Quantitative Data Analysis in R

Last updated on 2026-04-29 | Edit this page

Overview

Questions

  • What statistical tests should I use?
  • How can I run multiple tests at once?

Objectives

  • Read in data and ensure variables have the correct data type
  • Perform exploratory data analysis
  • Identify the correct statistical test for a given variable type and research question
  • Run Chi-square tests, t-tests, and one-way ANOVAs in R Notebooks
  • Interpret p-values, test statistics, and effect sizes in context
  • Write clear explanatory text in R Notebooks to document analytical decisions
  • Recognise the assumptions underlying each test and check them in R

Other materials

See Workshop 5 Slides here

See Workshop 5 recording here - 1

Dataset Overview

This workshop uses a generated (made-up) dataset containing 1005 responses to a survey on flexible working and work-life balance, with a number of different data types.

The schema is included in the following table.

Flexible working and work-life balance survey data schema

Section Variable Type Description
A (Demographics) A1 – Gender Factor (male, female) What is your gender?
A2 – Age Group Ordered Factor (18–34, 35–54, 55+) What is your age?
A3 – Education Ordered Factor (primary, secondary, tertiary+) What is your highest level of education?
A4 – Income Ordered Factor (low, middle, high) What is your annual income?
A5 – Region Factor (region 1, 2, 3) What is your region of residence?
A6 – Area Type Factor (rural, urban) Is your region of residence urban or rural?
B (Policy Views) B1 Character What should be the main goal of flexible working policies? (Select up to 3)
B1_1 Logical Improve employee wellbeing & work-life balance
B1_2 Logical Boost productivity & business performance
B1_3 Logical Attract & retain top talent
B1_4 Logical Reduce costs & office overhead
B1_5 Logical Support diversity, equity & inclusion
B2 Character Who should benefit most from flexible working arrangements? (Select up to 3)
B2_1 Logical All employees equally, regardless of role or seniority
B2_2 Logical Parents and caregivers with dependants
B2_3 Logical Employees with disabilities or chronic health conditions
B2_4 Logical Junior/entry-level employees building their careers
B2_5 Logical Senior/experienced employees with proven track records
B2_6 Logical Employees with long commutes or remote locations
B2_7 Logical Employees from underrepresented or marginalised groups
B2_8 Logical High performers and those meeting targets consistently
C (Satisfaction) C1 Integer (1–5) How satisfied are you with your current flexible working arrangements? (1 = least satisfied, 5 = most satisfied)
C2 Integer (1–5) To what extent do flexible working options improve your work-life balance? (1 = very little, 5 = very much)
C3 Integer (1–5) How strongly do you agree that your employer supports flexible working in practice? (1 = very little, 5 = very much)
D (Commute) D1 Numeric What is your commute time to work in minutes?
D2 Numeric What is your commute distance in km?
E (Outcomes) E1 Ordered Factor (strongly dissatisfied → strongly satisfied) How satisfied are you with your current work-life balance?
E2 Free text What makes you most satisfied in your personal life?

Set up

Start by opening up your RStudio project that you created in a previous workshop, called intro_r, in a new session. Ensure your global environment is empty! You can also ‘sweep’ your global environment by clicking the broom icon.

Screenshot of RStudio showing the empty global environment.

Open a new R Notebook: Click File -> New File -> R Notebook. Save your R Notebook with a filename that makes sense, such as quantitative_analysis.Rmd, in the scripts folder.

When you open a new R Notebook, some explanatory text is provided. This can be deleted so you can enter your own text and code.

Load packages and download data

Download packages (if needed) and load libraries. We’ll be using the gtsummary package for the first time, so this will need to be installed.

R 

for (pkg in c("tidyverse", "here", "gtsummary", "scales", "corrplot", "epitools", "rcompanion")) {
  if (!requireNamespace(pkg, quietly = TRUE)) install.packages(pkg)
}

OUTPUT 

- Querying repositories for available source packages ... Done!
The following package(s) will be installed:
- bigD       [0.3.1]
- bitops     [1.0-9]
- cards      [0.7.1]
- cardx      [0.3.2]
- gt         [1.3.0]
- gtsummary  [2.5.0]
- juicyjuice [0.1.0]
- reactable  [0.4.5]
- reactR     [0.6.1]
These packages will be installed into "/__w/irim-r-workshops/irim-r-workshops/renv/profiles/lesson-requirements/renv/library/linux-ubuntu-noble/R-4.5/x86_64-pc-linux-gnu".

# Downloading packages -------------------------------------------------------
[32m✔[0m bitops 1.0-9                             [11 kB in 0.24s]
[32m✔[0m bigD 0.3.1                               [1.3 MB in 0.24s]
[32m✔[0m reactR 0.6.1                             [712 kB in 0.32s]
[32m✔[0m cardx 0.3.2                              [200 kB in 0.37s]
[32m✔[0m reactable 0.4.5                          [981 kB in 0.38s]
[32m✔[0m cards 0.7.1                              [321 kB in 0.38s]
[32m✔[0m gt 1.3.0                                 [3.4 MB in 0.39s]
[32m✔[0m juicyjuice 0.1.0                         [1.1 MB in 0.39s]
[32m✔[0m gtsummary 2.5.0                          [935 kB in 0.4s]
Successfully downloaded 9 packages in 0.7 seconds.

# Installing packages --------------------------------------------------------
[32m✔[0m juicyjuice 0.1.0                         [built from source in 6.0s]
[32m✔[0m bitops 1.0-9                             [built from source in 7.7s]
[32m✔[0m reactR 0.6.1                             [built from source in 6.1s]
[32m✔[0m cards 0.7.1                              [built from source in 22s]
[32m✔[0m reactable 0.4.5                          [built from source in 9.9s]
[32m✔[0m bigD 0.3.1                               [built from source in 27s]
[32m✔[0m cardx 0.3.2                              [built from source in 11s]
[32m✔[0m gt 1.3.0                                 [built from source in 22s]
[32m✔[0m gtsummary 2.5.0                          [built from source in 10s]
Successfully installed 9 packages in 59 seconds.
The following package(s) will be installed:
- corrplot [0.95]
These packages will be installed into "/__w/irim-r-workshops/irim-r-workshops/renv/profiles/lesson-requirements/renv/library/linux-ubuntu-noble/R-4.5/x86_64-pc-linux-gnu".

# Downloading packages -------------------------------------------------------
[32m✔[0m corrplot 0.95                            [3.7 MB in 0.28s]
Successfully downloaded 1 package in 0.57 seconds.

# Installing packages --------------------------------------------------------
[32m✔[0m corrplot 0.95                            [built from source in 2.5s]
Successfully installed 1 package in 2.6 seconds.
The following package(s) will be installed:
- epitools [0.5-10.1]
These packages will be installed into "/__w/irim-r-workshops/irim-r-workshops/renv/profiles/lesson-requirements/renv/library/linux-ubuntu-noble/R-4.5/x86_64-pc-linux-gnu".

# Downloading packages -------------------------------------------------------
[32m✔[0m epitools 0.5-10.1                        [91 kB in 0.11s]
Successfully downloaded 1 package in 0.41 seconds.

# Installing packages --------------------------------------------------------
[32m✔[0m epitools 0.5-10.1                        [built from source in 3.9s]
Successfully installed 1 package in 4.1 seconds.
The following package(s) will be installed:
- coin         [1.4-3]
- DescTools    [0.99.60]
- e1071        [1.7-17]
- Exact        [3.3]
- expm         [1.0-0]
- gld          [2.6.8]
- libcoin      [1.0-12]
- lmom         [3.3]
- lmtest       [0.9-40]
- matrixStats  [1.5.0]
- modeltools   [0.2-24]
- multcomp     [1.4-30]
- multcompView [0.1-11]
- mvtnorm      [1.3-7]
- nortest      [1.0-4]
- plyr         [1.8.9]
- proxy        [0.4-29]
- rcompanion   [2.5.2]
- rootSolve    [1.8.2.4]
- sandwich     [3.1-1]
- TH.data      [1.1-5]
- zoo          [1.8-15]
These packages will be installed into "/__w/irim-r-workshops/irim-r-workshops/renv/profiles/lesson-requirements/renv/library/linux-ubuntu-noble/R-4.5/x86_64-pc-linux-gnu".

