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Embed Size px x x x x Tests are often called distribution free tests. The Sign Test is a nonparametric test that can be used to test a population median against a hypothesized value, k. Hypotheses or Slide 4 Sign Test To use the sign test, first compare each entry in the sample to the hypothesized median, k. If the entry is below the median, assign it a sign.

If the entry is equal to the median, assign it a 0. Ignore 0s. If they are not approximately equal, however, it is likely that the null hypothesis will be rejected.

Slide 6 Application A meteorologist claims that the daily median temperature for the month of January in San Diego is 57 Fahrenheit. The temperatures in degrees Fahrenheit for 18 randomly selected January days are listed below. Write the null and alternative hypothesis.

State the level of significance. Determine the sampling distribution. Find the test statistic. Find the rejection region. Find the critical value. Reject H 0 if the test statistic is less than or equal to 2. Slide 9 7. Make your decision. Interpret your decision. The test statistic, 8, does not fall in the critical region. Fail to reject the null hypothesis. There is not enough evidence to reject the meteorologists claim that the median daily temperature for January in San Diego is The sign test can also be used with paired data such as before and after.

Find the difference between corresponding values and record the sign. Use the same procedure. Slide 10 The Wilcoxon Test Section Find the difference for each pair: Sample 1 value Sample 2 value Find the absolute value of the difference. Rank order these differences. Find the sum of the positive ranks. Find the sum of the negative ranks. Select the smaller of the absolute values of the sums. To find the test statistic, w s Slide 12 Application The table shows the daily headache hours suffered by 12 patients before and after receiving a new drug for seven weeks.

H a : The new drug reduces headache hours. Claim Slide 13 2. The sum of the negative ranks is 1. The critical value is 2. There is not enough evidence to conclude the new drug reduces headache hours. Slide 15 Wilcoxon Rank-Sum Test The Wilcoxon rank-sum test is a nonparametric test that can be used to determine whether two independent samples were selected from populations having the same distribution.

Both samples must be at least Then n 1 represents the size of the smaller sample and n 2 the size of the larger sample.

When the samples are the same size, it does not matter which is n 1. Find the z-score for the value of R. H 0: There is no difference in the population distributions. H a: There is a difference in the population distributions. Combine the data and rank the values. Then separate the data according to sample and find the sum of the ranks for each sample.

Given three or more independent samples, the test statistic H for the Kruskal-Wallis test is: where k represents the number of samples, n i is the size of the i th sample, N is the sum of the sample sizes, and R i is the sum of the ranks of the i th sample. Reject the null hypothesis when H is greater than the critical number.

Always use a right-tail test. To do so, you randomly select 10 accountants in each state and record their hourly pay rate as shown below. At the. H a : There is a difference in the hourly pay in the 3 states. The sampling distribution is chi-square with d. From Table 6, the critical value is 9. New York salaries are in ranks: 8, 14, 19, 21, 23, 24, 27, 28, 29, 30 The sum is Virginia salaries are in ranks: 1, 9, 10, 11, 12, 16, There is a difference in the salaries of the 3 states.

Make Your Decision Interpret your Decision 9. Rank Correlation The Spearman rank correlation coefficient, r s, is a measure of the strength of the relationship between two variables. The Spearman rank correlation coefficient is calculated using the ranks of paired sample data entries. The formula for the Spearman rank correlation coefficient is where n is the number of paired data entries and d is the difference between the ranks of a paired data entry.

The hypotheses: There is no correlation between the variables. Slide 26 Rank Correlation Seven candidates applied for a nursing position. The seven candidates were placed in rank order first by x and then by y. The results of the rankings are listed below. Using a. There is no correlation between the variables. There is a significant correlation between the variables.

There is not enough evidence to support the claim that there is a significant correlation. Post on Mar views. Category: Documents 12 download.

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## Ron Larson - EstatÃstica aplicada.pdf

Embed Size px x x x x Tests are often called distribution free tests. The Sign Test is a nonparametric test that can be used to test a population median against a hypothesized value, k. Hypotheses or Slide 4 Sign Test To use the sign test, first compare each entry in the sample to the hypothesized median, k. If the entry is below the median, assign it a sign. If the entry is equal to the median, assign it a 0.

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## chapter 11 elementary statistics larson farber nonparametric tests

ISSN: X. DOI: OCLC: ZDB-ID: BECK, K. IEEE Computer, v. IEEE Software, v.

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## Ron Larson - EstatÃstica aplicada.pdf

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