Need help with Wilcoxon rank-sum test

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In summary: In this case, the test statistic is 3.10 and the p-value is 0.002, which suggests significant differences in the length of stay between the two hospitals.
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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!
 
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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.
 

FAQ: Need help with Wilcoxon rank-sum test

1. What is a Wilcoxon rank-sum test?

A Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a non-parametric statistical test used to determine if there is a significant difference between two independent groups. It is used when the data is not normally distributed or when the sample sizes are small.

2. When should a Wilcoxon rank-sum test be used?

A Wilcoxon rank-sum test should be used when the data does not meet the assumptions for a parametric test, such as a t-test. This includes when the data is not normally distributed, when the sample sizes are small, or when the data is measured on an ordinal scale.

3. How does a Wilcoxon rank-sum test work?

A Wilcoxon rank-sum test works by ranking all of the data from both groups together, from lowest to highest. The ranks are then summed for each group, and the group with the lower sum is considered the smaller group. The test statistic is then calculated by comparing the smaller group's sum to the expected sum for a random distribution.

4. What is the null hypothesis in a Wilcoxon rank-sum test?

The null hypothesis in a Wilcoxon rank-sum test is that there is no significant difference between the two independent groups being compared. In other words, the two groups come from the same population and any differences observed are due to chance.

5. How do I interpret the results of a Wilcoxon rank-sum test?

If the p-value is less than the chosen significance level (usually 0.05), then the null hypothesis is rejected and it can be concluded that there is a significant difference between the two groups. If the p-value is greater than the significance level, then the null hypothesis cannot be rejected and it can be concluded that there is no significant difference between the two groups.

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