Chi-Square Test Explained: When and How to Use It, with Real Data

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Below, we explain the chi-square test step by step and run it live on real data from ScholarsColab.

Chi-square test at a glance

Worked example: do research fields prefer journals or conferences?

We run a complete chi-square test, notebook-style, on real publication data. Every result is calculated live, and you can run the same code yourself.

The data: 41,792 papers, mostly published between 1998 and 2026, by 967 ScholarsColab mentors (data updated 15 October 2026). The file you will load is anonymised: no paper titles, journal names or researcher identities.

Step 1: Load the data

import numpy as np
import pandas as pd
from datetime import date

# The ScholarsColab Research Methods Index (papers level): anonymised, updated daily
DATA = "https://scholarscolab.com/wp-json/scholarscolab/v1/research-methods-data?level=papers"
papers = pd.read_csv(DATA, comment="#")   # lines starting with # hold the citation

def p_text(p):
    return "< 0.001" if p < 0.001 else f"= {p:.3f}"

print(papers.shape)
papers.head()

(41792, 15)

Step 2: Build the contingency table

Our two categorical variables are the research discipline and the type of venue (journal or conference). A contingency table counts the papers in every combination.

jc = papers[papers["venue_type"].isin(["journal", "conference"])]
table = pd.crosstab(jc["discipline"], jc["venue_type"])
table

Step 3: Run the test and compare observed with expected counts

The test asks: if discipline and venue type were unrelated, how many papers would we expect in each cell? Those expected counts are shown below the result.

from scipy import stats
chi2, p, dof, expected = stats.chi2_contingency(table)
n = table.to_numpy().sum()
cramers_v = np.sqrt(chi2 / (n * (min(table.shape) - 1)))
print(f"chi2 = {chi2:.1f}, df = {dof}, p {p_text(p)}, Cramér's V = {cramers_v:.2f}")
pd.DataFrame(expected, index=table.index, columns=table.columns).round(0)

chi2 = 2803.7, df = 6, p < 0.001, Cramér's V = 0.27

Step 4: Show the pattern in a chart

import matplotlib.pyplot as plt
share = (table["conference"] / table.sum(axis=1) * 100).sort_values()
overall = table["conference"].sum() / n * 100

fig, ax = plt.subplots(figsize=(8, 4))
ax.barh(share.index, share.values, color="lightgreen", edgecolor="green")
ax.axvline(overall, color="green", linestyle="--", label=f"All disciplines: {overall:.1f}%")
ax.set_xlabel("% of papers published at conferences")
ax.legend()
plt.tight_layout()
plt.show()

Types of chi-square test

How to run a chi-square test

1. Arrange the counts in a table with one variable in rows and the other in columns.
2. Check the assumptions: counts (not percentages), independent observations, and expected counts of at least 5 in most cells.
3. Run the test in SPSS, R, Python or Excel (CHISQ.TEST).
4. Report χ², degrees of freedom, sample size and p-value, for example, from the test above: χ²(6, N = 37,357) = 2,803.7, p < 0.001.
5. Add an effect size such as Cramér’s V, and look at which cells differ most from expected.

Common mistakes reviewers point out

• Running the test on percentages instead of counts.
• Too many small expected counts; use Fisher’s exact test for small tables.
• Stopping at “significant” without saying which categories differ or how strongly.
• Counting the same person more than once.

Frequently asked questions

Use this data in your own work

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