Chi Squared Cdf Calculator

Chi-Squared CDF Formula:

\[ CDF = \frac{\gamma(df/2, \chi^2/2)}{\Gamma(df/2)} \]

Chi-Squared CDF:

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1. What is the Chi-Squared CDF?

The Chi-Squared Cumulative Distribution Function (CDF) calculates the probability that a chi-squared distributed random variable is less than or equal to a specific value. It's widely used in hypothesis testing and statistical analysis.

2. How Does the Calculator Work?

The calculator uses the chi-squared CDF formula:

\[ CDF = \frac{\gamma(df/2, \chi^2/2)}{\Gamma(df/2)} \]

Where:

\( \chi^2 \) — Chi-squared test statistic (dimensionless)
\( df \) — Degrees of freedom (integer)
\( \gamma(s, x) \) — Lower incomplete gamma function
\( \Gamma(s) \) — Complete gamma function

Explanation: The formula calculates the probability that a chi-squared random variable with given degrees of freedom is less than or equal to the test statistic value.

3. Importance of Chi-Squared CDF

Details: The chi-squared CDF is essential for statistical hypothesis testing, goodness-of-fit tests, and confidence interval estimation. It helps determine the statistical significance of observed differences between expected and actual results.

4. Using the Calculator

Tips: Enter the chi-squared test statistic (must be ≥ 0) and degrees of freedom (must be a positive integer). The calculator will compute the cumulative probability.

5. Frequently Asked Questions (FAQ)

Q1: What is the chi-squared distribution used for?
A: The chi-squared distribution is primarily used in hypothesis testing, particularly for testing independence in contingency tables and goodness-of-fit tests.

Q2: How do I interpret the CDF value?
A: The CDF value represents the probability that a chi-squared random variable with the given degrees of freedom is less than or equal to your test statistic.

Q3: What are typical values for degrees of freedom?
A: Degrees of freedom depend on the specific test. For a contingency table, it's (rows-1)×(columns-1). For variance estimation, it's n-1 where n is sample size.

Q4: When is the chi-squared test appropriate?
A: The test is appropriate when you have categorical data, expected frequencies are at least 5 in each cell, and observations are independent.

Q5: What's the relationship between CDF and p-value?
A: For a right-tailed test, p-value = 1 - CDF. The CDF gives the probability of obtaining a test statistic less than or equal to the observed value.