Chi-Square Calculator

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Test for goodness of fit and independence

Categories

Observed Values

Expected Values

Using the Chi-Square Calculator

Goodness of Fit Test

  • Use when comparing one variable against expected values
    • Example: Does local age distribution match census?
    • Example: Do survey responses follow expected proportions?

Independence Test

  • Use when testing relationship between two variables
    • Example: Does education level affect employment status?
    • Example: Is gender independent of voting preference?

Interpreting Results

  • If significant (p < 0.05 or p < 0.01):
    • Goodness of Fit: Your data differs significantly from expected distribution
    • Independence Test: The variables are significantly related - one variable influences or predicts the other
  • If NOT significant:
    • Goodness of Fit: Your data matches expected distribution
    • Independence Test: The variables are independent - no evidence that one influences the other

Requirements for Valid Results

  • Expected frequencies >= 5 in each cell
  • Independent observations
  • Mutually exclusive categories
  • Raw counts (not percentages)