Chi-Squared Statistic Calculator
Calculate Chi-Squared contribution for one category.
Formula first
Overview
The Chi-Squared statistic measures the discrepancy between observed and expected frequencies in categorical data. It serves as the mathematical foundation for assessing how well a sample distribution fits a population model or if two categorical variables are independent.
Symbols
Variables
O = Observed, E = Expected, \chi^2 = Value
Apply it well
When To Use
When to use: Apply this statistic when you have categorical variables and wish to perform a goodness-of-fit test or a test of independence. It is most reliable when the expected frequency for each category is 5 or greater and the data is collected through random sampling.
Why it matters: This calculation allows researchers to differentiate between meaningful patterns and random fluctuations in fields like genetics, sociology, and quality control. It is vital for validating scientific hypotheses where outcomes are counts rather than measurements.
Avoid these traps
Common Mistakes
- Squaring O-E before dividing.
- Using percentages instead of counts.
One free problem
Practice Problem
A biologist expects 100 fruit flies to have red eyes based on a genetic cross, but observes 110. Calculate the Chi-squared value (X) for this specific outcome.
Solve for:
Hint: Subtract the expected value from the observed value, square the result, then divide by the expected value.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Wikipedia: Chi-squared test
- Probability and Statistics for Engineering and the Sciences" by Jay L. Devore
- Britannica: Chi-square distribution
- Introductory Statistics by OpenStax, Chapter 11
- Statistics by David Freedman, Robert Pisani, Roger Purves, 4th Edition, W. W. Norton & Company, 2007, Chapter 28
- Standard curriculum — Mathematical Statistics