Chapter 14-7. Chi-squared Test (3 types)

Higher category : 【Statistics】 Chapter 14. Statistcal Test

Figure. 1. chi-squared distribution table

1. chi-square goodness-of-fit test

⑴ problem situation (contingency table): if the situation is genetic experiment, Oi and Ej are not proportions but numbers of population

Figure. 2. problem situation of chi-square goodness-of-fit test

⑵ setting hypotheses

H₀ : the sample Xi follows the given probability distribution

H₁ : the sample Xi does not follow the given probability distribution

⑶ calculation of test statistic

⑷ critical region: significance level is α. it is well established when the sample size is big

⑴ problem situation (contingency table)

Figure. 3. problem situation of chi-square test of independence

⑵ setting hypotheses

H₀ : X and Y are independent

H₁ : X and Y are not independent

⑶ calculation of test statistic: calculate the predicted value by using marginal probability distribution and the relationship of independence

⑷ critical region: significance level is α. it is well established when the sample size is big

⑴ problem situation (contingency table)

Figure. 4. problem situation of chi-square test of homogeneity

⑵ setting hypotheses

H₀ : Group₁ and Group₂ follow the same probability distribution

H₁ : Group₁ and Group₂ don’t follow the same probability distribution

⑶ calculation of test statistic

① equal probability distribution is clearly different from independence conceptually

② however, chi-square test of homogeneity follows a very similar calculation to a chi-square test of independence

⑷ critical region: significance level is α. it is well established when the sample size is big

Input : 2019.10.05 11:13