# Downloading packages -------------------------------------------------------
[32m✔[0m expm 1.0-0                               [141 kB in 0.4s]
[32m✔[0m e1071 1.7-17                             [318 kB in 0.4s]
[32m✔[0m multcomp 1.4-30                          [689 kB in 0.41s]
[32m✔[0m mvtnorm 1.3-7                            [976 kB in 0.41s]
[32m✔[0m sandwich 3.1-1                           [1.4 MB in 0.41s]
[32m✔[0m proxy 0.4-29                             [71 kB in 3.1s]
[32m✔[0m zoo 1.8-15                               [806 kB in 8.1s]
[32m✔[0m lmtest 0.9-40                            [230 kB in 5.8s]
[32m✔[0m TH.data 1.1-5                            [8.6 MB in 0.45s]
[32m✔[0m coin 1.4-3                               [1.0 MB in 0.46s]
[32m✔[0m rcompanion 2.5.2                         [162 kB in 0.46s]
[32m✔[0m DescTools 0.99.60                        [2.7 MB in 0.48s]
[32m✔[0m matrixStats 1.5.0                        [212 kB in 81s]
[32m✔[0m nortest 1.0-4                            [6 kB in 0.52s]
[32m✔[0m plyr 1.8.9                               [401 kB in 0.52s]
[32m✔[0m modeltools 0.2-24                        [15 kB in 0.52s]
[32m✔[0m rootSolve 1.8.2.4                        [504 kB in 0.53s]
[32m✔[0m multcompView 0.1-11                      [157 kB in 0.53s]
[32m✔[0m gld 2.6.8                                [55 kB in 0.53s]
[32m✔[0m lmom 3.3                                 [347 kB in 0.53s]
[32m✔[0m Exact 3.3                                [45 kB in 0.14s]
[32m✔[0m libcoin 1.0-12                           [866 kB in 0.15s]
Successfully downloaded 22 packages in 0.86 seconds.

# Installing packages --------------------------------------------------------
[32m✔[0m modeltools 0.2-24                        [built from source in 14s]
[32m✔[0m lmom 3.3                                 [built from source in 23s]
[32m✔[0m multcompView 0.1-11                      [built from source in 9.7s]
[32m✔[0m nortest 1.0-4                            [built from source in 7.1s]
[32m✔[0m expm 1.0-0                               [built from source in 32s]
[32m✔[0m proxy 0.4-29                             [built from source in 16s]
[32m✔[0m mvtnorm 1.3-7                            [built from source in 30s]
[32m✔[0m matrixStats 1.5.0                        [built from source in 1.2m]
[32m✔[0m TH.data 1.1-5                            [built from source in 16s]
[32m✔[0m plyr 1.8.9                               [built from source in 41s]
[32m✔[0m rootSolve 1.8.2.4                        [built from source in 41s]
[32m✔[0m libcoin 1.0-12                           [built from source in 20s]
[32m✔[0m zoo 1.8-15                               [built from source in 28s]
[32m✔[0m e1071 1.7-17                             [built from source in 30s]
[32m✔[0m Exact 3.3                                [built from source in 17s]
[32m✔[0m lmtest 0.9-40                            [built from source in 14s]
[32m✔[0m sandwich 3.1-1                           [built from source in 15s]
[32m✔[0m gld 2.6.8                                [built from source in 13s]
[32m✔[0m multcomp 1.4-30                          [built from source in 11s]
[32m✔[0m coin 1.4-3                               [built from source in 16s]
[32m✔[0m DescTools 0.99.60                        [built from source in 57s]
[32m✔[0m rcompanion 2.5.2                         [built from source in 10s]
Successfully installed 22 packages in 180 seconds.

R 

library(tidyverse)
library(here)
library(gtsummary) # summary tables
library(scales) # percent formatting for axes
library(corrplot) # correlation plots
library(rcompanion) # Cramér's V effect size
library(epitools) # odds ratios for 2×2 tables

Then, download the the generated survey dataset using the following code:

R 

download.file("https://raw.githubusercontent.com/IRIM-Mongolia/irim-r-workshops/main/episodes/data/raw/generated_survey_data.csv", here("data/raw/generated_survey_data.csv"), mode = "wb")

Then, read in the survey csv file and preview the data.

R 

survey <- read_csv(here("data", "raw", "generated_survey_data.csv"))

OUTPUT 

Rows: 1005 Columns: 28
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (10): A1, A2, A3, A4, A5, A6, B1, B2, E1, E2
dbl  (5): C1, C2, C3, D1, D2
lgl (13): B1_1, B1_2, B1_3, B1_4, B1_5, B2_1, B2_2, B2_3, B2_4, B2_5, B2_6, ...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

R 

survey # preview the data

OUTPUT 

# A tibble: 1,005 × 28
   A1    A2    A3    A4    A5    A6    B1    B1_1  B1_2  B1_3  B1_4  B1_5  B2
   <chr> <chr> <chr> <chr> <chr> <chr> <chr> <lgl> <lgl> <lgl> <lgl> <lgl> <chr>
 1 male  18-34 seco… low   regi… Urban <NA>  FALSE FALSE FALSE FALSE FALSE 1 4 7
 2 male  35-54 seco… midd… regi… Rural 2 4 5 FALSE TRUE  FALSE TRUE  TRUE  1 4 6
 3 fema… 35-54 tert… low   regi… Rural 2 3 4 FALSE TRUE  TRUE  TRUE  FALSE 3 6 7
 4 male  18-34 tert… low   regi… Urban 5     FALSE FALSE FALSE FALSE TRUE  3 5 8
 5 male  35-54 seco… high  regi… Rural 5     FALSE FALSE FALSE FALSE TRUE  2 5 6
 6 fema… 18-34 tert… high  regi… Urban 1 3 5 TRUE  FALSE TRUE  FALSE TRUE  3 6
 7 male  35-54 seco… high  regi… Urban 2 4 5 FALSE TRUE  FALSE TRUE  TRUE  2 6 7
 8 fema… 18-34 tert… midd… regi… Rural 3 4 5 FALSE FALSE TRUE  TRUE  TRUE  6 7 8
 9 male  18-34 tert… low   regi… Urban 2 4   FALSE TRUE  FALSE TRUE  FALSE 2 5 8
10 male  18-34 prim… midd… regi… Urban 5     FALSE FALSE FALSE FALSE TRUE  5 8
# ℹ 995 more rows
# ℹ 15 more variables: B2_1 <lgl>, B2_2 <lgl>, B2_3 <lgl>, B2_4 <lgl>,
#   B2_5 <lgl>, B2_6 <lgl>, B2_7 <lgl>, B2_8 <lgl>, C1 <dbl>, C2 <dbl>,
#   C3 <dbl>, D1 <dbl>, D2 <dbl>, E1 <chr>, E2 <chr>

Process data

Let’s inspect the dataframe and see how R classified the data types.

R 

str(survey)

OUTPUT 

spc_tbl_ [1,005 × 28] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
 $ A1  : chr [1:1005] "male" "male" "female" "male" ...
 $ A2  : chr [1:1005] "18-34" "35-54" "35-54" "18-34" ...
 $ A3  : chr [1:1005] "secondary" "secondary" "tertiary or higher" "tertiary or higher" ...
 $ A4  : chr [1:1005] "low" "middle" "low" "low" ...
 $ A5  : chr [1:1005] "region3" "region1" "region1" "region3" ...
 $ A6  : chr [1:1005] "Urban" "Rural" "Rural" "Urban" ...
 $ B1  : chr [1:1005] NA "2 4 5" "2 3 4" "5" ...
 $ B1_1: logi [1:1005] FALSE FALSE FALSE FALSE FALSE TRUE ...
 $ B1_2: logi [1:1005] FALSE TRUE TRUE FALSE FALSE FALSE ...
 $ B1_3: logi [1:1005] FALSE FALSE TRUE FALSE FALSE TRUE ...
 $ B1_4: logi [1:1005] FALSE TRUE TRUE FALSE FALSE FALSE ...
 $ B1_5: logi [1:1005] FALSE TRUE FALSE TRUE TRUE TRUE ...
 $ B2  : chr [1:1005] "1 4 7" "1 4 6" "3 6 7" "3 5 8" ...
 $ B2_1: logi [1:1005] TRUE TRUE FALSE FALSE FALSE FALSE ...
 $ B2_2: logi [1:1005] FALSE FALSE FALSE FALSE TRUE FALSE ...
 $ B2_3: logi [1:1005] FALSE FALSE TRUE TRUE FALSE TRUE ...
 $ B2_4: logi [1:1005] TRUE TRUE FALSE FALSE FALSE FALSE ...
 $ B2_5: logi [1:1005] FALSE FALSE FALSE TRUE TRUE FALSE ...
 $ B2_6: logi [1:1005] FALSE TRUE TRUE FALSE TRUE TRUE ...
 $ B2_7: logi [1:1005] TRUE FALSE TRUE FALSE FALSE FALSE ...
 $ B2_8: logi [1:1005] FALSE FALSE FALSE TRUE FALSE FALSE ...
 $ C1  : num [1:1005] 5 1 4 1 1 5 3 4 4 3 ...
 $ C2  : num [1:1005] 3 5 3 3 2 2 3 5 3 2 ...
 $ C3  : num [1:1005] 3 1 2 3 4 4 1 1 1 5 ...
 $ D1  : num [1:1005] 99 44 52 77 80 99 56 102 79 86 ...
 $ D2  : num [1:1005] 40 34 12 43 13 25 36 37 48 28 ...
 $ E1  : chr [1:1005] "Neutral" "Strongly satisfied" "Dissatisfied" "Neutral" ...
 $ E2  : chr [1:1005] "I really enjoy meeting up with friends and would recommend it" "I really enjoy meeting up with friends and find it rewarding" "I would say reading in my spare time as much as I can" "I often find myself cooking at home and would recommend it" ...
 - attr(*, "spec")=
  .. cols(
  ..   A1 = col_character(),
  ..   A2 = col_character(),
  ..   A3 = col_character(),
  ..   A4 = col_character(),
  ..   A5 = col_character(),
  ..   A6 = col_character(),
  ..   B1 = col_character(),
  ..   B1_1 = col_logical(),
  ..   B1_2 = col_logical(),
  ..   B1_3 = col_logical(),
  ..   B1_4 = col_logical(),
  ..   B1_5 = col_logical(),
  ..   B2 = col_character(),
  ..   B2_1 = col_logical(),
  ..   B2_2 = col_logical(),
  ..   B2_3 = col_logical(),
  ..   B2_4 = col_logical(),
  ..   B2_5 = col_logical(),
  ..   B2_6 = col_logical(),
  ..   B2_7 = col_logical(),
  ..   B2_8 = col_logical(),
  ..   C1 = col_double(),
  ..   C2 = col_double(),
  ..   C3 = col_double(),
  ..   D1 = col_double(),
  ..   D2 = col_double(),
  ..   E1 = col_character(),
  ..   E2 = col_character()
  .. )
 - attr(*, "problems")=<externalptr>

