文档介绍：生物统计课件
Paired Samples: Wilcoxon Signed Rank Test (p. 37)
Non-parametric analog of the paired t-test
Also known as Mann-Whitney U test
Notation:
X is the variable under investigation in some population
Paired difference d = X2 - X1
Let Md be the true (population) median of the difference d
Forms of hypotheses:
H0: Md = 0
H1: Md < 0 (one sided alternative)
H1: Md > 0 (one sided alternative)
H1: Md 0 (two sided alternative)
Wilcoxon Signed Rank Test (Mann-Whitney U test)
Test statistic:
Compute the differences d = X2-X1 (for each observation)
If d = 0, eliminate that data point from calculations and reduce n accordingly
Rank the differences, ignoring the signs of the differences.
If there are equal differences, average the corresponding ranks.
Affix the sign of each difference to its rank
Compute T = sum of the positively signed ranks, or the absolute value of the sum of the negatively signed ranks, whichever is smaller.
Wilcoxon Signed Rank Test (continued)
If n < 12:
One-sided P-values are given in Table
Two-sided tests, multiply P-values given in Table by 2.
If N > 12:
Assume that T is approximately normal with mean T and
standard deviation T and calculate a z-test defined as:
P-values are obtained from Table
Example 1: Wilcoxon Signed Rank Test ()
Research Question:
“Does a pericardial tamponade affect blood flow of the left ventricle in anesthetized dogs? ”
Design: measure coronary blood flow pre
and post a pericardial tamponade
H0: Md = 0 vs. H1: Md 0 (two-sided)
Significance level α =
Data: n = 13 dogs
Example 1: Data
Example 1: (continued)
Test statistic: T = absolute value of sum of negative ranks
T = |(-1) + (- 4)| = |-5| = 5
n = 12
One-sided p-value = from Table
Two-sided p = 2× =
Conclusion:
These data show that there is a statistically significant difference in median blood flow due to the tamponade (p = ).
Example 2: (p. 40)
Suppose t