Descriptive Statistics and Frequencies

Overview

Before running any statistical tests, you should understand your data. Descriptive statistics summarize what is typical, what is unusual, and how responses are distributed.

mariposa provides four functions for data exploration:

Function	Best for
`describe()`	Numeric variables — means, medians, spread
`frequency()`	Categorical variables — counts and percentages
`crosstab()`	Relationships between two categorical variables
`codebook()`	Full data dictionary with types, labels, and values

All four support survey weights and grouped analysis.

Summary Statistics with describe()

Basic Usage

survey_data %>%
  describe(age)
#> 
#> Descriptive Statistics
#> ----------------------
#>  Variable  Mean Median     SD Range IQR Skewness    N Missing
#>       age 50.55     50 16.976    77  24    0.172 2500       0
#> ----------------------------------------

Multiple Variables

survey_data %>%
  describe(age, income, life_satisfaction)
#> 
#> Descriptive Statistics
#> ----------------------
#>           Variable     Mean Median       SD Range  IQR Skewness    N Missing
#>                age   50.550     50   16.976    77   24    0.172 2500       0
#>             income 3753.934   3500 1432.802  7200 1900    0.730 2186     314
#>  life_satisfaction    3.628      4    1.153     4    2   -0.501 2421      79
#> ----------------------------------------

With Survey Weights

Add weights for population-representative statistics:

survey_data %>%
  describe(age, income, life_satisfaction, weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>                age   50.514     50   17.084    77   25    0.159      2468.8
#>             income 3743.099   3500 1423.966  7200 1900    0.725      2158.9
#>  life_satisfaction    3.625      4    1.152     4    2   -0.499      2390.9
#> ----------------------------------------

Grouped Analysis

Compare statistics across subgroups:

survey_data %>%
  group_by(region) %>%
  describe(income, life_satisfaction, weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#> 
#> Group: region = East
#> --------------------
#> ----------------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>             income 3760.687   3600 1388.321  7200 1700    0.721       421.9
#>  life_satisfaction    3.623      4    1.203     4    2   -0.558       457.4
#> ----------------------------------------
#> 
#> Group: region = West
#> --------------------
#> ----------------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>             income 3738.586   3500 1433.325  7200 1900    0.727      1738.1
#>  life_satisfaction    3.625      4    1.139     4    2   -0.481      1934.8
#> ----------------------------------------

Choosing Statistics

The show argument controls which statistics are displayed:

# Just the essentials
survey_data %>%
  describe(age, income, show = c("mean", "sd", "range"))
#> 
#> Descriptive Statistics
#> ----------------------
#>  Variable     Mean       SD Range    N Missing
#>       age   50.550   16.976    77 2500       0
#>    income 3753.934 1432.802  7200 2186     314
#> ----------------------------------------

# Everything available
survey_data %>%
  describe(age, show = "all")
#> 
#> Descriptive Statistics
#> ----------------------
#>  Variable  Mean Median     SD   SE Range IQR Skewness Kurtosis Variance Mode
#>       age 50.55     50 16.976 0.34    77  24    0.172   -0.364  288.185   18
#>  Q25 Q50 Q75    N Missing
#>   38  50  62 2500       0
#> ----------------------------------------

Understanding the Output

n: Number of valid (non-missing) cases
mean (\(\bar{x}\)): The arithmetic average
sd: Standard deviation — how spread out the values are
median: The middle value (50th percentile)
min / max: The range of observed values
skewness: Distribution symmetry. Values near 0 indicate symmetry; values beyond \(\pm 1\) indicate notable skew
kurtosis: Tail heaviness. Values near 0 indicate a normal-like shape

Frequency Tables with frequency()

Basic Frequency

survey_data %>%
  frequency(education)
#> Frequency: education
#>   4 categories, N valid = 2500, missing = 0
#> Use summary() for detailed output.

Understanding the Output

Frequency: Number of respondents in each category
Percent: Percentage of all cases, including missing
Valid Percent: Percentage of non-missing cases only
Cumulative Percent: Running total of valid percentages

Use Valid Percent when missing values are truly missing (e.g., skip patterns). Use Percent when non-response is itself meaningful.

Weighted Frequencies

survey_data %>%
  frequency(education, weights = sampling_weight)
#> Frequency: education [Weighted]
#>   4 categories, N valid = 2516, missing = 0
#> Use summary() for detailed output.

