Need help with Wilcoxon rank-sum test

[Yoha]

Hi guys,

Can anybody help with regards to this question??

Suppose we want to compare the length of hospital stay for patients with same diagnosis at two different hospitals hospital

First hospital: 5,8,10,13,21,26,29,32,33,44,60
Second hospital: 10,27,35,44,60,68,73,76,86,87,96,125,238

Question1: why might t-test not be very useful in this case? Book said, data is very skewed, but how I can find that myself.

Qestion 2:
Carry out non-parametric procedure for testing the length of stay are comparable in the two hospitals

The question is answered in the back of the book and I did calculate it by software, but I would like to know how to do it manually, I tried to apply Wilcoxon sum test formula but failed to get the same numbers.

The answers: use Wilcoxon rank-sum test(large-sample test), R1=83.5, T=3.10 , p=.002

Thanks for your help!

 

[Jhero]

Answer 1: A t-test is not very useful in this case because the data is not normally distributed, or even symmetric. The data from both hospitals is quite skewed, with the majority of the data points being much lower than the mean. This means that a t-test would not be an appropriate method for comparison.Answer 2: The Wilcoxon rank-sum test is an appropriate non-parametric procedure for testing whether the length of stay is comparable in the two hospitals. To calculate the test statistic manually, you would need to combine the two datasets and rank the data points from smallest to largest. Then, sum up the ranks for each hospital and subtract the smaller sum from the larger sum. This difference is the test statistic. You can compare this test statistic to a standard table to get the p-value.