# GastroenterologyWe present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.

Gastroenterology
We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.
If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups?
Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data?
Relationship between protein concentration $\left(mg/mL\right)$ of duodenal secretions to pancreatic function as measured by trypsin secretion:
$\left[U/\frac{kg}{hr}\right]$
Tapsin secreton [UGA]

$\begin{array}{|cc|}\hline \text{Subject number}& \text{Protetion concentration}\\ 1& 1.7\\ 2& 2.0\\ 3& 2.0\\ 4& 2.2\\ 5& 4.0\\ 6& 4.0\\ 7& 5.0\\ 8& 6.7\\ 9& 7.8\\ \hline\end{array}$

$\begin{array}{|cc|}\hline \text{Subject number}& \text{Protetion concentration}\\ 1& 1.4\\ 2& 2.4\\ 3& 2.4\\ 4& 3.3\\ 5& 4.4\\ 6& 4.7\\ 7& 6.7\\ 8& 7.9\\ 9& 9.5\\ 10& 11.7\\ \hline\end{array}$

$\begin{array}{|cc|}\hline \text{Subject number}& \text{Protetion concentration}\\ 1& 2.9\\ 2& 3.8\\ 3& 4.4\\ 4& 4.7\\ 5& 5.5\\ 6& 5.6\\ 7& 7.4\\ 8& 9.4\\ 9& 10.3\\ \hline\end{array}$

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Step 1 Given data is:
Tapsin secreton $\left[U/\left(kg/hr\right)\right]$

$\begin{array}{|cc|}\hline \text{Subject number}& \text{Protetion concentration}\\ 1& 1.7\\ 2& 2.0\\ 3& 2.0\\ 4& 2.2\\ 5& 4.0\\ 6& 4.0\\ 7& 5.0\\ 8& 6.7\\ 9& 7.8\\ \hline\end{array}$

$\begin{array}{|cc|}\hline \text{Subject number}& \text{Protetion concentration}\\ 1& 1.4\\ 2& 2.4\\ 3& 2.4\\ 4& 3.3\\ 5& 4.4\\ 6& 4.7\\ 7& 6.7\\ 8& 7.9\\ 9& 9.5\\ 10& 11.7\\ \hline\end{array}$

$\begin{array}{|cc|}\hline \text{Subject number}& \text{Protetion concentration}\\ 1& 2.9\\ 2& 3.8\\ 3& 4.4\\ 4& 4.7\\ 5& 5.5\\ 6& 5.6\\ 7& 7.4\\ 8& 9.4\\ 9& 10.3\\ \hline\end{array}$
Step 2
1) By using Kruskal-Wallis test to compare 3 groups we get, Combining score of all the three groups, arranging them into ascending order and assigning them ra
.

$\begin{array}{|ccc|}\hline \text{Observation}& \text{Rank}& \text{Groups}\\ 1.4& 1& B\\ 1.7& 2& A\\ 2& 3.5& A\\ 2& 3.5& A\\ 2.2& 5& A\\ 2.4& 6.5& B\\ 2.4& 6.5& B\\ 2.9& 8& C\\ 3.3& 9& B\\ 3.8& 10& C\\ 4& 11.5& A\\ 4& 11.5& A\\ 4.4& 13.5& B\\ 4.4& 13.5& C\\ 4.7& 15.5& B\\ 4.7& 15.5& C\\ 5& 17.5& A\\ 5& 17.5& C\\ 5.6& 19& C\\ 6.7& 20.5& A\\ 6.7& 20.5& B\\ 7.4& 22& C\\ 7.6& 23& B\\ 7.8& 24& A\\ 9.4& 25& C\\ 9.5& 26& B\\ 10.3& 27& C\\ 11.7& 28& B\\ \hline\end{array}$
${n}_{A}=9$
${n}_{B}=10$
${n}_{C}=9$