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NON-PARAMETRIC STATISTICAL TESTS IN RESEARCH: ANALYZING HYPOTHESES AND DATA

An exercise on using non-parametric statistical tests to analyze research hypotheses and data.

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    COUN 503 Page 1 of 3 N ON - P ARAMETRIC S TATISTICAL T ESTS IN R ESEARCH : A NALYZING H YPOTHESES AND D ATA W EB C ALCULATOR E XERCISE 4 Non - parametric tests (Chi - square tests, Wilcoxon - rank - sum & Wilcoxon signed - ranks test s ) Note: When searching for a web calculator for the Wilcoxon - rank - sum test, please be aware that this test is also called the “Mann - Whitney U test”. This test is used for Ordinal data and for an independent groups design. 1. A high school counselor wants to examine whether the teenage pregnancy rate at her school is different from the rate nationwide. She knows that the rate nationwide is 15 %. She randomly selects 80 female students from her high school. She finds that 9 out of 80 students are either pregnant now or have been pregnant previously. a. What statistical test should be used to analyze the data? Z - test using propotion. b. Identify H 0 and H a for this study H 0 : p = 0.15 H a : p ≠ 0.15 c. Conduct the appropriate analysis z = (phat – p)/sqrt(p*(1 - p)/N) z = (9/80 – 0.15)/sqrt(0.15*0.85/80) z = - 0.93933 d. Should H 0 be rejected? What should the researcher conclude? The critical values for alpha = 0.05 are +/ - 1.96. The test statis tic is not outside of those values. Therefore, we do not reject the null hypothesis. The researcher should conclude that the pregnancy rate at the school is not different from the nationwide rate with a p value of .348 2. You notice at the gym that it appears more women tend to work out together, whereas more men tend to work out alone. To determine whether this difference is significant, you collect data on the workout preferences for a sample of men and women at your gym. The data follows. Males Females Together 5 8 Alone 7 6 a. What statistical test should be used to analyze the data? Chi - square b. Identify H 0 and H a for this study H 0 : No association between gender and working alone/together. H a : Association between working along/together.

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