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Descriptive Statistics and Cross-tabulation

Descriptive Statistics and Cross-tabulation
Also known as: Basic statistics、Simple tabulation、Cross-tabulation table、Frequency distribution

Summarizes data distributions using frequencies, percentages, means and medians. Show units, denominators and missingness, and avoid describing the whole distribution through one summary statistic. [1] [2]

Descriptive statistics and cross-tabulation analysis plan — openReferences and checked sections
Difficulty
Introductory
Cost
Low
Duration
Planning example, not a universal standard duration: several hours–2 days, including data cleaning, tabulation and charts
Content updated: 2026-09-13Source checked: 2026-09-13 (includes AI cross-checking)No documented human reviewIncludes fictional examples

How it works at a glance

The mean is the sum divided by the count; the median is the middle value in ordered data. With skewness or extreme values, they convey different information. [1]

Cross-tabulation organizes counts and percentages by combinations of characteristics. This page's practical examples specify row or column denominators and the period, distinguishing observed differences from causal effects. [2]

  1. Clean data and check variables
  2. Produce frequency distributions and percentages
  3. Calculate central tendency and dispersion
  4. Create cross-tabulations
  5. Calculate effect sizes where needed
  6. Create charts and interpret findings
Sequence of implementation steps. See “Implementation steps” for details of each stage.

When to use it and when it is unsuitable

When to use it

  • When obtaining and reporting an initial overview after collecting survey or monitoring data
  • When comparing service reach or satisfaction by beneficiary characteristics, such as gender, age or area
  • When preparing numerical summaries and charts as a basis for an evaluation report
  • When showing before-and-after changes through means or medians and communicating their magnitude with effect sizes

When it is unsuitable

  • When demonstrating causation, whether the intervention produced outcomes. Descriptive statistics describe relationships but cannot establish causation.
  • Generalizing from very few observations is highly limited, although individual values can still be described.
  • Evaluations containing only qualitative data, such as open responses or interviews. Thematic or content analysis is appropriate.

Participants, roles, and deliverables

Participants and roles

1–2 evaluators working with data collectors and, where separate, statistical staff

Main deliverables

  • Frequency distributions and descriptive statistics
  • Cross-tabulations by characteristics or groups
  • Effect-size worksheet for before-and-after comparisons
  • Basic analysis report with charts

Implementation steps

  1. Clean data and check variables
    Check missing values, outliers and entry errors, and identify measurement scales: nominal, ordinal, interval or ratio. This stage is essential because usable statistics depend on scales.
  2. Produce frequency distributions and percentages
    Calculate frequencies and valid percentages for each variable. Examine distributions using frequency tables for categorical data, or histograms or listed values for continuous data, according to counts and purpose. Specify missing-data treatment.
  3. Calculate central tendency and dispersion
    Choose means, medians, standard deviations or interquartile ranges according to distribution and intended message. Normality is not required to use a mean; show effects of skewness and outliers.
  4. Create cross-tabulations
    Tabulate combinations of 2 relevant variables, such as group × satisfaction. Consistently use row or column percentages and state the choice in notes. A chi-square test may examine association.
  5. Calculate effect sizes where needed
    When summarizing differences, show differences in original units or a suitable scale, and state denominators and populations. For inference, add intervals appropriate to sampling design and assumptions. Do not require p-values for descriptive statistics or judge importance by fixed effect-size categories.
  6. Create charts and interpret findings
    Select bar, line, pie or box plots suited to the purpose. Add interpretations against evaluation questions rather than presenting numbers alone.

Strengths and limitations

Strengths

  • Accessible with Excel or spreadsheet software and limited statistical expertise.
  • Presents data in understandable form as a basis for evaluation reporting.
  • Effect sizes complement significance tests' dependence on sample size.
  • Cross-tabulation visualizes subgroup differences and supports equity evaluation.

Limitations

  • Can describe correlation and association but cannot establish causation.
  • An inappropriate summary statistic misrepresents conditions, for example when 1 outlier substantially changes the mean.
  • Mechanically cross-tabulating many variables creates multiple-comparison problems and chance significant associations.
  • Cannot capture the richness of qualitative open responses or observations.

Common pitfalls

  • Reporting means without checking distributional skewness or outliers. Always examine histograms or box plots and add medians where necessary.
  • Confusing small p-values with important findings. Even tiny differences may be significant in large datasets. Always report effect sizes and confidence intervals together.
  • Do not compare differently sized groups solely by counts. Show counts, denominators and percentages, including instability of percentages in small groups.

Conditions of use and evidence

  • Interpret summary statistics by comparing means and medians when distributions are skewed or contain extreme values. [1]
Fictional example; not actual results

Summarize consultation waiting times

A fictional illustrative example with 5 waiting times of 5, 5, 10, 10 and 70 minutes.

IndicatorValueInterpretation
Mean20 minutes100 minutes total ÷ 5 cases
Median10 minutesThe middle, third ordered value
Minimum–maximum5–70 minutes1 long wait

Common errors in judgment

Common mistake

Replacing non-response with 0 before averaging

How to revise

State missing counts and treatment and use valid responses as the denominator.

ReasonAn observed zero differs from missing data.

Common mistake

Mixing denominators in characteristic-specific percentages

How to revise

State row or column percentages in the table.

ReasonIdentical counts answer different questions depending on denominators.

Organize your thinking by writing

Descriptive statistics and cross-tabulation analysis plan

A practical template is available to fill in and print on A4 paper.

Open worksheet

Related methods

Survey / QuestionnaireRegression AnalysisData VisualizationMixed Methods ResearchEvaluation Report Writing

References and checked sections

  1. NIST/SEMATECH e-Handbook: Measures of Location
    NIST
    Section consulted
    Definition of Location / Why Different Measures
    How it relates to the text
    Interpret summary statistics by comparing means and medians when distributions are skewed or contain extreme values.
    Source checked: (includes AI cross-checking)
  2. NIST/SEMATECH e-Handbook 7.4.5: How can we compare the results of classifying according to several categories?
    NIST
    Section consulted
    Contingency Table approach / Contingency table classifying defects / Column and Row probabilities
    How it relates to the text
    Basic contingency table structure: combine classifications in rows and columns and record counts in cells.
    Source checked: (includes AI cross-checking)

Editorial and checking information

Content updated: Source checked: (includes AI cross-checking)No documented human reviewIncludes fictional examplesEditorial policy and scope of checkingCite this pageReport a correction

How to cite this page

EvalCompass Editorial Team. “Descriptive Statistics and Cross-tabulation”. EvalCompass, updated 2026-09-13. https://evalcompass.jun-nakatani.com/en/methods/descriptive-statistics/
Add the date you accessed the page. Text created by this site is available under CC BY 4.0. Quotations, external materials, and bundled fonts have their own terms of use. When reusing content, credit the source, link to the license, and indicate any changes.

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Change history
  • — Checked sources for definitions and applicability conditions and added fictional examples, judgment rationales and all-field examples. Revised unverified historical or adoption claims, and adjusted fixed counts, thresholds and institutional generalizations in procedures and cautions. Aligned distribution checks with listing small sets of values. Rechecked example and completion-check correspondence and conditional procedures. Matched cross-tabulation definitions to the relevant NIST contingency-table section, separately from mean and median sources.