Which of the following distributions approximate the Kruskal-Wallis test statistic K when $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \ldots . . = \mu _ { i }$ is true, and the number of populations or treatments I=3 and the sample sizes $J _ { i } \geq 6 ( i = 1,2,3 ) \text { or } I 3 \text { and } J _ { i } \geq 5 ( i = 1 , \ldots . , I ) ?$
A) Standard normal distribution
B) T distribution with I-1 degrees of freedom
C) F distribution with I-1 and $J _ { i } - 1$
Degrees of freedom.
D) Chi-squared distribution with I-1 degrees of freedom.
E) Either B or C.

Question

Which of the following distributions approximate the Kruskal-Wallis test statistic K when $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \ldots . . = \mu _ { i }$ is true, and the number of populations or treatments I=3 and the sample sizes $J _ { i } \geq 6 ( i = 1,2,3 ) \text { or } I > 3 \text { and } J _ { i } \geq 5 ( i = 1 , \ldots . , I ) ?$
A) Standard normal distribution
B) T distribution with I-1 degrees of freedom
C) F distribution with I-1 and $J _ { i } - 1$
Degrees of freedom.
D) Chi-squared distribution with I-1 degrees of freedom.
E) Either B or C.

Quizplus · Accepted Answer

The Kruskal-Wallis test statistic K, under the null hypothesis that all group medians are equal, follows a chi-squared distribution with I-1 degrees of freedom when the number of groups (I) is greater than 2 and each group has a sufficient number of observations (as specified in the question). This approximation becomes more accurate as the sample sizes increase.

Which of the Following Distributions Approximate the Kruskal-Wallis Test Statistic H0:μ1=μ2=…..=μiH _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \ldots . . = \mu _ { i }H0​:μ1​=μ2​=…..=μi​

Which of the Following Distributions Approximate the Kruskal-Wallis Test Statistic $H _ { 0 } : \mu _ { 1 } = \mu _ { 2 } = \ldots . . = \mu _ { i }$