Chi-Square Calculator

Calculate the chi-square test statistic to compare observed frequencies with expected frequencies for statistical hypothesis testing.

Quick Facts

Common Use
Goodness of Fit
Tests if data fits expected distribution
Critical Value (df=1)
3.841
At 0.05 significance level
Degrees of Freedom
df = n - 1
n = number of categories
Requirement
Expected >= 5
Each expected frequency

Your Results

Calculated
Chi-Square Statistic
0
Test statistic value
Degrees of Freedom
0
df = n - 1
Number of Categories
0
Data points used

Key Takeaways

  • Chi-square tests compare observed frequencies to expected frequencies
  • A larger chi-square value indicates greater deviation from expected values
  • Use a chi-square table to find the critical value for your significance level
  • Each expected frequency should be at least 5 for valid results
  • Degrees of freedom = number of categories minus 1

What Is the Chi-Square Test?

The chi-square test is a statistical method used to determine if there is a significant difference between observed frequencies and expected frequencies in categorical data. It's widely used in hypothesis testing to evaluate whether the difference between what we observe and what we expect is due to chance or represents a real difference.

There are two main types of chi-square tests: the goodness of fit test (comparing observed data to an expected distribution) and the test of independence (determining if two categorical variables are related). This calculator performs the goodness of fit test.

Chi-Square Formula

χ² = Σ [(O - E)² / E]
χ² = Chi-Square statistic
O = Observed frequency
E = Expected frequency
Σ = Sum across all categories

How to Use This Calculator

Enter your observed values and expected values as comma-separated numbers. For example, if you observed 25, 30, and 45 occurrences across three categories, and expected 33, 33, and 34, enter:

  • Observed: 25, 30, 45
  • Expected: 33, 33, 34

Click "Calculate" to get your chi-square statistic and degrees of freedom. Compare this value to a chi-square critical value table to determine statistical significance.

Interpreting Results

The chi-square statistic tells you how much the observed data deviates from what was expected. To determine if this deviation is statistically significant:

  • Calculate degrees of freedom: df = (number of categories) - 1
  • Choose a significance level (commonly 0.05)
  • Find the critical value from a chi-square distribution table
  • If your chi-square statistic > critical value, reject the null hypothesis