Researchers examined the effect of phosphate supplementation on bone formation in six healthy adult dogs. For each dog, bone formation was measured twice: once after 12 weeks of phosphate supplementation and once after a 12-week control period. The results in percent bone growth per year are shown below. Do the data provide evidence that phosphate supplementation significantly stimulates bone formation? $\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Dog ID } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Control } & 1.73 & 3.37 & 3.59 & 2.05 & 1.86 & 3.60 \\\hline \text { Phosphate } & 8.16 & 4.58 & 3.98 & 5.24 & 3.04 & 7.03 \\\hline\end{array}$
What is the standardized value z of the Wilcoxon signed rank test, W⁺?

Question

Researchers examined the effect of phosphate supplementation on bone formation in six healthy adult dogs. For each dog, bone formation was measured twice: once after 12 weeks of phosphate supplementation and once after a 12-week control period. The results in percent bone growth per year are shown below. Do the data provide evidence that phosphate supplementation significantly stimulates bone formation?

\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Dog ID } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Control } & 1.73 & 3.37 & 3.59 & 2.05 & 1.86 & 3.60 \\\hline \text { Phosphate } & 8.16 & 4.58 & 3.98 & 5.24 & 3.04 & 7.03 \\\hline\end{array}

What is the standardized value z of the Wilcoxon signed rank test, W⁺?

Quizplus · Accepted Answer

The Wilcoxon signed rank test is a non-parametric test used to compare two related samples to assess whether their population mean ranks differ. It is used here because the data involve paired differences (phosphate supplementation vs. control for each dog). To calculate the standardized value $z$ for the Wilcoxon signed rank test, one would first calculate the differences between the paired observations, rank these differences (ignoring the sign), assign signs to these ranks based on the direction of the difference, sum the ranks for the positive and negative differences separately, and then use these sums to calculate the $z$ value. The calculation involves considering the sample size, the sum of the ranks, and the formula for the $z$ value in the context of the Wilcoxon signed rank test. Given the specific data and the context of the question, a $z$ value of 2.20 suggests that there is evidence to support the hypothesis that phosphate supplementation significantly stimulates bone formation, as a $z$ value greater than 2 typically indicates statistical significance at the 0.05 level in a two-tailed test.

Researchers Examined the Effect of Phosphate Supplementation on Bone Formation