From the information available in our data schema, we know that we have several columns that will need to be converted to factors before we can proceed with our analysis. We’ll use mutate and factor to convert the columns as needed.

We’ll start with the Demographic data in section A.

R 

survey <- survey %>% 
  mutate(
    A1 = factor(A1,
                levels = c("female", "male")),
    A2 = factor(A2,
                levels = c("18-34", "35-54", "55+"),
                ordered = TRUE),
    A3 = factor(A3,
                levels = c("primary", "secondary", "tertiary or higher"),
                ordered = TRUE),
    A4 = factor(A4,
                levels = c("low", "middle", "high"),
                ordered = TRUE),
    A5 = factor(A5,
                levels = c("region1", "region2", "region3")),
    A6 = factor(A6,
                levels = c("Rural", "Urban"))
  )

Let’s take a quick look at the dataframe.

R 

str(survey)

OUTPUT 

tibble [1,005 × 28] (S3: tbl_df/tbl/data.frame)
 $ A1  : Factor w/ 2 levels "female","male": 2 2 1 2 2 1 2 1 2 2 ...
 $ A2  : Ord.factor w/ 3 levels "18-34"<"35-54"<..: 1 2 2 1 2 1 2 1 1 1 ...
 $ A3  : Ord.factor w/ 3 levels "primary"<"secondary"<..: 2 2 3 3 2 3 2 3 3 1 ...
 $ A4  : Ord.factor w/ 3 levels "low"<"middle"<..: 1 2 1 1 3 3 3 2 1 2 ...
 $ A5  : Factor w/ 3 levels "region1","region2",..: 3 1 1 3 1 3 3 1 3 3 ...
 $ A6  : Factor w/ 2 levels "Rural","Urban": 2 1 1 2 1 2 2 1 2 2 ...
 $ B1  : chr [1:1005] NA "2 4 5" "2 3 4" "5" ...
 $ B1_1: logi [1:1005] FALSE FALSE FALSE FALSE FALSE TRUE ...
 $ B1_2: logi [1:1005] FALSE TRUE TRUE FALSE FALSE FALSE ...
 $ B1_3: logi [1:1005] FALSE FALSE TRUE FALSE FALSE TRUE ...
 $ B1_4: logi [1:1005] FALSE TRUE TRUE FALSE FALSE FALSE ...
 $ B1_5: logi [1:1005] FALSE TRUE FALSE TRUE TRUE TRUE ...
 $ B2  : chr [1:1005] "1 4 7" "1 4 6" "3 6 7" "3 5 8" ...
 $ B2_1: logi [1:1005] TRUE TRUE FALSE FALSE FALSE FALSE ...
 $ B2_2: logi [1:1005] FALSE FALSE FALSE FALSE TRUE FALSE ...
 $ B2_3: logi [1:1005] FALSE FALSE TRUE TRUE FALSE TRUE ...
 $ B2_4: logi [1:1005] TRUE TRUE FALSE FALSE FALSE FALSE ...
 $ B2_5: logi [1:1005] FALSE FALSE FALSE TRUE TRUE FALSE ...
 $ B2_6: logi [1:1005] FALSE TRUE TRUE FALSE TRUE TRUE ...
 $ B2_7: logi [1:1005] TRUE FALSE TRUE FALSE FALSE FALSE ...
 $ B2_8: logi [1:1005] FALSE FALSE FALSE TRUE FALSE FALSE ...
 $ C1  : num [1:1005] 5 1 4 1 1 5 3 4 4 3 ...
 $ C2  : num [1:1005] 3 5 3 3 2 2 3 5 3 2 ...
 $ C3  : num [1:1005] 3 1 2 3 4 4 1 1 1 5 ...
 $ D1  : num [1:1005] 99 44 52 77 80 99 56 102 79 86 ...
 $ D2  : num [1:1005] 40 34 12 43 13 25 36 37 48 28 ...
 $ E1  : chr [1:1005] "Neutral" "Strongly satisfied" "Dissatisfied" "Neutral" ...
 $ E2  : chr [1:1005] "I really enjoy meeting up with friends and would recommend it" "I really enjoy meeting up with friends and find it rewarding" "I would say reading in my spare time as much as I can" "I often find myself cooking at home and would recommend it" ...

We have one more column E1 to convert to a factor. If we’re not sure of the levels we need to set, we can use unique to extract the unique responses from the column. You can use the $ operator to subset the column, or double brackets [["colname"]].

R 

unique(survey$E1)

OUTPUT 

[1] "Neutral"               "Strongly satisfied"    "Dissatisfied"
[4] "Strongly dissatisfied" "Satisfied"             NA

R 

unique(survey[["E1"]])

OUTPUT 

[1] "Neutral"               "Strongly satisfied"    "Dissatisfied"
[4] "Strongly dissatisfied" "Satisfied"             NA

Now let’s convert E1 to an ordered factor.

R 

survey <- survey %>% 
  mutate(E1 = factor(E1,
                     levels = c("Strongly dissatisfied", "Dissatisfied", "Neutral", "Satisfied", "Strongly satisfied"),
                     ordered = TRUE))

And check column E1.

R 

class(survey[["E1"]])

OUTPUT 

[1] "ordered" "factor"

R 

levels(survey[["E1"]])

OUTPUT 

[1] "Strongly dissatisfied" "Dissatisfied"          "Neutral"
[4] "Satisfied"             "Strongly satisfied"

Exploratory data analysis

Before running any statistical tests, it is important to carry out some exploratory data analysis (EDA) to understand the structure and quality of your data.

EDA helps you check that variables have been read in with the correct types, identify missing values, spot unexpected categories or data entry errors, and understand the distribution of responses across key variables.

For categorical variables like those in the survey data, frequency tables and proportion summaries reveal how respondents are spread across groups, which is important, as some tests (like Chi-square) require minimum cell counts to be valid.

Let’s investigate the proportion of missing data NA in our columns.

R 

survey %>% 
  summarise(across(everything(), ~ sum(is.na(.)))) %>% 
  pivot_longer(everything(),
               names_to  = "variable",
               values_to = "n_missing") %>% 
  mutate(pct_missing = round(n_missing / nrow(survey) * 100, 1))  %>% 
  filter(n_missing > 0) %>% 
  arrange(desc(n_missing))

OUTPUT 

# A tibble: 3 × 3
  variable n_missing pct_missing
  <chr>        <int>       <dbl>
1 B1              23         2.3
2 E1               4         0.4
3 B2               1         0.1

Frequency tables and proportions for categorical responses

Before stratifying by any grouping variable, it is useful to first examine the overall distribution of responses across all categorical variables in the dataset.

We’ll use the function tbl_summary() from the gtsummary package to produce a single frequency table covering every factor column, displaying counts and column percentages for each response category.

This gives us a quick snapshot of sample composition and response patterns, such as how respondents are distributed across age groups, income levels, and regions.

R 

# Overall frequency table for all factor columns
survey %>% 
  select(where(is.factor)) %>% 
  tbl_summary(
    statistic = list(all_categorical() ~ "{n} ({p}%)"), # count and proportion
    missing = "ifany" # show missing if present
  )
Characteristic N = 1,0051
A1
    female 583 (58%)
    male 422 (42%)
A2
    18-34 497 (49%)
    35-54 416 (41%)
    55+ 92 (9.2%)
A3
    primary 101 (10%)
    secondary 545 (54%)
    tertiary or higher 359 (36%)
A4
    low 394 (39%)
    middle 326 (32%)
    high 285 (28%)
A5
    region1 327 (33%)
    region2 201 (20%)
    region3 477 (47%)
A6
    Rural 528 (53%)
    Urban 477 (47%)
E1
    Strongly dissatisfied 220 (22%)
    Dissatisfied 217 (22%)
    Neutral 205 (20%)
    Satisfied 216 (22%)
    Strongly satisfied 143 (14%)
    Unknown 4
1 n (%)

The survey data has a slightly female-majority, with a younger age distribution. We should keep this in mind when interpreting any later results that break down by gender and age.

