	1	0	0
Dipendente	0	154	0
direttore	1	0	0
direttrice	1	0	0
Dirigente	32	0	0
Eletto	1	0	0
funzionario con incarico di componente	0	1	0
Funzionario Ufficio Cultura - Biblioteca	0	1	0
personale tecnico amministrativo - subalterno	0	1	0
PM Esperti PNRR	0	1	0
posizione organizzativa	1	0	0
Prima Ricercatrice	0	1	0
Responsabile Amministrativo Scolastico	1	0	0
ricercatore	0	1	0
Segretario particolare del sindaco di Alghero	0	1	0
Segreteria di presidenza	0	1	0
Vice capo ufficio di gabinetto ministero università e ricerca	1	0	0

df |>
  tabyl(role3) |>
  gt_tabyl(
    title = "Role, three categories"
  )

Role, three categories
role3	n	percent
apicale	42	19.7%
non_apicale	163	76.5%
esterno	8	3.8%

2.3 Step 2 — collapse to two categories

Since esterno group is small we merge it into non_apicale**.

df <- df |>
  mutate(
    role2 = fct_collapse(role3, non_apicale = c("non_apicale", "esterno")),
    role2 = factor(role2, levels = c("apicale", "non_apicale"))
  )

df |>
  tabyl(role2) |>
  gt_tabyl(
    title = "Role, two-category stratum"
  )

Role, two-category stratum
role2	n	percent
apicale	42	19.7%
non_apicale	171	80.3%

3 Institution type stratum

df |>
  tabyl(org_type) |>
  arrange(desc(n)) |>
  gt_tabyl(
    title = "Raw values of the organization type field",
    subtitle = "As submitted by participants, before any recoding"
  ) |>
  cols_width(org_type ~ px(520))

Raw values of the organization type field
As submitted by participants, before any recoding
org_type	n	percent
Regione o Provincia (incluse Province autonome)	60	28.2%
Amministrazione centrale dello Stato	50	23.5%
Comune, Città metropolitana, Unione di comuni	33	15.5%
Azienda sanitaria o ospedaliera pubblica (ASL/ATS, AO, IRCCS pubblico)	25	11.7%
Altro ente pubblico (camera di commercio, ordine professionale, ente strumentale, azienda speciale…)	16	7.5%
Società a partecipazione pubblica / in house	9	4.2%
Impresa o società privata (incluse società di consulenza)	2	0.9%
Lavoro come libero/a professionista o consulente	2	0.9%
Sindacato	2	0.9%
Università	2	0.9%
AGENAS	1	0.5%
Commissione Europea	1	0.5%
Corte dei conti	1	0.5%
Ente pubblico di ricerca sociale	1	0.5%
PROVINCIA	1	0.5%
Terzo settore (associazioni, cooperative, fondazioni private, ETS)	1	0.5%
Università degli Studi Trento	1	0.5%
Università degli Studi di Bari	1	0.5%
Università di Trento	1	0.5%
Università di Trento - pta	1	0.5%
docente della scuola sec italiana FVG, email di riferimento istituzionale ilaria.zorino@liceomarinelli.edu.it , studente V anno Sapienza Facoltà Giurisprudenza LMG 01, esperto di debate	1	0.5%
ente pubblico di ricerca	1	0.5%

3.1 Three categories

The organization stratum is reduced to three levels:

• territoriale (sub-national government). Regions and autonomous provinces, municipalities, metropolitan cities etc.
• centrale (central government and supra-national). Central state administration, plus the Corte dei conti, AGENAS and the European Commission — bodies that operate at national or supra-national level.
• sanita_altri (health service and other bodies). Public health authorities and hospitals, other public bodies, publicly-owned and in-house companies, universities and research bodies, trade unions, private firms and freelancers, third sector, and the remaining free-text answers.

df <- df |>
  mutate(
    org3 = case_when(
      str_detect(
        org_clean,
        "^regione|provincia autonom|^comune|città metropolitana|unione di comuni|^provincia$"
      ) ~ "territoriale",
      str_detect(
        org_clean,
        "amministrazione centrale|corte dei conti|commissione europea|agenas"
      ) ~ "centrale",
      TRUE ~ "sanita_altri"
    ),
    org3 = factor(org3, levels = c("territoriale", "centrale", "sanita_altri"))
  )

