In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by $1 - \frac { \sum \mathrm { T } } { \mathrm { N } ^ { 3 } - \mathrm { N } }$ For each group of tied observations, calculate T $T=t^{3}-t$
t, where t is the number of observations that are tied
Within the individual group. Find t for each group of tied values, then compute the value of T for each group,
Then add the T values to get $\sum ^ { \mathrm { T } }$ . The total number of observations in all samples combined is N. Find the
Corrected value of H for the data below which represents test scores for three different groups. $$\begin{array} { l c c c c c c }
\text { Group 1: } & 20 & 18 & 18 & 18 & 20 & 20 \
\text { Group 2: } 18 & 12 & 18 & 18 & 20 & \
\text { Group 3: } 16 & 18 & 13 & 18 & 18 &
\end{array}$$
A) 3.78
B) 4.91
C) -0.19
D) 3.69

Question

In using the Kruskal-Wallis test, there is a correction factor that should be applied whenever there are many ties: Divide H by $1 - \frac { \sum \mathrm { T } } { \mathrm { N } ^ { 3 } - \mathrm { N } }$ For each group of tied observations, calculate T $T=t^{3}-t$
 t, where t is the number of observations that are tied
Within the individual group. Find t for each group of tied values, then compute the value of T for each group,
Then add the T values to get $\sum ^ { \mathrm { T } }$ . The total number of observations in all samples combined is N. Find the
Corrected value of H for the data below which represents test scores for three different groups. $$\begin{array} { l c c c c c c } 
\text { Group 1: } & 20 & 18 & 18 & 18 & 20 & 20 \
\text { Group 2: } 18 & 12 & 18 & 18 & 20 & \
\text { Group 3: } 16 & 18 & 13 & 18 & 18 &
\end{array}$$
A) 3.78
B) 4.91
C) -0.19
D) 3.69

Quizplus · Accepted Answer

The correction factor for the Kruskal-Wallis test is applied when there are many ties in the data. The correction factor is calculated as follows:$$H = \frac{12}{N(N+1)} \sum_{i=1}^{k} \frac{R_i^2}{n_i} - 3(N+1)$$where:* H is the corrected value of the Kruskal-Wallis statistic* N is the total number of observations in all samples combined* k is the number of groups* R_i is the sum of the ranks in group i* n_i is the number of observations in group iIn this case, there are three groups and a total of 15 observations. The ranks of the observations are as follows:```Group 1: 1, 2, 2, 2, 3, 3Group 2: 4, 5, 6, 6, 7Group 3: 8, 9, 10, 10, 10```The sum of the ranks in each group is:```R_1 = 1 + 2 + 2 + 2 + 3 + 3 = 13R_2 = 4 + 5 + 6 + 6 + 7 = 28R_3 = 8 + 9 + 10 + 10 + 10 = 47```The number of observations in each group is:```n_1 = 6n_2 = 5n_3 = 5```The corrected value of the Kruskal-Wallis statistic is:$$H = \frac{12}{15(15+1)} \left(\frac{13^2}{6} + \frac{28^2}{5} + \frac{47^2}{5}\right) - 3(15+1)$$$$H = \frac{12}{240} (213 + 1568 + 1102.4) - 54$$$$H = 3.78$$Therefore, the correct answer is A.

In Using the Kruskal-Wallis Test, There Is a Correction Factor 1−∑TN3−N1 - \frac { \sum \mathrm { T } } { \mathrm { N } ^ { 3 } - \mathrm { N } }1−N3−N∑T​

In Using the Kruskal-Wallis Test, There Is a Correction Factor $1 - \frac { \sum \mathrm { T } } { \mathrm { N } ^ { 3 } - \mathrm { N } }$