A research team investigated the protective effect of two variants of a vaccine against the simian immunodeficiency virus (SIV) in rhesus monkeys. They measured the viral load (in log scale) of monkeys randomly assigned to either a vaccine variant or a sham (fake) vaccine. Here is a partial software output for a Kruskal-Wallis test on the data:

Kruskal-Wallis Test on viral load
$\begin{array} { l r r r r } \text { vaccine } & \mathrm { N } & \text { Median } & \text { Ave Rank } & \mathrm { Z } \ 1 & 16 & 5.530 & 18.6 & - 0.18 \ 2 & 13 & 5.030 & 11.2 & - 3.25 \ \text { sham } & 8 & 6.860 & 32.5 & 3.98 \ \text { Overall } & 37 & & 19.0 & \end{array}$
$$\begin{array} { l }
\mathrm { H } = 19.29 \quad \mathrm { DF } = \quad \mathrm { P } = \
\mathrm { H } = 19.30 \quad \mathrm { DF } = \quad \mathrm { P } = \quad \text { (adjusted for ties) } \
\end{array}$$ The null hypothesis of the Kruskal-Wallis test is that viral load has the same distribution in all groups. What is the alternative hypothesis?

Question

A research team investigated the protective effect of two variants of a vaccine against the simian immunodeficiency virus (SIV) in rhesus monkeys. They measured the viral load (in log scale) of monkeys randomly assigned to either a vaccine variant or a sham (fake) vaccine. Here is a partial software output for a Kruskal-Wallis test on the data:
​
Kruskal-Wallis Test on viral load
$\begin{array} { l r r r r } \text { vaccine } & \mathrm { N } & \text { Median } & \text { Ave Rank } & \mathrm { Z } \ 1 & 16 & 5.530 & 18.6 & - 0.18 \ 2 & 13 & 5.030 & 11.2 & - 3.25 \ \text { sham } & 8 & 6.860 & 32.5 & 3.98 \ \text { Overall } & 37 & & 19.0 & \end{array}$
$$\begin{array} { l } 
\mathrm { H } = 19.29 \quad \mathrm { DF } = \quad \mathrm { P } = \
\mathrm { H } = 19.30 \quad \mathrm { DF } = \quad \mathrm { P } = \quad \text { (adjusted for ties) } \
\end{array}$$ The null hypothesis of the Kruskal-Wallis test is that viral load has the same distribution in all groups. What is the alternative hypothesis?

Quizplus · Accepted Answer

The Kruskal-Wallis test is a nonparametric test for comparing the median values across two or more independent groups. The alternative hypothesis is that the distributions of viral load are not equal across the groups. Therefore, D is the best choice because it implies that there are differences in viral load between the treatment groups, providing a general alternative for different distributions in the groups. A, B and C talk more specifically about differences in means or medians, while the Kruskal-Wallis test is not specific about them in the alternative hypothesis.

A Research Team Investigated the Protective Effect of Two Variants