What is an expected frequency in Chi-square?

It is the frequency that would be expected in a cell if no relationship existed between the row and column variables.

What happens if expected counts are less than 5?

When expected cell counts are very small, the chi-square approximation can be unreliable; Fisher's exact test is preferred.

How are degrees of freedom calculated?

Degrees of freedom equal (number of rows - 1) * (number of columns - 1).

Mathematics Tools• Chi^2 Test

Chi-Square Test Calculator (Independence & Goodness of Fit)

Determine whether there is a significant association between two categorical variables. Enter observed frequencies into interactive contingency tables to compute Pearson's Chi-square.

Data processed entirely in browser memory.

2x2 Contingency Table (Observed)

Row 1, Col 1

Row 1, Col 2

Row 2, Col 1

Row 2, Col 2

Pearson's Chi-Square (χ²)

χ² = 11.429

Significant Association (p < 0.05, df=1)

Expected Frequencies (E):

E11: 22.5

E12: 17.5

E21: 22.5

E22: 17.5

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How to Use Chi-Square Test Calculator

Define Table Dimensions

Choose 2x2 table or customize rows and columns.

Input Observed Frequencies

Fill observed counts into each contingency cell.

Review Chi-Square Statistic

View expected frequencies matrix, chi^2 score, degrees of freedom, and significance verdict.

About Chi-Square Test Calculator

Computes Pearson's statistic sum((O_ij - E_ij)^2 / E_ij) over all table cells, comparing observed counts against expected counts under the null hypothesis of independence.

Supported Formats

Contingency MatrixNumeric Grid

Operational Limits

•Assumes minimum expected cell frequency of 5 for valid asymptotic chi-square distribution.

Key Features

Interactive 2x2 and multi-cell contingency table editor
Automatic expected frequency matrix computation: E = (Row Total * Col Total) / Grand Total
Calculates chi^2 contribution per cell and total Chi-square statistic
Degrees of freedom calculation: df = (r - 1) * (c - 1)
Hypothesis significance verdict at alpha = 0.05 and alpha = 0.01

Frequently Asked Questions

It tests whether two categorical variables are independent or related in a given population.

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