Multiple Variables

survey_data %>%
  frequency(education, employment, region, weights = sampling_weight)
#> Frequency: education [Weighted]
#>   4 categories, N valid = 2516, missing = 0
#> Frequency: employment [Weighted]
#>   5 categories, N valid = 2516, missing = 0
#> Frequency: region [Weighted]
#>   2 categories, N valid = 2516, missing = 0
#> Use summary() for detailed output.

Grouped Frequencies

survey_data %>%
  group_by(gender) %>%
  frequency(education, weights = sampling_weight)
#> Frequency: education [Weighted]
#>   [gender = Male] 4 categories, N valid = 1195, missing = 0
#>   [gender = Female] 4 categories, N valid = 1321, missing = 0
#> Use summary() for detailed output.

Cross-Tabulation with crosstab()

Basic Crosstab

Examine the relationship between two categorical variables:

survey_data %>%
  crosstab(education, employment)
#> Crosstab: education x employment
#>   4 x 5 table, N = 2500
#>   Note: no significance test included - use chi_square() for a test of independence.
#> Use summary() for detailed output.

Understanding the Output

Count: Number of cases in each cell
Row %: Percentage within each row (sums to 100% across)
Column %: Percentage within each column (sums to 100% down)
Cell %: Percentage of the total sample

Row percentages answer: “Of people with this education level, what proportion has each employment status?”

Column percentages answer: “Of people with this employment status, what proportion has each education level?”

Weighted Crosstabs

survey_data %>%
  crosstab(education, employment, weights = sampling_weight)
#> Crosstab: education x employment [Weighted]
#>   4 x 5 table, N = 2516
#>   Note: no significance test included - use chi_square() for a test of independence.
#> Use summary() for detailed output.

Grouped Crosstabs

survey_data %>%
  group_by(region) %>%
  crosstab(education, employment, weights = sampling_weight)
#> Crosstab: education x employment [Weighted]
#>   [region = East] 4 x 5 table, N = 509
#>   [region = West] 4 x 5 table, N = 2007
#>   Note: no significance test included - use chi_square() for a test of independence.
#> Use summary() for detailed output.

Multiple Response Sets with multiple_response()

“Check all that apply” questions arrive as a series of 0/1 indicator variables. multiple_response() (SPSS MULT RESPONSE) analyzes them as one set, with the two percentage bases SPSS users expect: percent of responses (sums to 100%) and percent of cases (can sum above 100%, because respondents tick several boxes):

# Example set: institutions a respondent trusts highly (rating 4-5)
trust_set <- survey_data %>%
  mutate(
    gov     = as.integer(trust_government >= 4),
    media   = as.integer(trust_media >= 4),
    science = as.integer(trust_science >= 4)
  )

trust_set %>%
  multiple_response(gov, media, science, weights = sampling_weight) %>%
  summary()
#> 
#> Weighted Multiple Response Results
#> ----------------------------------
#> - Set: gov, media, science
#> - Counted value: 1
#> - Weights Variable: sampling_weight
#> 
#> Frequencies
#>   --------------------------------------------- 
#>   Option   Responses n  Responses %  % of Cases 
#>   --------------------------------------------- 
#>   gov            585.8         22.9        23.3 
#>   media          476.5         18.7        18.9 
#>   science       1490.3         58.4        59.2 
#>   --------------------------------------------- 
#>   Valid cases: 2516 | Total responses: 2553 | Excluded (all missing): 0
#>   % of Cases can sum above 100% (multiple mentions per case).

Cross the set against a demographic with by — mentions and case-based column percentages per group:

trust_set %>%
  multiple_response(gov, media, science, by = gender,
                    weights = sampling_weight) %>%
  summary()
#> 
#> Weighted Multiple Response Results
#> ----------------------------------
#> - Set: gov, media, science
#> - Counted value: 1
#> - Weights Variable: sampling_weight
#> - By: gender
#> 
#> Frequencies
#>   --------------------------------------------- 
#>   Option   Responses n  Responses %  % of Cases 
#>   --------------------------------------------- 
#>   gov            585.8         22.9        23.3 
#>   media          476.5         18.7        18.9 
#>   science       1490.3         58.4        59.2 
#>   --------------------------------------------- 
#>   Valid cases: 2516 | Total responses: 2553 | Excluded (all missing): 0
#>   % of Cases can sum above 100% (multiple mentions per case).
#> 
#> Crosstab: set BY gender (% of cases per column)
#>   --------------------------------- 
#>   Option          Male       Female 
#>   --------------------------------- 
#>   gov      280 (23.4%)  306 (23.2%) 
#>   media    214 (17.9%)  262 (19.8%) 
#>   science  694 (58.1%)  797 (60.3%) 
#>   --------------------------------- 
#>   Cases per column - Male: 1195, Female: 1321