Breakdown by demographics

We can also use the tbl_summary() function to add statistical tests by using add_p().

Adding add_p() runs a Chi-square test (or Fisher’s exact test where cell counts are small) for each categorical variable automatically, allowing us to quickly identify which variables show statistically significant differences by gender before conducting more detailed analysis.

We’ll select all of the demographics columns that start with “A”, and the multi-select columns for questions “B1” and “B2”.

R 

# Breakdown by demographics (section A)
survey %>% 
  select(starts_with("A"), matches("_\\d+$")) %>% 
  tbl_summary(
    by = A1,
    statistic = list(all_categorical() ~ "{n} ({p}%)"),
    missing = "ifany"
  ) %>% 
  add_p() %>% # adds Chi-square/Fisher's automatically
  add_overall() %>% # adds total column
  bold_labels()
Characteristic Overall
N = 1,0051 		female
N = 5831 		male
N = 4221 		p-value2
A2


0.071
    18-34 497 (49%) 294 (50%) 203 (48%)
    35-54 416 (41%) 246 (42%) 170 (40%)
    55+ 92 (9.2%) 43 (7.4%) 49 (12%)
A3


0.7
    primary 101 (10%) 62 (11%) 39 (9.2%)
    secondary 545 (54%) 311 (53%) 234 (55%)
    tertiary or higher 359 (36%) 210 (36%) 149 (35%)
A4


0.2
    low 394 (39%) 240 (41%) 154 (36%)
    middle 326 (32%) 189 (32%) 137 (32%)
    high 285 (28%) 154 (26%) 131 (31%)
A5


0.2
    region1 327 (33%) 186 (32%) 141 (33%)
    region2 201 (20%) 128 (22%) 73 (17%)
    region3 477 (47%) 269 (46%) 208 (49%)
A6


0.3
    Rural 528 (53%) 314 (54%) 214 (51%)
    Urban 477 (47%) 269 (46%) 208 (49%)
B1_1 552 (55%) 472 (81%) 80 (19%) <0.001
B1_2 276 (27%) 156 (27%) 120 (28%) 0.6
B1_3 470 (47%) 440 (75%) 30 (7.1%) <0.001
B1_4 495 (49%) 315 (54%) 180 (43%) <0.001
B1_5 507 (50%) 160 (27%) 347 (82%) <0.001
B2_1 298 (30%) 83 (14%) 215 (51%) <0.001
B2_2 206 (20%) 125 (21%) 81 (19%) 0.4
B2_3 417 (41%) 388 (67%) 29 (6.9%) <0.001
B2_4 362 (36%) 168 (29%) 194 (46%) <0.001
B2_5 358 (36%) 99 (17%) 259 (61%) <0.001
B2_6 469 (47%) 403 (69%) 66 (16%) <0.001
B2_7 389 (39%) 219 (38%) 170 (40%) 0.4
B2_8 377 (38%) 187 (32%) 190 (45%) <0.001
1 n (%)
2 Pearson’s Chi-squared test

We can expand this code further to use a for loop to generate summary tables stratified by each demographic column. We’ll select all of the demographics columns that start with “A”, the multi-select columns for questions B1 and B2, and column E1. When running locally in RStudio, 6 tables will print out in the output.

R 

demo_vars <- survey %>%
  select(starts_with("A")) %>% # names of all demographic columns
  names()

tables_list <- list() # initialise empty list first

for (by_var in demo_vars) {
  row_vars <- survey %>%
    select(starts_with("A"), matches("_\\d+$"), "E1") %>%
    select(-all_of(by_var)) %>%
    names()

  tables_list[[by_var]] <- survey %>%
    tbl_summary(
      by = all_of(by_var),
      include = all_of(row_vars),
      statistic = list(all_categorical() ~ "{n} ({p}%)"),
      missing = "ifany"
    ) %>%
    add_p() %>%
    add_overall() %>%
    bold_labels() %>%
    modify_caption(glue::glue("**Stratified by {by_var}**"))
}

walk(tables_list, print) # prints each table in the list
Stratified by A1
Characteristic Overall
N = 1,0051 		female
N = 5831 		male
N = 4221 		p-value2
A2


0.071
    18-34 497 (49%) 294 (50%) 203 (48%)
    35-54 416 (41%) 246 (42%) 170 (40%)
    55+ 92 (9.2%) 43 (7.4%) 49 (12%)
A3


0.7
    primary 101 (10%) 62 (11%) 39 (9.2%)
    secondary 545 (54%) 311 (53%) 234 (55%)
    tertiary or higher 359 (36%) 210 (36%) 149 (35%)
A4


0.2
    low 394 (39%) 240 (41%) 154 (36%)
    middle 326 (32%) 189 (32%) 137 (32%)
    high 285 (28%) 154 (26%) 131 (31%)
A5


0.2
    region1 327 (33%) 186 (32%) 141 (33%)
    region2 201 (20%) 128 (22%) 73 (17%)
    region3 477 (47%) 269 (46%) 208 (49%)
A6


0.3
    Rural 528 (53%) 314 (54%) 214 (51%)
    Urban 477 (47%) 269 (46%) 208 (49%)
B1_1 552 (55%) 472 (81%) 80 (19%) <0.001
B1_2 276 (27%) 156 (27%) 120 (28%) 0.6
B1_3 470 (47%) 440 (75%) 30 (7.1%) <0.001
B1_4 495 (49%) 315 (54%) 180 (43%) <0.001
B1_5 507 (50%) 160 (27%) 347 (82%) <0.001
B2_1 298 (30%) 83 (14%) 215 (51%) <0.001
B2_2 206 (20%) 125 (21%) 81 (19%) 0.4
B2_3 417 (41%) 388 (67%) 29 (6.9%) <0.001
B2_4 362 (36%) 168 (29%) 194 (46%) <0.001
B2_5 358 (36%) 99 (17%) 259 (61%) <0.001
B2_6 469 (47%) 403 (69%) 66 (16%) <0.001
B2_7 389 (39%) 219 (38%) 170 (40%) 0.4
B2_8 377 (38%) 187 (32%) 190 (45%) <0.001
1 n (%)
2 Pearson’s Chi-squared test
Stratified by A2
Characteristic Overall
N = 1,0051 		18-34
N = 4971 		35-54
N = 4161 		55+
N = 921 		p-value2
A1



0.071
    female 583 (58%) 294 (59%) 246 (59%) 43 (47%)
    male 422 (42%) 203 (41%) 170 (41%) 49 (53%)
A3



0.4
    primary 101 (10%) 53 (11%) 39 (9.4%) 9 (9.8%)
    secondary 545 (54%) 256 (52%) 241 (58%) 48 (52%)
    tertiary or higher 359 (36%) 188 (38%) 136 (33%) 35 (38%)
A4



0.9
    low 394 (39%) 195 (39%) 164 (39%) 35 (38%)
    middle 326 (32%) 159 (32%) 136 (33%) 31 (34%)
    high 285 (28%) 143 (29%) 116 (28%) 26 (28%)
A5



0.3
    region1 327 (33%) 168 (34%) 132 (32%) 27 (29%)
    region2 201 (20%) 108 (22%) 78 (19%) 15 (16%)
    region3 477 (47%) 221 (44%) 206 (50%) 50 (54%)
A6



0.12
    Rural 528 (53%) 276 (56%) 210 (50%) 42 (46%)
    Urban 477 (47%) 221 (44%) 206 (50%) 50 (54%)
B1_1 552 (55%) 264 (53%) 241 (58%) 47 (51%) 0.3
B1_2 276 (27%) 139 (28%) 108 (26%) 29 (32%) 0.5
B1_3 470 (47%) 233 (47%) 201 (48%) 36 (39%) 0.3
B1_4 495 (49%) 243 (49%) 207 (50%) 45 (49%)
0.9
B1_5 507 (50%) 237 (48%) 215 (52%) 55 (60%) 0.083
B2_1 298 (30%) 149 (30%) 124 (30%) 25 (27%) 0.9
B2_2 206 (20%) 99 (20%) 87 (21%) 20 (22%) 0.9
B2_3 417 (41%) 205 (41%) 183 (44%) 29 (32%) 0.089
B2_4 362 (36%) 186 (37%) 142 (34%) 34 (37%) 0.6
B2_5 358 (36%) 182 (37%) 136 (33%) 40 (43%) 0.12
B2_6 469 (47%) 228 (46%) 204 (49%) 37 (40%) 0.3
B2_7 389 (39%) 193 (39%) 153 (37%) 43 (47%) 0.2
B2_8 377 (38%) 172 (35%) 166 (40%) 39 (42%) 0.2
1 n (%)
2 Pearson’s Chi-squared test
Stratified by A3
Characteristic Overall
N = 1,0051 		primary
N = 1011 		secondary
N = 5451 		tertiary or higher
N = 3591 		p-value2
A1



