STEP 1: State the hypotheses •Based on the hypothesised value
STEP 2: Calculate the difference d •For each pair of data, by subtracting the second value from the first.
STEP 3: Find test statistic •Sort the differences •from lowest to highest by ignoring the signs of the differences •Find the absolute of the sum values • of the negative ranks, and find the sum of the positive ranks •Let T be the smallest of the two sums found
STEP 4: Formulate the decision rule •Critical value method •Find critical value •Exclude ties: that is, any matched pairs in which both values are equal. Let n be the number of pairs of data for which the difference d is not 0 •From Table A- 8, using n and
STEP 5: Make the statistical decision •Reject or do not reject the null hypothesis
The null and alternative hypotheses for each type of test are as follows.
• Left-tailed test: • H0: median 1= median 2 • H1: median < median 2 • Right-tailed test: • H0: median 1 = median 2 • H1: median > median 2 • Two-tailed test: • H0: median 1 = median 2 • H1: median ≠ median 2
â&#x20AC;˘ Compare the effects of two Is soporific drugs. Each subject receives Drug 1 and Drug 2. Use Wilcoxon sign rank test at 5% significance level.
Step 1: State the hypotheses • H0: The median of the differences is equal to 0. • H1: The median of the differences is not equal to 0. • H0: There is no difference between Drug 1 and Drug 2 • H1: There is a difference between Drug 1 and Drug 2
Step 2: Calculate the difference d • d = Drug 2 – Drug 1
Step 3: Find test statistic • Find x • Absolute value of sum of negative ranks: 3 • Sum of positive ranks: 42 • T be the smallest of the two sums, T = 3.
Step 4: Formulate decision rule • Test statistic< critical value, reject • From Table A- 8, using n = 9 and = 0.05 in two tails, critical value is 5 • test statistic x = 3 is less than to the critical value of 5, so we reject the null hypothesis.
Step 5: Make statistical decision • We conclude that there is a difference between Drug 1 and Drug 2.