Data Dictionary with codebook()

For a comprehensive overview of your entire dataset, use codebook():

codebook(survey_data)

This opens an interactive HTML view in the RStudio Viewer showing variable names, types, labels, value distributions, and missing data patterns. It is the fastest way to orient yourself in a new dataset.

Complete Example

A typical descriptive analysis workflow:

# 1. Explore the dataset
find_var(survey_data, "trust|satisfaction")
#>   col              name                                           label
#> 1  10 life_satisfaction Life satisfaction (1=dissatisfied, 5=satisfied)
#> 2  11  trust_government        Trust in government (1=none, 5=complete)
#> 3  12       trust_media             Trust in media (1=none, 5=complete)
#> 4  13     trust_science           Trust in science (1=none, 5=complete)

# 2. Summarize numeric variables
survey_data %>%
  describe(age, income, life_satisfaction,
           weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>                age   50.514     50   17.084    77   25    0.159      2468.8
#>             income 3743.099   3500 1423.966  7200 1900    0.725      2158.9
#>  life_satisfaction    3.625      4    1.152     4    2   -0.499      2390.9
#> ----------------------------------------

# 3. Check categorical distributions
survey_data %>%
  frequency(education, employment,
            weights = sampling_weight)
#> Frequency: education [Weighted]
#>   4 categories, N valid = 2516, missing = 0
#> Frequency: employment [Weighted]
#>   5 categories, N valid = 2516, missing = 0
#> Use summary() for detailed output.

# 4. Cross-tabulate key relationships
survey_data %>%
  crosstab(education, employment,
           weights = sampling_weight)
#> Crosstab: education x employment [Weighted]
#>   4 x 5 table, N = 2516
#>   Note: no significance test included - use chi_square() for a test of independence.
#> Use summary() for detailed output.

# 5. Compare across regions
survey_data %>%
  group_by(region) %>%
  describe(income, life_satisfaction,
           weights = sampling_weight)
#> 
#> Weighted Descriptive Statistics
#> -------------------------------
#> 
#> Group: region = East
#> --------------------
#> ----------------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>             income 3760.687   3600 1388.321  7200 1700    0.721       421.9
#>  life_satisfaction    3.623      4    1.203     4    2   -0.558       457.4
#> ----------------------------------------
#> 
#> Group: region = West
#> --------------------
#> ----------------------------------------
#>           Variable     Mean Median       SD Range  IQR Skewness Effective_N
#>             income 3738.586   3500 1433.325  7200 1900    0.727      1738.1
#>  life_satisfaction    3.625      4    1.139     4    2   -0.481      1934.8
#> ----------------------------------------

Practical Tips

Start with descriptives before testing. Understanding distributions, ranges, and missing data patterns prevents surprises in later analyses.
Check for impossible values. Negative ages, incomes above plausible limits, or out-of-range Likert responses indicate data quality issues.
Look at skewness. Values beyond \(\pm 1\) suggest the distribution departs notably from normality. This affects the choice between parametric and non-parametric tests.
Always use weights when available. Unweighted statistics describe your sample; weighted statistics estimate the population.
Consider your audience. For technical readers, include SD, skewness, and kurtosis. For general audiences, focus on means, medians, and percentages.

Descriptive Statistics and Frequencies

Overview

Summary Statistics with describe()

Basic Usage

Multiple Variables

With Survey Weights

Grouped Analysis

Choosing Statistics

Understanding the Output

Frequency Tables with frequency()

Basic Frequency

Understanding the Output

Weighted Frequencies

Multiple Variables

Grouped Frequencies

Cross-Tabulation with crosstab()

Basic Crosstab

Understanding the Output

Weighted Crosstabs

Grouped Crosstabs

Multiple Response Sets with multiple_response()

Data Dictionary with codebook()

Complete Example

Practical Tips

Summary

Next Steps