1. What is Chi-Square P-Value?

The chi-square p-value represents the probability of observing a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true. It's used in chi-square tests of independence and goodness-of-fit tests.

2. How Does the Calculator Work?

The calculator uses the chi-square cumulative distribution function:

Where:

• \( \chi^2 \) — The calculated chi-square test statistic
• \( df \) — Degrees of freedom for the test
• \( \text{chisqcdf} \) — Chi-square cumulative distribution function

Explanation: The calculator numerically approximates the area under the chi-square distribution curve from your test statistic to infinity.

3. Importance of P-Value Calculation

Details: The p-value helps determine statistical significance. Typically, p < 0.05 suggests rejecting the null hypothesis, though the exact threshold depends on your field and study design.

4. Using the Calculator

Tips: Enter your chi-square test statistic (must be ≥0) and degrees of freedom (must be ≥1). The calculator will compute the right-tailed p-value.

5. Frequently Asked Questions (FAQ)

Q1: What does a small p-value mean?
A: A small p-value (typically <0.05) suggests your observed data would be unlikely if the null hypothesis were true.

Q2: How do I determine degrees of freedom?
A: For contingency tables: df = (rows-1)*(columns-1). For goodness-of-fit: df = categories - 1 - parameters estimated.

Q3: What's the difference between one-tailed and two-tailed tests?
A: Chi-square tests are inherently one-tailed (right-tailed) as they test for any deviation from expected counts.

Q4: When is the chi-square test appropriate?
A: When you have categorical data, expected counts ≥5 in most cells, and independent observations.

Q5: What if my p-value is exactly 0.05?
A: This is at the conventional threshold for significance. Consider effect size, confidence intervals, and practical significance in interpretation.