3.1.1 CHECK

Please check if all ok!

df |>
  tabyl(org_type, org3) |>
  gt() |>
  tab_header(
    title = "Raw organization value to the three-category classification"
  ) |>
  opt_align_table_header(align = "left") |>
  cols_width(org_type ~ px(460)) |>
  tab_options(
    table.font.size = px(12),
    heading.title.font.size = px(15),
    heading.subtitle.font.size = px(12),
    data_row.padding = px(3)
  )

Raw organization value to the three-category classification
org_type	territoriale	centrale	sanita_altri
AGENAS	0	1	0
Altro ente pubblico (camera di commercio, ordine professionale, ente strumentale, azienda speciale…)	0	0	16
Amministrazione centrale dello Stato	0	50	0
Azienda sanitaria o ospedaliera pubblica (ASL/ATS, AO, IRCCS pubblico)	0	0	25
Commissione Europea	0	1	0
Comune, Città metropolitana, Unione di comuni	33	0	0
Corte dei conti	0	1	0
docente della scuola sec italiana FVG, email di riferimento istituzionale ilaria.zorino@liceomarinelli.edu.it , studente V anno Sapienza Facoltà Giurisprudenza LMG 01, esperto di debate	0	0	1
ente pubblico di ricerca	0	0	1
Ente pubblico di ricerca sociale	0	0	1
Impresa o società privata (incluse società di consulenza)	0	0	2
Lavoro come libero/a professionista o consulente	0	0	2
PROVINCIA	1	0	0
Regione o Provincia (incluse Province autonome)	60	0	0
Sindacato	0	0	2
Società a partecipazione pubblica / in house	0	0	9
Terzo settore (associazioni, cooperative, fondazioni private, ETS)	0	0	1
Università	0	0	2
Università degli Studi di Bari	0	0	1
Università degli Studi Trento	0	0	1
Università di Trento	0	0	1
Università di Trento - pta	0	0	1

df |>
  tabyl(org3) |>
  gt_tabyl(
    title = "Organization type, final three-category stratum"
  )

Organization type, final three-category stratum
org3	n	percent
territoriale	94	44.1%
centrale	53	24.9%
sanita_altri	66	31.0%

4 Randomization blocks

The two strata are crossed to form the blocks.

df <- df |>
  mutate(block = interaction(role2, org3, drop = TRUE, sep = "_"))

df |>
  tabyl(block) |>
  gt_tabyl(
    title = "Size of each randomization block"
  )

Size of each randomization block
block	n	percent
apicale_territoriale	19	8.9%
non_apicale_territoriale	75	35.2%
apicale_centrale	7	3.3%
non_apicale_centrale	46	21.6%
apicale_sanita_altri	16	7.5%
non_apicale_sanita_altri	50	23.5%

apicale_centrale only have 6 individuals. We should probably combine it with non_apicale_centrale and a single block - centrale. Or we can leave it as it is, and collapse it during the analyses (all fine).

5 Assignment to arms

Each block is assigned to roughly 50% treatment and 50% control. Blocks with odd number of participants are randomly rounded up or down.

set.seed(20260907)

df <- df |>
  mutate(
    arm = block_ra(
      blocks     = block,
      prob       = 0.5,
      conditions = c("Control", "Treatment")
    )
  )

df |>
  tabyl(block, arm) |>
  adorn_totals(c("row", "col")) |>
  gt() |>
  tab_header(
    title = "Assignment to arms within each block"
  ) |>
  opt_align_table_header(align = "left") |>
  tab_options(table.font.size = px(13), heading.title.font.size = px(15))

Assignment to arms within each block
block	Control	Treatment	Total
apicale_territoriale	9	10	19
non_apicale_territoriale	37	38	75
apicale_centrale	3	4	7
non_apicale_centrale	23	23	46
apicale_sanita_altri	8	8	16
non_apicale_sanita_altri	25	25	50
Total	105	108	213

