Calculator Suite

Chi-Square Test Calculator

Chi-Square Analysis

Perform chi-square goodness of fit tests and tests of independence with comprehensive statistical analysis

Analysis Settings
Test Configuration
Choose your chi-square test type and analysis parameters
Goodness of Fit Data
Enter observed and expected frequencies for each category

Enter the actual counts for each category

Enter the theoretical expected counts for each category

Labels for each category (leave empty for auto-generated labels)

Educational Resources

Chi-Square Formulas
Mathematical foundations of chi-square testing

Test Statistic

χ2=∑i(Oi−Ei)2Ei\chi^2 = \sum_{i} \frac{(O_i - E_i)^2}{E_i}

OiO_i = Observed frequency in cell i

EiE_i = Expected frequency in cell i

χ2\chi^2 = Chi-square test statistic

Expected Frequency (Independence)

Eij=Ri×CjNE_{ij} = \frac{R_i \times C_j}{N}

RiR_i = Row i total

CjC_j = Column j total

NN = Grand total

Degrees of Freedom

Goodness of Fit: df=k−1df = k - 1
Independence: df=(r−1)(c−1)df = (r-1)(c-1)

kk = Number of categories

rr = Number of rows, cc = Number of columns

Understanding Chi-Square Tests

Goodness of Fit Test

Tests whether observed frequencies match an expected theoretical distribution. Useful for testing fairness, normality, or model fit.

Test of Independence

Tests whether two categorical variables are independent. Examines associations in contingency tables.

Key Assumptions

  • • Random sampling
  • • Expected frequencies ≥ 5 in most cells
  • • Independent observations
  • • Categorical data
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