Uji kuadrat-chi Pearson

Artikel ieu keur dikeureuyeuh, ditarjamahkeun tina basa Inggris. Bantuanna didagoan pikeun narjamahkeun.

Tes Pearson's chi-kuadrat (χ²) salah sahiji variasi tina tes chi-kuadrat – procedure statistik nu hasilna di-evaluasi dumasar kana sebaran chi-kuadrat. Tes ieu mimiti dipaluruh ku Karl Pearson.

It tests a null hypothesis that the relative frequencies of occurrence of observed events follow a specified frequency distribution. The events are assumed to be independent and have the same distribution, and the outcomes of éach event must be mutually exclusive. A simple example is the hypothesis that an ordinary six-sided die is "fair", i.e., all six outcomes occur equally often. Péarson's chi-square is the original and most widely-used chi-square test.

Chi-square is calculated by finding the difference between éach observed and théoretical frequency for éach possible outcome, squaring them, dividing éach by the théoretical frequency, and taking the sum of the results. The number of degrees of freedom is equal to the number of possible outcomes, minus 1:

${\displaystyle \chi _{n-1}^{2}=\sum _{i=1}^{n}{(O_{i}-E_{i})^{2} \over E_{i}}}$

where

${\displaystyle O_{i}}$ = an observed frequency;

${\displaystyle E_{i}}$ = an expected (theoretical) frequency, asserted by the null hypothesis;

${\displaystyle n}$ = the number of possible outcomes of each event.

Péarson's chi-square is used to assess two types of comparison: tests of goodness of fit and tests of independence. A test of goodness of fit establishes whether or not an observed frequency distribution differs from a théoretical distribution. A test of independence assesses whether paired observations on two variables, expressed in a contingency table, are independent of éach other – for example, whether péople from different regions differ in the frequency with which they report that they support a political candidate.

A chi-square probability of 0.05 or less is commonly interpreted by applied workers as justification for rejecting the null hypothesis that the row variable is unrelated (that is, only randomly related) to the column variable. The alternate hypothesis is not rejected when the variables have an associated relationship.