How to use the CHISQ.INV() function in Excel

This function returns the inverse of the left-tailed chi-squared (χ²) distribution.

• Given a probability (cumulative probability), it finds the corresponding χ² value (x) such that:
  • If probability = CHISQ.DIST(x; df; TRUE), then CHISQ.INV(probability; df) = x.
• Used to determine critical values for hypothesis testing (e.g., goodness-of-fit tests).

Syntax

CHISQ.INV(probability; degrees_freedom)

Arguments

Background

1. Inverse Chi-Squared Distribution:
   • Solves for x in:

P(X≤x)=probabilityP(X≤x)=probability

1. • Where:
     • P = Cumulative probability (area under the left tail).
     • x = Chi-squared statistic.
2. Left-Tailed vs. Right-Tailed:
   • CHISQ.INV(): Left-tailed inverse (returns the χ² value for a given cumulative probability).
   • CHISQ.INV.RT(): Right-tailed inverse (returns the χ² value for 1 – probability).
3. Key Applications:
   • Hypothesis Testing: Find critical values to reject/fail to reject the null hypothesis.
   • Confidence Intervals: Calculate bounds for variance estimates.

Example

 The CHISQ.DIST() function is the inverse function of CHISQ.INV().

Key Notes

1. Degrees of Freedom (df):
   • Determines the shape of the χ² distribution. For a contingency table, df = (rows – 1) * (columns – 1).
2. Common Use Cases:
   • Goodness-of-Fit Tests: Compare observed vs. expected frequencies (e.g., Mendel’s pea experiments).
   • Independence Tests: Check if two categorical variables are related.
3. Error Handling:
   • Returns #NUM! if:
     • probability ≤ 0 or ≥ 1.
     • degrees_freedom < 1.