What Is the Chi-Square Test of Independence Calculator?
A chi-square test of independence calculator determines whether bivariate categorical frequency patterns occur by random chance.
How Does the Chi-Square Test of Independence Calculator Work?
Compares observed cross-tabulations against theoretical frequencies assuming complete statistical independence.
Chi-Square Test of Independence Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
χ² = ∑ [(O - E)² ÷ E] · E = (Row Total × Col Total) ÷ N
Sums normalized squared deviations between observed and expected frequencies across all four cells for 1 degree of freedom.
How to Use the Chi-Square Test of Independence Calculator
- Enter the four cell frequencies of your 2×2 contingency table.
Step-by-Step Example Calculation
Observed counts [[30, 10], [15, 25]]
Input Values:
cellA:30
cellB:10
cellC:15
cellD:25
Understanding Your Result
Shows Pearson χ² statistic, Yates-corrected statistic, expected frequencies, and significance decision.
Factors That Affect the Result
- Sample size and expected cell counts (all expected cells should ideally be ≥ 5).
When Should You Use This Calculator?
- Survey cross-tabulation analysis, A/B testing conversion divergence, and genetics phenotypic distribution checks.
Assumptions & Limitations
- Observations must be mutually independent random counts.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Karl Pearson (1900) chi-square distribution goodness-of-fit.