Pertain to critical values for a Wilcoxon signed-rank test....

Pertain to critical values for a Wilcoxon signed-rank test. Use Table V in Appendix A to determine the critical value(s) in each case. For a left-tailed or two-tailed test, you will also need the relation $W_{1-A}=n(n+1) / 2-W_{A}.$ Sample size $=19 ;$ Significance level $=0.10$ a. Right tailed b. Left tailed c. Two tailed

Pertain to critical values for a Wilcoxon signed-rank test. Use Table V in Appendix A to determine the critical value(s) in each case. For a left-tailed or two-tailed test, you will also need the relation $W_{1-A}=n(n+1) / 2-W_{A}.$
Sample size $=19 ;$ Significance level $=0.10$
a. Right tailed
b. Left tailed
c. Two tailed

Key Concepts

Wilcoxon Signed-Rank Test

The Wilcoxon signed?rank test is a nonparametric statistical test used to compare paired or matched samples. It assesses whether their population mean ranks differ and is a robust alternative to the paired t-test, especially when the data do not meet the normality assumption.

Critical Values in Hypothesis Testing

Critical values are thresholds derived from the sampling distribution under the null hypothesis. In hypothesis testing, if the test statistic exceeds these critical values, the null hypothesis is rejected. They are determined by the significance level and the specific distribution of the test statistic.

Tail Test Configurations

Tail test configurations (one-tailed or two-tailed) determine the area in the distribution where extreme values are considered significant. A right-tailed test rejects the null when the test statistic is too high, a left-tailed test when it is too low, and a two-tailed test when it deviates sufficiently in either direction.

Significance Level

The significance level, often denoted as alpha (?), represents the probability of committing a Type I error, which is rejecting a true null hypothesis. It determines the critical region(s) and influences the critical values used in tests.

Symmetry Relationship Between Critical Values

In the Wilcoxon signed-rank test, there is a complementary relationship between the critical values for left-tailed and right-tailed tests. This symmetry is expressed by the relation W??? = n(n+1)/2 - W?, which allows conversion between the critical values for different tail tests.

Transcript

00:02 In this exercise, we're going to be getting the critical values for wilcoxon signed rank test.

00:08 We are given that the sample size is 19 and the significance level is 0 .10.

00:15 So we're going to get the critical values for three cases, a right tail test, a left tail test and a two -tailed test.

00:22 So let's begin and get the critical values for a right -tailed test.

00:29 Now, so the critical values here are the y values with an area of 0 .10 to the right.

00:40 So we need to go to the table 5 and then go all the way down to a sample size of 19 and then pick the correct values accordingly.

00:54 So for sample size of 19 and the right tail test we are looking for the w values to the right that have an area of the the the w values with an area of 0 .10 to the right and this is obtained directly by looking at the column that has that area of 0 .10 to the right and that corresponds to to 128.

01:29 Next for our left tail test what we would want to do is to get the w1 minus 0 .10 and i very simply the y values with an area of 0 .1 to the left and we obtain it using the formula n n plus 1 all over 2 minus w 0 .10.

02:05 So we need to work this out by substituting the values accordingly.

02:10 And the sample size is in this case is 19.

02:13 So 19 multiplied by 19 plus 1, all over 2 minus the value 128 has obtained from the previous step.

02:24 So this will be 19 multiplied by 19 times plus 1, which is 20.

02:31 So that's 19 times 20 which equals 380...

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