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ssrs 2012 barcode font Nonparametric Tests in Software
CHAPTER 10 Nonparametric Tests Read QRCode In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Denso QR Bar Code Generator In None Using Barcode drawer for Software Control to generate, create QRCode image in Software applications. Remark 3 A value corresponding to sample 2 is given by the statistic U N1N2 N2(N2 2 1) R2 (5) Quick Response Code Recognizer In None Using Barcode recognizer for Software Control to read, scan read, scan image in Software applications. Generating QR Code ISO/IEC18004 In Visual C# Using Barcode generator for .NET Control to generate, create QR Code image in VS .NET applications. and has the same sampling distribution as statistic (2), with the mean and variance of formulas (3). Statistic (5) is related to statistic (2), for if U1 and U2 are the values corresponding to statistics (2) and (5), respectively, then we have the result U1 We also have R1 where N N1 R2 N(N 2 1) (7) U2 N1N2 (6) Creating QR In Visual Studio .NET Using Barcode printer for ASP.NET Control to generate, create QR Code image in ASP.NET applications. Denso QR Bar Code Creation In .NET Using Barcode generator for .NET framework Control to generate, create QR Code 2d barcode image in .NET framework applications. N2. Result (7) can provide a check for calculations.
Create QR Code In VB.NET Using Barcode generator for VS .NET Control to generate, create QR Code JIS X 0510 image in .NET framework applications. GS1128 Generator In None Using Barcode generator for Software Control to generate, create UCC  12 image in Software applications. Remark 4 The statistic U in equation (2) is the total number of times that sample 1 values precede sample 2 values when all sample values are arranged in increasing order of magnitude. This provides an alternative counting method for finding U. Barcode Drawer In None Using Barcode printer for Software Control to generate, create bar code image in Software applications. Drawing UPC Code In None Using Barcode generation for Software Control to generate, create GS1  12 image in Software applications. The Kruskal Wallis H Test
Code 128B Creation In None Using Barcode generation for Software Control to generate, create Code 128 Code Set C image in Software applications. Code39 Maker In None Using Barcode creation for Software Control to generate, create Code 39 Full ASCII image in Software applications. The U test is a nonparametric test for deciding whether or not two samples come from the same population. A generalization of this for k samples is provided by the Kruskal Wallis H test, or briefly the H test. This test may be described thus: Suppose that we have k samples of sizes N1, N2, . . . , Nk, with the total size of all samples taken together being given by N N1 N2 c Nk. Suppose further that the data from all the samples taken together are ranked and that the sums of the ranks for the k samples are R1, R2, . . . , Rk, respectively. If we define the statistic H Make I2/5 In None Using Barcode creation for Software Control to generate, create I2/5 image in Software applications. ANSI/AIM Code 128 Encoder In None Using Barcode generator for Office Excel Control to generate, create Code 128A image in Excel applications. k R2 j 12 N(N 1) ja Nj 1
Print GS1 128 In ObjectiveC Using Barcode drawer for iPad Control to generate, create EAN 128 image in iPad applications. Reading Barcode In .NET Framework Using Barcode Control SDK for ASP.NET Control to generate, create, read, scan barcode image in ASP.NET applications. then it can be shown that the sampling distribution of H is very nearly a chisquare distribution with k 1 degrees of freedom, provided that N1, N2, . . . , Nk are all at least 5. The H test provides a nonparametric method in the analysis of variance for oneway classification, or onefactor experiments, and generalizations can be made. Encoding Code 128B In ObjectiveC Using Barcode generator for iPad Control to generate, create Code 128C image in iPad applications. Making ANSI/AIM Code 128 In ObjectiveC Using Barcode encoder for iPhone Control to generate, create Code 128B image in iPhone applications. The H Test Corrected for Ties
Making Data Matrix ECC200 In None Using Barcode generator for Online Control to generate, create Data Matrix ECC200 image in Online applications. Drawing Barcode In Java Using Barcode generation for Android Control to generate, create bar code image in Android applications. In case there are too many ties among the observations in the sample data, the value of H given by statistic (8) is smaller than it should be. The corrected value of H, denoted by Hc, is obtained by dividing the value given in statistic (8) by the correction factor 1 a (T N3 T) N
where T is the number of ties corresponding to each observation and where the sum is taken over all the observations. If there are no ties, then T 0 and factor (9) reduces to 1, so that no correction is needed. In practice, the correction is usually negligible (i.e., it is not enough to warrant a change in the decision). The Runs Test for Randomness
Although the word random has been used many times in this book (such as in random sampling and tossing a coin at random ), no previous chapter has given any test for randomness. A nonparametric test for randomness is provided by the theory of runs. To understand what a run is, consider a sequence made up of two symbols, a and b, such as a a (10) CHAPTER 10 Nonparametric Tests
In tossing a coin, for example, a could represent heads and b could represent tails. Or in sampling the bolts produced by a machine, a could represent defective and b could represent nondefective. A run is defined as a set of identical (or related) symbols contained between two different symbols or no symbol (such as at the beginning or end of the sequence). Proceeding from left to right in sequence (10), the first run, indicated by a vertical bar, consists of two a s; similarly, the second run consists of three b s, the third run consists of one a, etc. There are seven runs in all. It seems clear that some relationship exists between randomness and the number of runs. Thus for the sequence a (11) there is a cyclic pattern, in which we go from a to b, back to a again, etc., which we could hardly believe to be random. In that case we have too many runs (in fact, we have the maximum number possible for the given number of a s and b s). On the other hand, for the sequence a a a a a a (12) there seems to be a trend pattern, in which the a s and b s are grouped (or clustered) together. In such case there are too few runs, and we could not consider the sequence to be random. Thus a sequence would be considered nonrandom if there are either too many or too few runs, and random otherwise. To quantify this idea, suppose that we form all possible sequences consisting of N1 a s and N2 b s, for a total of N symbols in all (N1 N2 N ). The collection of all these sequences provides us with a sampling distribution. Each sequence has an associated number of runs, denoted by V. In this way we are led to the sampling distribution of the statistic V. It can be shown that this sampling distribution has a mean and variance given, respectively, by the formulas mV 2N1N2 N1 N2 1 s2 V 2N1N2(2N1N2 (N1 N2)2(N1 N1 N2 N2) 1) (13) By using formulas (13), we can test the hypothesis of randomness at appropriate levels of significance. It turns out that if both N1 and N2 are at least equal to 8, then the sampling distribution of V is very nearly a normal distribution. Thus Z V mV sV (14)

