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WILCOXON SIGNED RANK

TEST

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES

WILCOXON SIGNED RANK TEST

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES The Wilcoxon signed rank test is a nonparametric hypothesis test in which the original data are transformed into ranks. The Wilcoxon signed rank test may be conducted for a) Single population median b) Matched-pair data from two dependent samples

WILCOXON SIGNED RANK TEST

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES

WILCOXON SIGNED RANK TEST

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES

WILCOXON SIGNED RANK TEST

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES The counseling staff of Clear Creek County School District has implemented a new program this year to reduce bullying in their elementary schools. The school district does not know if the new program resulted in improvement or deterioration. To evaluate the program’s effectiveness, the school district has decided to compare the percent of successful interventions this year with the program in place.

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES Table 3.1, the 12 elementary school counselors, or participants, reported the percent of successful interventions last year and the percent this year. Step 1 State the null and alternative hypotheses.

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES Table 3.1, the 12 elementary school counselors, or participants, reported the percent of successful interventions last year and the percent this year. Step 2 State the level of risk (or the level of significance) associated with the null hypothesis.

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES Table 3.1, the 12 elementary school counselors, or participants, reported the percent of successful interventions last year and the percent this year. Step 4 Determine the critical values and the rejection region. Our sample size is reduced to n=10 since there are two participants having same percent of successful interventions from previous year to present.

Step 4 Determine the critical values and the rejection region. Our sample size is reduced to n= since there are two participants having same percent of successful interventions from previous year to present. Since (2-tailed) and n = 10, which gives us.

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES

Step 6 Compute the test statistic In small-sample case (n 30), use this table to find the test statistic

𝒅𝒂𝒕𝒂

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES Table 3.1, the 12 elementary school counselors, or participants, reported the percent of successful interventions last year and the percent this year. Step 7 Make a decision Since and , then is rejected.

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES Table 3.1, the 12 elementary school counselors, or participants, reported the percent of successful interventions last year and the percent this year. Step 8 Interpretation There is a significant difference between the percent of successful interventions last year and this year.

WILCOXON SIGNED RANK TEST (SMALL-

SAMPLE CASE)

FOR MATCHED-PAIR DATA FROM TWO DEPENDENT SAMPLES Table 3.1, the 12 elementary school counselors, or participants, reported the percent of successful interventions last year and the percent this year. Step 9 Conclusion Evidence exists that the new bullying program is providing positive benefits toward the improvement of student behavior as perceived by the school counselors.