Exam 14: Nonparametric Methods

A class of 12 statistics students completed the course with the following exam averages and homework averages. Student Exam Averages Homewark Averages 1 70 76 2 79 83 3 65 66 4 85 72 5 89 77 6 87 86 7 95 88 8 88 91 9 77 87 10 67 79 11 90 93 12 96 89 Calculate and interpret the Spearman coefficient of rank correlation and use the 0.05 level of significance in testing whether its true value could be something other than 0.

Airline Ten business people who fly frequently were asked to rank four airlines in terms of the quality of service.The people assigned scores using a 5-point scale where: 1 = bad,2 = poor,3 = average,4 = good,and 5 = excellent.The results are shown below: Airline Person A B C D 1 1 3 5 2 2 5 4 2 1 3 2 5 3 2 4 4 2 4 1 5 3 3 1 5 6 4 4 5 3 7 3 4 1 4 8 2 5 2 1 9 5 3 4 2 10 5 5 4 3 -The test question is: Can we conclude at the 5% significance level that there are differences in service quality among the four airlines? Using Excel or Minitab,what is the p-value for the above test?

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -State the null and alternative hypotheses. H₀: ____________________________ H₁: ____________________________

Like the randomized block ANOVA,the ____________________ test compares the effectiveness of treatments,but it is concerned with their medians rather than their mean.

The ____________________ test evaluates the randomness of a series of observations by analyzing the number of ____________________ it contains.

Compare the Friedman test with the randomized block ANOVA in terms of: (a)their respective null and alternative hypotheses,and (b)the assumptions required in order to use each test.

Diet programs A consumer research organization will evaluate the results of two diet programs,Take-It-Off and Melt-Away.Persons are randomly sampled from each of the programs and their weight loss results follow. Take-It- Off Melt-Away 150 130 75 68 40 20 68 54 30 27 98 -The test question is: Do the data indicate that the two programs are equally effective? What is the calculated test statistic W?

FAA The FAA recorded the number of complaints per month for three airlines.The data were: Airline Airline Airline 3248 2462 1544 2876 2838 2381 2943 3042 2279 3486 3211 2163 2777 1968 1459 -The test question is: Do the three airlines have the same median number of complaints? In testing the hypotheses,what is the appropriate critical value for the 0.025 significance level?

Because of the cost of producing television shows and the profits associated with successful shows,television network executives are keenly interested in public opinion.A network has recently developed three comedy series.The pilot of each series is shown in to 10 randomly selected people who evaluate each show on a 9-point scale where 1 = terrible and 9 = excellent.From the results shown below,can we infer at the 5% significance level that differences exist among the show's evaluations? Assessments of Television Shows Person Show 1 Show 2 Show 3 1 6 4 7 2 5 4 5 3 7 6 8 4 7 7 8 5 9 9 9 6 5 7 6 7 4 4 5 8 6 3 7 9 5 6 6 10 7 7 8 H₀: ____________________ H₁: ____________________ Test statistic = ____________________ Critical Value = ____________________ Conclusion: ___________________________ Interpretation: _________________________________________________________

The significance level for a Wilcoxon signed rank test for one sample is 0.02.The alternative hypothesis is m ≠ m₀,and the sample size is 14.What is/are the appropriate critical value(s)? Separate your answers with commas,for example x,y,z,etc.

A nonparametric method to compare two populations,when the samples are matched pairs and the data are quantitative where the normality requirement necessary to perform the parametric test is unsatisfied,is the:

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -State the appropriate conclusion employing a 0.05 significance level.

Treatments Treatments Blocks 1 2 3 1 12 20 16 2 13 18 14 3 13 20 12 4 15 16 18 5 8 10 10 6 10 17 16 No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? -No assumptions are made about the population distributions or variances of the above sample data.The test question is: Are the medians of the treatments equal? For the hypotheses,what is the appropriate critical value for the 0.05 significance level?

The sign test evaluates the randomness of a series of observations by analyzing the number of consecutive data values that are similar.

Seven Dwarfs Several years ago a television station interviewed individuals and asked them to name the "Seven Dwarfs" from the story of "Snow White." The amount of time (in seconds)to name the dwarfs was recorded by age group.The data were: Under 12 12 to 25 Over 25 60 120 75 45 65 45 38 60 75 30 48 55 35 150 100 -The test question is: Do the different age groups require the same median time to name the Dwarfs? What is the rank of the value 38 in the Under 12 sample?

Unlike the Wilcoxon signed rank test,the ____________________ test assumes data are ordinal.

The significance level for a Wilcoxon signed rank test for matched pairs is 0.05.The alternative hypothesis is H₁: m_d > 0.The appropriate critical value for n = 20 nonzero differences is:

Differentiate between the Wilcoxon signed rank test and the Wilcoxon rank sum test,and explain the circumstances under which each should be applied.

A one-sample t-test is the parametric counterpart to the Wilcoxon signed rank test for one sample.