Skip to main content
Calcimator

Chi-Square Test Calculator

Perform a chi-square goodness-of-fit test comparing observed and expected frequencies across four categories.

Inputs

Results

Chi-Square Statistic (χ²)

6.25

P-Value (approx)

0.1

Degrees of Freedom3
Significant at α=0.05 (1=Yes)0
Significant at α=0.01 (1=Yes)0
How to Use This Calculator
  1. Enter Observed Count 1, Expected Count 1, and Observed Count 2.
  2. Set Expected Count 2, Observed Count 3, and Expected Count 3.
  3. Adjust Observed Count 4, Expected Count 4 as needed.
  4. Review Chi-Square Statistic (χ²) and P-Value (approx).
  5. Use Degrees of Freedom and Significant at α=0.05 (1=Yes) to inform your decision.

How the result changes with Observed Count 1

Observed Count 1Chi-Square Statistic (χ²)P-Value (approx)
10,0002,480,043.750
35,00030,555,043.750
65,000105,495,043.750
90,000202,320,043.750

What each input means

Observed Count 1
Observed frequency for the first category.
Expected Count 1
Expected frequency for the first category under the null hypothesis.
Observed Count 2
Observed frequency for the second category.
Expected Count 2
Expected frequency for the second category under the null hypothesis.
Observed Count 3
Observed frequency for the third category.
Expected Count 3
Expected frequency for the third category under the null hypothesis.
Observed Count 4
Observed frequency for the fourth category.
Expected Count 4
Expected frequency for the fourth category under the null hypothesis.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Observed Count 1 = 50, Expected Count 1 = 40, Observed Count 2 = 30, Expected Count 2 = 40 = 8 input(s) provided
  2. Calculate Chi-Square Statistic
    Chi-Square Statistic
    6.25 = 6.25
  3. Calculate P-Value
    P-Value
    0.0984 = 0.0984
  4. Calculate Degrees of Freedom
    Degrees of Freedom = df
    3 = 3
  5. Calculate Significant at α=0.05
    Significant at α=0.05
    0 = 0

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators.

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Statistics

T-Test Calculator

Calculate the t-statistic, degrees of freedom, and approximate p-value for a one-sample t-test.

Statistics

Fisher's Exact Test Calculator

Perform Fisher's exact test on a 2x2 contingency table to determine if there is a significant association between two categorical variables.

Statistics

Multiple Regression Calculator

Evaluate a multiple regression model using SSR, SSE, number of predictors, and sample size. Calculate R², adjusted R², F-statistic, and model fit metrics.

More in Math & Statistics.