Calculadora de Qui-Quadrado (1 par)

The Chi-Square Calculator (1 pair) is an educational tool that demonstrates the calculation of the χ² value for a single pair of values: observed (O) and expected (E). The formula used is χ² = (O − E)² / E. Although the full chi-square test involves summing several terms for different categories, this calculator simplifies the concept by showing the calculation for just one pair, ideal for understanding the basic mechanics of the formula.

How it works: you enter the observed and expected values in the corresponding fields. The calculator then subtracts the expected from the observed, squares the result, and divides by the expected value. The result is the χ² value for that pair. This value alone is not sufficient for a complete hypothesis test, but it serves as a building block to understand how each term contributes to the final statistic.

When to use: this calculator is useful for statistics students who are learning the chi-square formula and want to verify manual calculations. It can also be used by professionals who need to quickly calculate the contribution of a single category to the test. However, for actual tests with multiple categories, it is necessary to sum the χ² values of each pair and compare with a critical value from the chi-square distribution with the appropriate degrees of freedom.

Common cautions: remember that the expected value (E) must be greater than zero to avoid division by zero. Also, the chi-square test assumes that data are independent and that expected frequencies are sufficiently large (usually ≥ 5). The isolated result of a single pair should not be used to make statistical decisions; it is only a part of the complete calculation.