Hospital Admissions For the matched pairs listed in Exercise 1...

Question

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

e. The value of the test statistic T

Accepted Answer

Hello everyone. Let's take a look at this question together. A researcher wants to evaluate whether a noise reduction headphone improves concentration. 6 participants were tested for the number of words recalled with and without the headphones. The data are below, and here we have a table of the 6 participants and the number of words recalled without headphones and with headphones. Use the Wilcoxson signed ranks test to find the test statistic T, which is the smaller of the sum of the positive or negative ranks. Use a 0.05 significance level. Is it answer choice A 2.5, answer choice B, 2.0. Answer choice C 1.5 or answer choice D 1.0. So the first step in solving this problem is stating the hypotheses where our null hypothesis is that the noise reduction headphones do not affect the number of words recalled where the median difference is equal to zero, and our alternative hypothesis is that the noise reduction headphones affect the number of Words were called where the median difference is not equal to zero. And so to determine if we reject or fail to reject the null hypothesis, we must calculate the differences, which is calculated by taking the with headphones value and subtracting the without headphones value from it, giving us the following data table of our participants, the number of words recalled without headphones, with headphones, and the difference. And then we eliminate the pairs with zero differences, and then we eliminate the pairs with 0 difference, which looking at our data table, we can see that participant 4 has a difference of 0. So then we exclude this pair from further analysis. And then our next step is to rank the absolute values of the non-zero differences, which we can see in our data table. We now have the participant, the difference, the absolute difference, the rank, and the signed rank. And we can also identify that for the absolute difference of 3, we have a tie among 4 observations. So then each gets the average rank of all. Of the numbers of their values together, which is then divided by 4, giving us 3.5, and then we calculate the sums of the positive and negative ranks, starting with the sum of the positive ranks, which when added altogether, we are given 14 and the sum of the negative ranks is 1. And then the next step is to determine the test statistic T. Where T is the minimum of the sum of the positive ranks and the sum of the negative ranks, which we know that the sum of the positive and negative ranks is 14 and 1 respectively, so T is equal to 1. Then we can find the critical value, which 4 N equals 5, which is the number of non-zero differences, and a significant level of 0.05, where this is a two-tailed test, the critical value is 1.

Hospital Admissions For the matched pairs listed in Exercise 1, identify the following components used in the Wilcoxon signed-ranks test:

e. The value of the test statistic T

Key Concepts

Wilcoxon Signed-Ranks Test

Test Statistic T

Matched Pairs Design

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