5.1 Overall balance

df |>
  tabyl(arm) |>
  gt_tabyl(
    title = "Overall size of the two arms"
  )

Overall size of the two arms
arm	n	percent
Control	105	49.3%
Treatment	108	50.7%

5.2 Balance check on the stratifying variables

By construction the arms should be near-identical on role and organization.

df |>
  tabyl(role2, arm) |>
  adorn_totals("row") |>
  gt() |>
  tab_header(title = "Balance on role") |>
  opt_align_table_header(align = "left") |>
  tab_options(table.font.size = px(13), heading.title.font.size = px(15))

Balance on role
role2	Control	Treatment
apicale	20	22
non_apicale	85	86
Total	105	108

df |>
  tabyl(org3, arm) |>
  adorn_totals("row") |>
  gt() |>
  tab_header(title = "Balance on organization type") |>
  opt_align_table_header(align = "left") |>
  tab_options(table.font.size = px(13), heading.title.font.size = px(15))

Balance on organization type
org3	Control	Treatment
territoriale	46	48
centrale	26	27
sanita_altri	33	33
Total	105	108

6 Export

timestamp <- format(Sys.time(), "%Y-%m-%d_%H-%M-%S")

# 2. Build the output file path
file_name <- paste0("capire_assignment_", timestamp, ".xlsx")
file_path <- here("output", file_name)

# 3. Ensure directory exists and save
if (!dir.exists(here("output"))) {
  dir.create(here("output"), recursive = TRUE)
}

df |>
  select(name, surname, email, org, role, role2, org3, block, arm) |>
  ungroup() |>
  arrange(arm, block, name, surname) |> 
  writexl::write_xlsx(file_path)

sessionInfo()

R version 4.6.1 (2026-06-24 ucrt)
Platform: x86_64-w64-mingw32/x64
Running under: Windows 11 x64 (build 26200)

Matrix products: default
  LAPACK version 3.12.1

locale:
[1] LC_COLLATE=Italian_Italy.utf8  LC_CTYPE=Italian_Italy.utf8   
[3] LC_MONETARY=Italian_Italy.utf8 LC_NUMERIC=C                  
[5] LC_TIME=Italian_Italy.utf8    

time zone: Europe/Rome
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] gt_1.3.0        randomizr_2.0.1 janitor_2.2.1   here_1.0.2     
 [5] lubridate_1.9.5 forcats_1.0.1   stringr_1.6.0   dplyr_1.2.1    
 [9] purrr_1.2.2     readr_2.2.0     tidyr_1.3.2     tibble_3.3.1   
[13] ggplot2_4.0.3   tidyverse_2.0.0

loaded via a namespace (and not attached):
 [1] sass_0.4.10        generics_0.1.4     xml2_1.6.0         stringi_1.8.9     
 [5] hms_1.1.4          digest_0.6.39      magrittr_2.0.5     evaluate_1.0.5    
 [9] grid_4.6.1         timechange_0.4.0   RColorBrewer_1.1-3 fastmap_1.2.0     
[13] cellranger_1.1.0   rprojroot_2.1.1    jsonlite_2.0.0     writexl_2.0.1     
[17] crosstalk_1.2.2    scales_1.4.0       jquerylib_0.1.4    cli_3.6.6         
[21] rlang_1.3.0        cachem_1.1.0       withr_3.0.3        yaml_2.3.12       
[25] otel_0.2.0         tools_4.6.1        tzdb_0.5.0         DT_0.34.0         
[29] vctrs_0.7.3        R6_2.6.1           lifecycle_1.0.5    snakecase_0.11.1  
[33] fs_2.1.0           htmlwidgets_1.6.4  pkgconfig_2.0.3    bslib_0.12.0      
[37] pillar_1.11.1      gtable_0.3.6       glue_1.8.1         Rcpp_1.1.2        
[41] xfun_0.60          tidyselect_1.2.1   knitr_1.51         farver_2.1.2      
[45] htmltools_0.5.9    rmarkdown_2.32     compiler_4.6.1     S7_0.2.2          
[49] readxl_1.5.0