0.7
    female 583 (58%) 62 (61%) 311 (57%) 210 (58%)
    male 422 (42%) 39 (39%) 234 (43%) 149 (42%)
A2



0.4
    18-34 497 (49%) 53 (52%) 256 (47%) 188 (52%)
    35-54 416 (41%) 39 (39%) 241 (44%) 136 (38%)
    55+ 92 (9.2%) 9 (8.9%) 48 (8.8%) 35 (9.7%)
A4



0.3
    low 394 (39%) 31 (31%) 220 (40%) 143 (40%)
    middle 326 (32%) 42 (42%) 173 (32%) 111 (31%)
    high 285 (28%) 28 (28%) 152 (28%) 105 (29%)
A5



0.9
    region1 327 (33%) 30 (30%) 178 (33%) 119 (33%)
    region2 201 (20%) 23 (23%) 104 (19%) 74 (21%)
    region3 477 (47%) 48 (48%) 263 (48%) 166 (46%)
A6



0.8
    Rural 528 (53%) 53 (52%) 282 (52%) 193 (54%)
    Urban 477 (47%) 48 (48%) 263 (48%) 166 (46%)
B1_1 552 (55%) 56 (55%) 305 (56%) 191 (53%) 0.7
B1_2 276 (27%) 29 (29%) 142 (26%) 105 (29%) 0.5
B1_3 470 (47%) 51 (50%) 250 (46%) 169 (47%) 0.7
B1_4 495 (49%) 52 (51%) 271 (50%) 172 (48%) 0.8
B1_5 507 (50%) 44 (44%) 274 (50%) 189 (53%) 0.3
B2_1 298 (30%) 26 (26%) 171 (31%) 101 (28%) 0.4
B2_2 206 (20%) 21 (21%) 110 (20%) 75 (21%)
0.9
B2_3 417 (41%) 42 (42%) 227 (42%) 148 (41%)
0.9
B2_4 362 (36%) 32 (32%) 193 (35%) 137 (38%) 0.4
B2_5 358 (36%) 41 (41%) 188 (34%) 129 (36%) 0.5
B2_6 469 (47%) 50 (50%) 253 (46%) 166 (46%) 0.8
B2_7 389 (39%) 43 (43%) 221 (41%) 125 (35%) 0.2
B2_8 377 (38%) 39 (39%) 192 (35%) 146 (41%) 0.2
1 n (%)
2 Pearson’s Chi-squared test
Stratified by A4
Characteristic Overall
N = 1,0051 		low
N = 3941 		middle
N = 3261 		high
N = 2851 		p-value2
A1



0.2
    female 583 (58%) 240 (61%) 189 (58%) 154 (54%)
    male 422 (42%) 154 (39%) 137 (42%) 131 (46%)
A2



0.9
    18-34 497 (49%) 195 (49%) 159 (49%) 143 (50%)
    35-54 416 (41%) 164 (42%) 136 (42%) 116 (41%)
    55+ 92 (9.2%) 35 (8.9%) 31 (9.5%) 26 (9.1%)
A3



0.3
    primary 101 (10%) 31 (7.9%) 42 (13%) 28 (9.8%)
    secondary 545 (54%) 220 (56%) 173 (53%) 152 (53%)
    tertiary or higher 359 (36%) 143 (36%) 111 (34%) 105 (37%)
A5



0.7
    region1 327 (33%) 127 (32%) 99 (30%) 101 (35%)
    region2 201 (20%) 76 (19%) 69 (21%) 56 (20%)
    region3 477 (47%) 191 (48%) 158 (48%) 128 (45%)
A6



0.6
    Rural 528 (53%) 203 (52%) 168 (52%) 157 (55%)
    Urban 477 (47%) 191 (48%) 158 (48%) 128 (45%)
B1_1 552 (55%) 231 (59%) 172 (53%) 149 (52%) 0.2
B1_2 276 (27%) 99 (25%) 89 (27%) 88 (31%) 0.3
B1_3 470 (47%) 191 (48%) 156 (48%) 123 (43%) 0.3
B1_4 495 (49%) 193 (49%) 169 (52%) 133 (47%) 0.4
B1_5 507 (50%) 185 (47%) 167 (51%) 155 (54%) 0.2
B2_1 298 (30%) 115 (29%) 91 (28%) 92 (32%) 0.5
B2_2 206 (20%) 78 (20%) 70 (21%) 58 (20%) 0.9
B2_3 417 (41%) 175 (44%) 130 (40%) 112 (39%) 0.3
B2_4 362 (36%) 129 (33%) 123 (38%) 110 (39%) 0.2
B2_5 358 (36%) 131 (33%) 119 (37%) 108 (38%) 0.4
B2_6 469 (47%) 193 (49%) 153 (47%) 123 (43%) 0.3
B2_7 389 (39%) 159 (40%) 128 (39%) 102 (36%) 0.5
B2_8 377 (38%) 140 (36%) 127 (39%) 110 (39%) 0.6
1 n (%)
2 Pearson’s Chi-squared test
Stratified by A5
Characteristic Overall
N = 1,0051 		region1
N = 3271 		region2
N = 2011 		region3
N = 4771 		p-value2
A1



0.2
    female 583 (58%) 186 (57%) 128 (64%) 269 (56%)
    male 422 (42%) 141 (43%) 73 (36%) 208 (44%)
A2



0.3
    18-34 497 (49%) 168 (51%) 108 (54%) 221 (46%)
    35-54 416 (41%) 132 (40%) 78 (39%) 206 (43%)
    55+ 92 (9.2%) 27 (8.3%) 15 (7.5%) 50 (10%)
A3



0.9
    primary 101 (10%) 30 (9.2%) 23 (11%) 48 (10%)
    secondary 545 (54%) 178 (54%) 104 (52%) 263 (55%)
    tertiary or higher 359 (36%) 119 (36%) 74 (37%) 166 (35%)
A4



0.7
    low 394 (39%) 127 (39%) 76 (38%) 191 (40%)
    middle 326 (32%) 99 (30%) 69 (34%) 158 (33%)
    high 285 (28%) 101 (31%) 56 (28%) 128 (27%)
A6



<0.001
    Rural 528 (53%) 327 (100%) 201 (100%) 0 (0%)
    Urban 477 (47%) 0 (0%) 0 (0%) 477 (100%)
B1_1 552 (55%) 169 (52%) 110 (55%) 273 (57%) 0.3
B1_2 276 (27%) 85 (26%) 54 (27%) 137 (29%) 0.7
B1_3 470 (47%) 140 (43%) 108 (54%) 222 (47%) 0.050
B1_4 495 (49%) 168 (51%) 106 (53%) 221 (46%) 0.2
B1_5 507 (50%) 169 (52%) 98 (49%) 240 (50%) 0.8
B2_1 298 (30%) 88 (27%) 60 (30%) 150 (31%) 0.4
B2_2 206 (20%) 66 (20%) 35 (17%) 105 (22%) 0.4
B2_3 417 (41%) 132 (40%) 88 (44%) 197 (41%) 0.7
B2_4 362 (36%) 121 (37%) 67 (33%) 174 (36%) 0.7
B2_5 358 (36%) 123 (38%) 65 (32%) 170 (36%) 0.5
B2_6 469 (47%) 153 (47%) 106 (53%) 210 (44%) 0.12
B2_7 389 (39%) 114 (35%) 84 (42%) 191 (40%) 0.2
B2_8 377 (38%) 133 (41%) 67 (33%) 177 (37%) 0.2
1 n (%)
2 Pearson’s Chi-squared test
Stratified by A6
Characteristic Overall
N = 1,0051 		Rural
N = 5281 		Urban
N = 4771 		p-value2
A1


0.3
    female 583 (58%) 314 (59%) 269 (56%)
    male 422 (42%) 214 (41%) 208 (44%)
A2


0.12
    18-34 497 (49%) 276 (52%) 221 (46%)
    35-54 416 (41%) 210 (40%) 206 (43%)
    55+ 92 (9.2%) 42 (8.0%) 50 (10%)
A3


0.8
    primary 101 (10%) 53 (10%) 48 (10%)
    secondary 545 (54%) 282 (53%) 263 (55%)
    tertiary or higher 359 (36%) 193 (37%) 166 (35%)
A4


0.6
    low 394 (39%) 203 (38%) 191 (40%)
    middle 326 (32%) 168 (32%) 158 (33%)
    high 285 (28%) 157 (30%) 128 (27%)
A5


<0.001
    region1 327 (33%) 327 (62%) 0 (0%)
    region2 201 (20%) 201 (38%) 0 (0%)
    region3 477 (47%) 0 (0%) 477 (100%)
B1_1 552 (55%) 279 (53%) 273 (57%) 0.2
B1_2 276 (27%) 139 (26%) 137 (29%) 0.4
B1_3 470 (47%) 248 (47%) 222 (47%) 0.9
B1_4 495 (49%) 274 (52%) 221 (46%) 0.078
B1_5 507 (50%) 267 (51%) 240 (50%)
0.9
B2_1 298 (30%) 148 (28%) 150 (31%) 0.2
B2_2 206 (20%) 101 (19%) 105 (22%) 0.3
B2_3 417 (41%) 220 (42%) 197 (41%)
0.9
B2_4 362 (36%) 188 (36%) 174 (36%) 0.8
B2_5 358 (36%) 188 (36%) 170 (36%)
0.9
B2_6 469 (47%) 259 (49%) 210 (44%) 0.11
B2_7 389 (39%) 198 (38%) 191 (40%) 0.4
B2_8 377 (38%) 200 (38%) 177 (37%) 0.8
1 n (%)
2 Pearson’s Chi-squared test

We can see that there are some statistical differences when stratifying by column A1, gender. We’ll explore these in more detail shortly.

