654 CHAPTER 13 Nonparametric Tests We replace x by x + 0.5 as a correction for continuity (as discussed in Section 6-6). That is, the values of x are discrete, but since we are using a continuous probability distribution, a discrete value such as 10 is actually represented by the interval from 9.5 to 10.5. Because x represents the less frequent sign, we act conservatively by concerning ourselves only with x + 0.5; we get the test statistic z shown below and in the Key Elements box. z = 1 x + 0.52 - a n 2b 2 n 2 Sign Test Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Sign Test from the dropdown menu. 3. Known number of signs Select Given Number of Signs, choose the format for the claim, enter the significance level and numbers of positive and negative signs. Pairs of values Select Given Pairs of Values, choose the format for the claim, enter the significance level, and select the two data columns to include. 4. Click Evaluate. StatCrunch StatCrunch is able to test the claim that a single list of values is from a population with a median equal to some specified value. 1. Click Stat in the top menu. 2. Select Nonparametrics from the dropdown menu and Sign Test from the submenu. 3. Select the column containing the data to be analyzed. 4. Select Hypothesis test for median and for H0 enter the claimed median value. For HA select the desired format. 5. Click Compute! Minitab Minitab requires a single column of values. Matched pairs: Enter a column consisting of the differences. Nominal data in two categories: Enter a 1 for each value of one category and -1 for each value of the other category. Enter 0 for the claimed value of the median. Individual values to be tested with claimed median: Enter sample values in a single column. 1. Click Stat in the top menu. 2. Select Nonparametrics from the dropdown menu and select 1-Sample Sign from the submenu. 3. Under Variables select the column containing the data to be analyzed. 4. Select Test Median and enter the claimed median value. 5. Choose the format of the alternative hypothesis. 6. Click OK. TI-83, 84 Plus Calculator The TI-83>84 Plus calculator does not have a function dedicated to the sign test, but the calculator’s binomcdf function can be used to find the P-value for a sign test. 1. Press F then O keys to access the DISTR (distributions) menu. 2. Select binomcdf and click [. 3. Enter the values for trials n, p, and x to complete the command binomcdf(n,p,x). For trials enter the total number of positive and negative signs. For p enter 0.5. For x enter the number of the less frequent sign. 4. Press [. The result is the probability of getting x or fewer trials. Double this value for two-tailed tests. TIP: The final result is the P-value, so reject the null hypothesis if the P-value is less than or equal to the significance level. Otherwise, fail to reject the null hypothesis.
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