Chi Square Goodness of Fit Test

The chi-square goodness of fit test compares observed category frequencies of one categorical variable with frequencies expected under a specified distribution.

카이제곱 적합도 검정은 한 범주형 변수의 관측빈도를 지정한 분포에서 기대되는 빈도와 비교한다.

Do the observed counts in my four categories match the 9:3:3:1 ratio predicted by theory?

네 범주의 관측 빈도가 이론이 예측한 9:3:3:1 비율과 맞나요?

The chi-square goodness of fit test sums the squared differences between observed and expected counts divided by the expected counts. The statistic follows a chi-square distribution with the number of categories minus one degrees of freedom when expected counts are adequate.

When to use Chi Square Goodness of Fit Test

• One categorical variable is compared with a theoretical or known distribution.
• Category proportions are specified in advance, for example equal shares or census proportions.
• Expected counts are at least five per category.

When to use something else

• Two categorical variables are cross-classified; use the chi-square test of independence.
• Expected counts are small; use an exact multinomial test or merge categories.

Assumptions and requirements

• Observations are independent.
• Each observation falls into exactly one category.
• Expected counts are at least five in each category.
• Expected proportions are fixed in advance; equal shares are used when none are given.

What the analysis reports

• Chi-square statistic
• Degrees of freedom
• p value
• Cohen's w
• Observed, expected counts and standardized residuals

How to report it

A chi-square goodness-of-fit test indicated that the observed frequencies did not differ significantly from the expected distribution, χ²([df], N = [n]) = [chi2], p = [p].

Related methods

• Exact Binomial Test
• G Test of Independence
• Chi Square Test

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