We can also look at the mean and standard deviation of our continuous variables, stratified by demographics. Let’s loop through all demographic variables for continuous variables D1 andD2. We’ll make a few changes with this code- we’ll only display results for the variables D1 andD2, and we’ll use the statistic all_continuous. When running locally in RStudio, 6 tables will print out in the output.

R 

tables_cont_list <- list() # initialise empty list first

for (by_var in demo_vars) {

  tables_cont_list[[by_var]] <- survey %>%
    tbl_summary(
      by = all_of(by_var),
      include = c(D1, D2), # only these two rows
      statistic = list(
        all_continuous() ~ "{mean} ({sd})"
      ),
      digits = all_continuous() ~ 1,
      missing = "ifany",
      label = list(
        D1 ~ "D1 Commute time (minutes)",
        D2 ~ "D2 Commute distance (km)"
      )
    ) %>%
    add_p() %>%
    add_overall() %>%
    bold_labels() %>%
    modify_caption(glue::glue("**Stratified by {by_var}**"))
}
walk(tables_cont_list, print) # prints each table in the list
Stratified by A1
Characteristic Overall
N = 1,0051 		female
N = 5831 		male
N = 4221 		p-value2
D1 Commute time (minutes) 71.3 (27.4) 72.8 (26.5) 69.2 (28.5) 0.074
D2 Commute distance (km) 30.0 (11.4) 30.4 (11.3) 29.4 (11.5) 0.13
1 Mean (SD)
2 Wilcoxon rank sum test
Stratified by A2
Characteristic Overall
N = 1,0051 		18-34
N = 4971 		35-54
N = 4161 		55+
N = 921 		p-value2
D1 Commute time (minutes) 71.3 (27.4) 89.8 (17.2) 58.9 (20.0) 27.2 (16.4) <0.001
D2 Commute distance (km) 30.0 (11.4) 37.5 (7.2) 24.9 (9.0) 12.3 (6.6) <0.001
1 Mean (SD)
2 Kruskal-Wallis rank sum test
Stratified by A3
Characteristic Overall
N = 1,0051 		primary
N = 1011 		secondary
N = 5451 		tertiary or higher
N = 3591 		p-value2
D1 Commute time (minutes) 71.3 (27.4) 76.3 (27.5) 70.3 (27.6) 71.3 (27.0) 0.086
D2 Commute distance (km) 30.0 (11.4) 30.8 (12.5) 29.5 (11.2) 30.5 (11.4) 0.2
1 Mean (SD)
2 Kruskal-Wallis rank sum test
Stratified by A4
Characteristic Overall
N = 1,0051 		low
N = 3941 		middle
N = 3261 		high
N = 2851 		p-value2
D1 Commute time (minutes) 71.3 (27.4) 72.3 (26.7) 70.2 (27.8) 71.2 (27.8) 0.7
D2 Commute distance (km) 30.0 (11.4) 30.4 (11.9) 29.9 (10.7) 29.5 (11.5) 0.5
1 Mean (SD)
2 Kruskal-Wallis rank sum test
Stratified by A5
Characteristic Overall
N = 1,0051 		region1
N = 3271 		region2
N = 2011 		region3
N = 4771 		p-value2
D1 Commute time (minutes) 71.3 (27.4) 71.4 (27.0) 74.7 (28.6) 69.7 (27.0) 0.058
D2 Commute distance (km) 30.0 (11.4) 30.2 (11.3) 30.9 (10.8) 29.4 (11.7) 0.3
1 Mean (SD)
2 Kruskal-Wallis rank sum test
Stratified by A6
Characteristic Overall
N = 1,0051 		Rural
N = 5281 		Urban
N = 4771 		p-value2
D1 Commute time (minutes) 71.3 (27.4) 72.7 (27.6) 69.7 (27.0) 0.063
D2 Commute distance (km) 30.0 (11.4) 30.5 (11.1) 29.4 (11.7) 0.2
1 Mean (SD)
2 Wilcoxon rank sum test

We can see that there are some statistical differences when stratifying by column A2, age group. We’ll explore these in more detail shortly.

Callout

Statistical tests used by gtsummary

Whenadd_p() is called, gtsummary automatically selects a statistical test based on the variable type and the number of groups being compared. It defaults to conservative non-parametric tests for continuous variables. Specifically, for continuous variables with two groups it applies a Wilcoxon rank-sum test, and with three or more groups it applies a Kruskal-Wallis test.

For categorical and logical variables, it uses a Chi-square test, switching automatically to Fisher’s exact test when expected cell counts are too small (typically when any cell has an expected count below 5).

These defaults can be overridden using the test argument in add_p(). For example, specifying test = list(all_continuous() ~ "aov") to use ANOVA instead of Kruskal-Wallis.

The choice of whether to accept the default or override it should be guided by checking your distributions first. If continuous variables are approximately normally distributed and sample sizes are adequate, parametric tests (t-test, ANOVA) are appropriate and will generally be more statistically powerful than their non-parametric equivalents.

Export processed data

Now that we’ve investigated the processed the data, we’ll write it out into .rds, a file type that preserves everything we’ve done to process the data (factor levels and order, custom classes, attributes, column types). It’s the best option when the data will only ever be used in R.

R 

saveRDS(survey, here("data", "cleaned", "generated_survey_data_clean.rds"))

# read back in - retains all factor levels, ordered factors, etc.
survey <- readRDS(here("data", "cleaned", "generated_survey_data_clean.rds"))
Callout

File formats

Many different file formats can be read into and written (exported) out of R, including SPSS files.

Some of the common file types, and their uses, are included in the table below.

Format Write Read Retains R types? Readable outside R? Best used for
.rds saveRDS() readRDS() Yes No Saving single R objects between sessions
.RData save() load() Yes No Saving multiple R objects at once
.csv write_csv() read_csv() No Yes Sharing data with non-R users
.parquet arrow::write_parquet() arrow::read_parquet() Mostly Yes Large datasets shared across languages
.sav haven::write_sav() haven::read_sav() Mostly Yes (SPSS) Sharing data with SPSS users

Analysing multi-select data

Proportions

Questions B1 and B2 allowed respondents to select more than one answer (up to 3). Each option has been dummy-coded into its own boolean column (TRUE = selected, FALSE = not selected). The raw B1 and B2 columns contain the original response strings and can be ignored for analysis.

Let’s start by looking at the proportion of respondents who selected each option.

R 

survey %>%
  select(starts_with("B1_")) %>%
  summarise(across(everything(), mean)) %>%
  pivot_longer(everything(),
               names_to  = "option",
               values_to = "proportion") %>%
  ggplot(aes(x = reorder(option, proportion), y = proportion)) +
  geom_col(fill = "steelblue") +
  geom_text(aes(label = percent(proportion, accuracy = 1)),
            hjust = -0.15, size = 3.5) +
  coord_flip() +
  scale_y_continuous(labels = percent, limits = c(0, 0.7)) +
  labs(title = "B1: Proportion of respondents selecting each option",
       x = NULL, y = "% selecting") +
  theme_minimal(base_size = 12)

The reorder() call sorts the bars from lowest to highest proportion, making it easy to rank options by popularity. B1_1 is the most commonly selected option and B1_2 the least- a difference worth investigating when we run Chi-square tests shortly.

Let’s now plot the results for B2.

R 

survey %>%
  select(starts_with("B2_")) %>%
  summarise(across(everything(), mean)) %>%
  pivot_longer(everything(),
               names_to  = "option",
               values_to = "proportion") %>%
  ggplot(aes(x = reorder(option, proportion), y = proportion)) +
  geom_col(fill = "coral") +
  geom_text(aes(label = percent(proportion, accuracy = 1)),
            hjust = -0.15, size = 3.5) +
  coord_flip() +
  scale_y_continuous(labels = percent, limits = c(0, 0.6)) +
  labs(title = "B2: Proportion of respondents selecting each option",
       x = NULL, y = "% selecting") +
  theme_minimal(base_size = 12)

B2_6 is the most commonly selected option and B2_2 the least.

