1. What is Chi-square Q Value?

The chi-square (Q) statistic measures how observed values differ from expected values under a specific hypothesis. It's widely used in statistics to test goodness-of-fit, independence in contingency tables, and homogeneity.

2. How Does the Calculator Work?

The calculator uses the chi-square formula:

Where:

• \( O \) — Observed values
• \( E \) — Expected values
• \( \sum \) — Summation over all categories

Explanation: For each category, the calculator computes the squared difference between observed and expected values, divided by the expected value. These values are then summed to produce the chi-square statistic.

3. Importance of Chi-square Test

Details: The chi-square test helps determine whether observed frequencies differ significantly from expected frequencies. It's used in hypothesis testing across various fields including biology, marketing, social sciences, and quality control.

4. Using the Calculator

Tips: Enter observed and expected values as comma-separated or line-separated numbers. Both lists must have the same number of values. Expected values cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What does a high Q value indicate?
A: A high chi-square value suggests that observed data differs significantly from expected values, potentially leading to rejection of the null hypothesis.

Q2: How is this different from p-value?
A: The Q value is the test statistic, while the p-value is the probability of observing such an extreme value if the null hypothesis is true.

Q3: When should I use chi-square test?
A: Use it when you have categorical data and want to test relationships between variables or goodness-of-fit to a distribution.

Q4: Are there assumptions for this test?
A: Yes, including independent observations, adequate sample size (usually all expected counts ≥5), and categorical data.

Q5: Can I use this for continuous data?
A: Not directly - continuous data should be binned into categories first, though other tests may be more appropriate.