Exam 15: B:nonparametric Statistics

Reaction Times Narrative The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times. -Refer to Reaction Times Narrative. What experimental design is being used in this ?

Children and Antibiotics Narrative In a study of the palatability of antibiotics in children, a medical team used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics. The children's response was measured on a 10 centimetre (cm) visual analogue scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data, each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analogue scale from 0 to 10 cm. Antibiotic -Refer to Children and Antibiotics Narrative. Using an appropriate statistical package for a two-way classification, produce a normal probability plot of the residuals as well as a plot of residuals vs. antibiotics. Do the usual analysis of variance assumptions appear to be satisfied? Report the ANOVA results.

Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population locations differ. Sample 1: 17 20 18 25 16 22 Sample 2: 17 25 33 38 15 26 21

Reaction Times Narrative The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times. -Refer to Reaction Times Narrative. Describe what the test statistic is. What is the value of in this ?

Children and Antibiotics Narrative In a study of the palatability of antibiotics in children, a medical team used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics. The children's response was measured on a 10 centimetre (cm) visual analogue scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data, each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analogue scale from 0 to 10 cm. Antibiotic -Refer to Children and Antibiotics Narrative. What design is used in collecting these data?

Books Manuscripts Narrative In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better. -Refer to Books Manuscripts Narrative. Explain how to use the p-value for testing the hypotheses at the 5% significance level.

Teaching Methods Narrative Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another. -Refer to Teaching Methods Narrative. Can we conclude the teaching methods are equally effective? Explain.

TV Commercials Narrative It is important to sponsors of television shows that viewers remember as much as possible about the commercials. The advertising executive of a large company is trying to decide which of two commercials to use on a weekly half-hour comedy. To help make a decision, she decides to have 12 individuals watch both commercials. After each viewing, each respondent is given a quiz consisting of 10 questions. The number of correct responses was recorded and is listed below. Assume that the quiz results are not normally distributed. Quiz Scores -Refer to TV Commercials Narrative. Do these data provide enough evidence at the 5% significance level to conclude that the two commercials differ? Justify your conclusion.

A dog kennel manager was interested in determining whether there is a difference in the time it takes a dog to complete an obstacle course for two different courses. A random sample of 36 dogs was selected and the time it took each dog to complete each course was recorded. In 12 cases it took the dog longer to complete course 1. Use the normal approximation to the sign test to determine if there is a significant difference in the time it takes to complete the two obstacle courses. Use = 0.05.

Gourmet Meals Narrative Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other? -Refer to Gourmet Meals Narrative. Test by using the sign test with a value of near 0.05. Use the binomial tables to find the exact rejection region for the test.

Attitude Test Narrative Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes. -Refer to Attitude Test Narrative. Describe what the test statistic is for the Wilcoxon signed-rank test. What is the value of the test statistic in this ?

Reaction Times Narrative The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times. -Refer to Reaction Times Narrative. What is the p-value for this ?

Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 to the right of distribution 2, based on samples of sizes = 7 and = 9. a. Should you use or as the test statistic? b. What is the rejection region for the test if c. What is the rejection region for the test if

Books Manuscripts Narrative In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better. -Refer to Books Manuscripts Narrative. Which test is appropriate for this situation?

In an investigation of the visual scanning behaviour of hearing-impaired children, measurements of eye movement rates were taken on nine hearing-impaired children and nine hearing children as shown in the table below. Does it appear that the distributions of eye-movement rates for hearing-impaired children and hearing children differ? Test at = 0.05 using the Wilcoxon rank sum test.

Reaction Times Narrative The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times. -Refer to Reaction Times Narrative. Is there a difference among the population distributions of reaction times? Justify your answer.

The following statistics are drawn from two independent samples: , ; , . Test at the 5% significance level to determine whether the two population locations differ.

Because of the rising costs of industrial accidents, many chemical, mining, and manufacturing firms have instituted safety courses. Employees are encouraged to take these courses designed to heighten safety awareness. A company is trying to decide which one of two courses to institute. To help make a decision, eight employees take course 1 and another eight take course 2. Each employee writes a test, which is marked out of a possible 25. The results are shown below. Do these data provide sufficient evidence at the 5% level of significance to conclude that the marks from course 2 are higher than those of course 1? Assume that the scores are not normally distributed.

Teaching Methods Narrative Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another. -Refer to Teaching Methods Narrative. What experimental design did the statistician use?

A computer laboratory manager was interested in whether there was a difference in functioning time before needing to be recharged for three battery packs for laptop computers. The manager took a random sample of six battery packs of each brand and tested them. The results, in hours of functioning before needing to be recharged, were recorded as follows: The manager, unsure that the assumptions for the usual parametric analysis of variance were valid, decided to employ nonparametric methods. Use the appropriate nonparametric procedure to determine whether the distribution of functioning time before needing to be recharged is the same for the three brands of battery packs. Use = 0.05.