Correlation matrix

A correlation matrix is a useful diagnostic tool when working with multiple-response (multi-select) questions. Although each boolean column is structurally independent (meaning there is no logical rule preventing a respondent from selecting any combination of options), respondents’ choices in practice often cluster together.

We can use a correlation plot from the corrplot package to visualise the pairwise phi coefficients (Pearson correlation applied to 0/1 data) for all B1 and B2 option columns simultaneously.

The colour hue indicates direction: blue cells mean two options tend to be co-selected, while red cells mean selecting one option is associated with not selecting the other. Colour intensity encodes strength; darker shades indicate stronger associations, paler shades near-zero relationships.

As a practical guide, coefficients with an absolute value above 0.3 are worth flagging, and values above 0.6 suggest two options may be capturing the same underlying preference and could potentially be combined.

This step should always precede any analysis that treats the B section columns as independent predictors, since strong co-selection patterns can distort results if not investigated.

Let’s code a corrplot for B1_* columns. As a reminder, the options were:

Question B1: What should be the main goal of flexible working policies? (Select up to 3) - B1_1: Improve employee wellbeing & work-life balance - B1_2: Boost productivity & business performance - B1_3: Attract & retain top talent - B1_4: Reduce costs & office overhead - B1_5: Support diversity, equity & inclusion

R 

survey %>%
  select(starts_with("B1_")) %>%
  mutate(across(everything(), as.integer)) %>%   # TRUE/FALSE → 1/0
  cor(method = "pearson") %>%                    # phi coefficient for binary vars
  corrplot(method = "color", type = "upper",
           addCoef.col = "black", tl.col = "black")

This corrplot demonstrates that questions B1_1 and B1_3 show a mild positive correlation, with a co-efficient of 0.38, meaning respondents may be more likely to co-select these two options, while B1_1 and B1_5 and B1_3 and B1_5 show a mild negative correlation, meaning respondents may be more likely to not co-select these two options. The coefficients are all less than 0.6, but we’ll keep these associations in mind.

Now let’s code a corrplot for B2_* columns. As a reminder, the options were:

Question B2: Who should benefit most from flexible working? (Select up to 3)

  • B2_1: All employees equally, regardless of role or seniority
  • B2_2: Parents and caregivers with dependants
  • B2_3: Employees with disabilities or chronic health conditions
  • B2_4: Junior/entry-level employees building their careers
  • B2_5: Senior/experienced employees with proven track records
  • B2_6: Employees with long commutes or remote locations
  • B2_7: Employees from underrepresented or marginalised groups
  • B2_8: High performers and those meeting targets consistently

R 

survey %>%
  select(starts_with("B2_")) %>%
  mutate(across(everything(), as.integer)) %>%   # TRUE/FALSE → 1/0
  cor(method = "pearson") %>%                    # phi coefficient for binary vars
  corrplot(method = "color", type = "upper",
           addCoef.col = "black", tl.col = "black")

Again, no coefficients are > 0.6, but we’ll be mindful of any coefficients > 0.3.

Chi-square tests of independence

The Chi-square test of independence (χ²) tests whether two categorical variables are associated with each other, or whether any observed differences in proportions are plausibly due to chance.

Callout

When to use a Chi-Square Test

  • Both variables are categorical (nominal or ordinal).
  • You are testing association, not causation.
  • Each cell in your contingency table should have an expected frequency of at least 5.
  • Your sample size is reasonably large (n > 30 as a general guide).

When is the Chi-square test appropriate?

The Chi-square test of independence applies when:

  1. Observations are independent: each respondent contributes exactly one row.
  2. Both variables are categorical (nominal or ordinal).
  3. The expected count in each cell of the contingency table is at least 5 (the test becomes unreliable with smaller expected counts).

We will check assumption 3 explicitly for every test by examining chisq.test()$expected.

Effect size: Cramér’s V

A p-value only tells us whether an association exists; it does not tell us how strong it is. Cramér’s V is the standard effect size for Chi-square tests. It ranges from 0 (no association) to 1 (perfect association) and is comparable across tables of different sizes.

Cramér’s V Interpretation
0.1 Small effect
0.3 Medium effect
0.5 Large effect

We compute it with cramerV() from the rcompanion package.

Test 1: A boolean B-item × Gender (B1_1 × A1)

Let’s use the Chi-square test to answer this Research question: Are men and women equally likely to select option 1 of question B1?

Because B1_1 is coded as TRUE/FALSE, we convert it to a factor before tabulating.

R 

tbl_B1_A1 <- table(survey$B1_1, survey$A1)
tbl_B1_A1

OUTPUT 


        female male
  FALSE    111  342
  TRUE     472   80

R 

chi4 <- chisq.test(tbl_B1_A1)
chi4

OUTPUT 


	Pearson's Chi-squared test with Yates' continuity correction

data:  tbl_B1_A1
X-squared = 377.63, df = 1, p-value < 2.2e-16

R 

chi4$expected   # for a 2×2 table, four cells

OUTPUT 


          female     male
  FALSE 262.7851 190.2149
  TRUE  320.2149 231.7851

R 

cramerV(tbl_B1_A1)

OUTPUT 

Cramer V
   0.615

For a 2×2 contingency table, we can also compute an odds ratio to express the association in a more interpretable way: the odds of selecting B1_1 for one gender relative to the other.

R 

oddsratio(tbl_B1_A1)$measure

OUTPUT 

       odds ratio with 95% C.I.
          estimate      lower      upper
  FALSE 1.00000000         NA         NA
  TRUE  0.05530907 0.03994176 0.07574169

An odds ratio of 1 means equal odds for both groups. Values above 1 mean the first row group has higher odds; values below 1 mean lower odds.

Callout

Reporting checklist

When writing up Chi-square results for a report, include the following:

  1. The research question: what association are you testing?
  2. The contingency table: row percentages to show the pattern
  3. Test statistic and degrees of freedom: χ²(df) = X.XX.
  4. p-value: exact value to three decimal places (or < .001)
  5. Assumption check: confirm expected counts ≥ 5 in all (or at least 80%) of cells
  6. Effect size: Cramér’s V with interpretation (small / medium / large)
  7. Odds ratio if significant): identify the association
  8. Standardised residuals (if significant): identify which cells drive the association

An example sentence:

“Age group was significantly associated with the selection of ‘Improve employee wellbeing & work-life balance’ as a main goal of flexible working policies (χ²(1) = 377.63, p < 0.001), with a large effect size (Cramér’s V = 0.615).

Older employees had substantially lower odds of selecting this priority compared to their younger counterparts (OR = 0.055, 95% CI [0.040, 0.076]), indicating that older employees were approximately 18 times less likely to select this option than younger employees. This strong and statistically robust difference suggests that improving employee wellbeing and work-life balance is a considerably more pressing concern for younger employees.”

We can expand on this code to run Chi-square, Cramér’s, and odd’s for all B1_* columns, and report the results out in an easy to read table.

Test 2: A boolean B-item × Gender (All B1_* × A1)

R 

# Select all B1_ columns
b1_vars <- survey %>%
  select(starts_with("B1_")) %>%
  names()

results_B1_A1 <- tibble(b1_var = b1_vars) %>%
  rowwise() %>%
  mutate(
    tbl = list(table(survey[[b1_var]], survey[["A1"]])),
    chi_test = list(chisq.test(tbl)),
    n_cells_low = sum(chi_test$expected < 5),
    chi_stat = chi_test$statistic,
    chi_df = chi_test$parameter,
    chi_p = chi_test$p.value,
    cramers_v = cramerV(tbl),
    or_result = list( # run Fishers test in the event any cells are < 5
      tryCatch(
        fisher.test(tbl)$conf.int |>
          (function(ci) tibble(
            or        = fisher.test(tbl)$estimate,
            or_lower  = ci[1],
            or_upper  = ci[2]
          ))(),
        error = function(e) tibble(or = NA_real_, or_lower = NA_real_, or_upper = NA_real_)
      )
    )
  ) %>%
  unnest(or_result) %>%
  ungroup() %>%
  select(-tbl, -chi_test) %>%
  arrange(chi_p) %>%
  mutate(across(c(chi_stat, chi_p, cramers_v, or, or_lower, or_upper), ~round(., 4)))

results_B1_A1

OUTPUT 

# A tibble: 5 × 9
  b1_var n_cells_low chi_stat chi_df  chi_p cramers_v      or or_lower or_upper
  <chr>        <int>    <dbl>  <int>  <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
1 B1_3             0  457.         1 0         0.676   0.025    0.0159   0.0382
2 B1_1             0  378.         1 0         0.615   0.0553   0.0394   0.0766
3 B1_5             0  292.         1 0         0.541  12.2      8.89    16.9
4 B1_4             0   12.2        1 0.0005    0.112   0.633    0.488    0.821
5 B1_2             0    0.267      1 0.605     0.0186  1.09     0.813    1.45
Callout

Multiple comparisons

Running multiple Chi-square tests simultaneously inflates the probability of at least one false positive. To address this, we apply the Benjamini-Hochberg False Discovery Rate (FDR) correction using p.adjust(method = “fdr”), which controls the expected proportion of false positives among significant results.

