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math.stats-chi-square Calculator
Calculates the chi-square test statistic from observed and expected frequencies, with degrees of freedom and interpretation. The chi-square test is the standard way to test whether two categorical variables are independent in a contingency table.
Inputs
Observed
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Expected
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Df
Number of values free to vary. For a t-test: df = n − 1. Affects critical values from t, chi-squared, and F distributions.
Alpha
p-value threshold below which you reject the null hypothesis. α = 0.05 is conventional (5% false-positive rate).
Results
χ² statistic
The value at the specified point or condition.
critical value (df=
The threshold the test statistic must exceed to reject the null hypothesis at the chosen significance level.
significant?
Sample size or count used in the calculation.
effect
Reference formula or conversion factor shown for context.
χ²=(O−E)²/E
Reference formula or conversion factor shown for context.
note
Supplementary information explaining an assumption, caveat, or important context for interpreting the result.