Calculate X2 Value Chi Square

Chi-Square Formula:

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Chi-Square Value (χ²):

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1. What Is The Chi-Square Test?

The chi-square test is a statistical method used to determine if there is a significant association between categorical variables. It compares observed frequencies with expected frequencies under the null hypothesis of no association.

2. How Does The Calculator Work?

The calculator uses the chi-square formula:

\[ \chi^2 = \sum \frac{(O_i - E_i)^2}{E_i} \]

Where:

\( O_i \) — Observed frequency (count)
\( E_i \) — Expected frequency (count)
\( \sum \) — Summation over all categories

Explanation: The test measures how much the observed data deviates from what would be expected if the null hypothesis were true.

3. Importance Of Chi-Square Calculation

Details: Chi-square tests are widely used in research for goodness-of-fit tests, tests of independence, and homogeneity tests across various fields including medicine, social sciences, and business analytics.

4. Using The Calculator

Tips: Enter observed and expected frequencies as comma-separated values. Both lists must have the same number of values. Expected frequencies must be greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a chi-square test?
A: Use it when you have categorical data and want to test if there's a significant association between variables or if observed frequencies match expected frequencies.

Q2: What are the assumptions of the chi-square test?
A: The test assumes independence of observations, adequate sample size, and expected frequencies of at least 5 in each category.

Q3: How do I interpret the chi-square value?
A: Compare your calculated chi-square value to critical values from the chi-square distribution table based on your degrees of freedom and significance level.

Q4: What if my expected frequencies are less than 5?
A: For small expected frequencies, consider using Fisher's exact test or combining categories to increase expected frequencies.

Q5: Can chi-square test determine causation?
A: No, chi-square tests only show association between variables, not causation. Other study designs are needed to establish causal relationships.