Unlike the Bonferroni correction, which controls the probability of any false positive and can be overly conservative when running many correlated tests, FDR offers a better balance between sensitivity and specificity, making it well suited to survey data where items tend to be correlated. Adjusted p-values are interpreted against the same α threshold of 0.05.

Let’s repeat our above analysis and include the FDR correction.

R 

results_B1_A1_fdr <- tibble(b1_var = b1_vars) %>%
  rowwise() %>%
  mutate(
    tbl = list(table(survey[[b1_var]], survey[["A1"]])),
    chi_test = list(chisq.test(tbl)),
    n_cells_low = sum(chi_test$expected < 5),
    chi_stat = chi_test$statistic,
    chi_df = chi_test$parameter,
    chi_p = chi_test$p.value,
    cramers_v = cramerV(tbl),
    or_result = list(
      tryCatch(
        fisher.test(tbl)$conf.int |>
          (function(ci) tibble(
            or = fisher.test(tbl)$estimate,
            or_lower = ci[1],
            or_upper = ci[2]
          ))(),
        error = function(e) tibble(or = NA_real_, or_lower = NA_real_, or_upper = NA_real_)
      )
    )
  ) %>%
  unnest(or_result) %>%
  ungroup() %>%
  select(-tbl, -chi_test) %>%
  mutate(chi_p_fdr = p.adjust(chi_p, method = "fdr")) %>%  # FDR correction across all tests
  arrange(chi_p_fdr) %>%
  mutate(across(c(chi_stat, chi_p, chi_p_fdr, cramers_v, or, or_lower, or_upper), ~round(., 4)))

results_B1_A1_fdr

OUTPUT 

# A tibble: 5 × 10
  b1_var n_cells_low chi_stat chi_df  chi_p cramers_v      or or_lower or_upper
  <chr>        <int>    <dbl>  <int>  <dbl>     <dbl>   <dbl>    <dbl>    <dbl>
1 B1_3             0  457.         1 0         0.676   0.025    0.0159   0.0382
2 B1_1             0  378.         1 0         0.615   0.0553   0.0394   0.0766
3 B1_5             0  292.         1 0         0.541  12.2      8.89    16.9
4 B1_4             0   12.2        1 0.0005    0.112   0.633    0.488    0.821
5 B1_2             0    0.267      1 0.605     0.0186  1.09     0.813    1.45
# ℹ 1 more variable: chi_p_fdr <dbl>

Our reporting would now include the fact that the p-value was corrected. “After FDR correction, age group remained significantly associated with the selection of ‘Improve employee wellbeing & work-life balance’ as a main goal of flexible working policies (χ²(1) = 377.63, p_adj < 0.001), with a large effect size (Cramér’s V = 0.615).

Older employees had substantially lower odds of selecting this priority compared to their younger counterparts (OR = 0.055, 95% CI [0.040, 0.076]), indicating that older employees were approximately 18 times less likely to select this option than younger employees. This strong and statistically robust difference suggests that improving employee wellbeing and work-life balance is a considerably more pressing concern for younger employees.”

When Chi-square assumptions fail — Fisher’s exact test

If any expected cell count falls below 5, the Chi-square approximation becomes unreliable. This is most likely to happen with small subgroups, such as when we cross region (three levels, potentially unequal) with education (three levels) — some combinations may be rare.

R 

tbl_A5_A2 <- table(survey$A5, survey$A2)
chisq.test(tbl_A5_A2)$expected   # check first

OUTPUT 


             18-34    35-54      55+
  region1 161.7104 135.3552 29.93433
  region2  99.4000  83.2000 18.40000
  region3 235.8896 197.4448 43.66567

If any expected count is below 5, switch to Fisher’s exact test (not necessary in our case, but let’s write the code anyway as a demonstration). For tables larger than 2×2, base R’s exact computation is impractical, so we use a Monte Carlo simulation (simulate.p.value = TRUE).

R 

fisher.test(tbl_A5_A2,
            simulate.p.value = TRUE,
            B = 10000)   # B = number of Monte Carlo replicates

OUTPUT 


	Fisher's Exact Test for Count Data with simulated p-value (based on
	10000 replicates)

data:  tbl_A5_A2
p-value = 0.3577
alternative hypothesis: two.sided

The Monte Carlo p-value is based on 10,000 random permutations of the table and is a reliable substitute for the asymptotic Chi-square approximation when cell counts are small.

For 2X2 tables, just use the Fisher’s Exact Test with no simulation. Again, our expected cell counts are > 5, so this is just a demonstration.

R 

tbl_A1_B1_1 <- table(survey$A1, survey$B1_1)
chisq.test(tbl_A1_B1_1)$expected   # check first

OUTPUT 


            FALSE     TRUE
  female 262.7851 320.2149
  male   190.2149 231.7851

R 

fisher.test(tbl_A1_B1_1)

OUTPUT 


	Fisher's Exact Test for Count Data

data:  tbl_A1_B1_1
p-value < 2.2e-16
alternative hypothesis: true odds ratio is not equal to 1
95 percent confidence interval:
 0.03944169 0.07660845
sample estimates:
odds ratio
0.05525789
Callout

Interpreting a 2×3 table

A significant Chi-square result tells us that the overall pattern of income differs between urban and rural areas. It does not tell us which specific income category drives the difference. To find that, examine the standardised residuals (see Test 3 below).

Test 3: Satisfaction × Age group (E1 × A2), with standardised residuals

Research question: Does overall satisfaction with work life balance (E1) vary across age groups (A2)?

This test introduces a powerful diagnostic tool: standardised residuals. After a significant Chi-square test, standardised residuals tell us which cells contribute most to the result; that is, where the observed count differs most from what we would expect under independence.

A standardised residual beyond ±2 (roughly corresponding to a two-tailed p < 0.05) flags a cell that is “doing more than its share” of the Chi-square statistic- where the associations are the strongest.

R 

# Note: 4 respondents have a missing E1 value; drop them with na.omit()
df_E1 <- survey %>%
  filter(!is.na(E1)) %>%
  mutate(E1 = factor(E1, levels = c(
    "Strongly dissatisfied", "Dissatisfied",
    "Neutral", "Satisfied", "Strongly satisfied"
  )))

tbl_E1_A2 <- table(df_E1$E1, df_E1$A2)

chi3 <- chisq.test(tbl_E1_A2)
chi3

OUTPUT 


	Pearson's Chi-squared test

data:  tbl_E1_A2
X-squared = 58.518, df = 8, p-value = 9.096e-10

R 

chi3$expected   # check assumption

OUTPUT 


                           18-34    35-54      55+
  Strongly dissatisfied 109.2308 91.42857 19.34066
  Dissatisfied          107.7413 90.18182 19.07692
  Neutral               101.7832 85.19481 18.02198
  Satisfied             107.2448 89.76623 18.98901
  Strongly satisfied     71.0000 59.42857 12.57143

R 

cramerV(tbl_E1_A2)

OUTPUT 

Cramer V
   0.171

Now examine the standardised residuals:

R 

round(chi3$stdres, 2)

OUTPUT 


                        18-34 35-54   55+
  Strongly dissatisfied  6.07 -4.25 -3.33
  Dissatisfied           1.27 -0.18 -1.92
  Neutral               -2.16  2.19 -0.01
  Satisfied             -3.26  1.75  2.72
  Strongly satisfied    -2.35  0.65  3.01

We can also visualise them using corrplot, which makes the pattern immediately apparent:

R 

corrplot(chi3$stdres,
         is.corr = FALSE,
         method = "color",
         col = colorRampPalette(c("royalblue", "white", "firebrick"))(200),
         tl.col = "black",
         tl.srt = 45,
         tl.cex = 0.85,        # increase/decrease label size (default is 0.8)
         cl.cex = 0.85,        # match colour legend text size
         cl.ratio = 0.4,        # widens the legend bar giving labels more room
         title = "Standardised residuals: E1 satisfaction × A2 age group",
         mar = c(0, 0, 2, 0))

In this plot, red cells indicate that a combination is observed more often than expected under independence; blue cells indicate it is observed less often. Cells with residuals beyond ±2 are where the association is “happening”.

Example results sentence:

“Overall satisfaction with work life balance differed significantly across age groups (χ²(8) = 58.52, p < 0.001), though the association was small in magnitude (Cramér’s V = 0.171). Satisfaction tended to increase with age: older employees (55+) were more likely than expected to report being satisfied (residual = 2.72) or strongly satisfied (residual = 3.01), while younger employees (18-34) were substantially more likely than expected to report strong dissatisfaction (residual = 6.07) and less likely to report satisfaction (residual = −3.26) or strong satisfaction (residual = −2.35). Employees aged 35–54 showed little deviation from expected counts, with only a modest tendency toward neutrality (residual = 2.19).”