ssrs 2012 barcode font is normally distributed with mean 0 and variance 1, and thus Appendix C can be used. in Software

Printer QR Code ISO/IEC18004 in Software is normally distributed with mean 0 and variance 1, and thus Appendix C can be used.

is normally distributed with mean 0 and variance 1, and thus Appendix C can be used.
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Further Applications of the Runs Test
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The following are other applications of the runs test to statistical problems: 1. ABOVE- AND BELOW-MEDIAN TEST FOR RANDOMNESS OF NUMERICAL DATA. To determine whether numerical data (such as collected in a sample) are random, first place the data in the same order in which they were collected. Then find the median of the data and replace each entry with the letter a or b according to whether its value is above or below the median. If a value is the same as the median, omit it from the sample. The sample is random or not according to whether the sequence of a s and b s is random or not. (See Problem 10.20.) 2. DIFFERENCES IN POPULATIONS FROM WHICH SAMPLES ARE DRAWN. Suppose that two samples of sizes m and n are denoted by a1, a2, . . . , am and b1, b2, . . . , bn, respectively. To decide whether the samples do or do not come from the same population, first arrange all m n sample values in a sequence of increasing values. If some values are the same, they should be ordered by a random process (such as by using random numbers). If the resulting sequence is random, we can conclude that the samples are not really different and thus come from the same population; if the sequence is not random, no such conclusion can be drawn. This test can provide an alternative to the Mann Whitney U test. (See Problem 10.21.)
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CHAPTER 10 Nonparametric Tests
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Spearman s Rank Correlation
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Nonparametric methods can also be used to measure the correlation of two variables, X and Y. Instead of using precise values of the variables, or when such precision is unavailable, the data may be ranked from 1 to N in order of size, importance, etc. If X and Y are ranked in such a manner, the coefficient of rank correlation, or Spearman s formula for rank correlation (as it is often called), is given by rS 1 6 a D2 N(N 2 1) (15)
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where D denotes the differences between the ranks of corresponding values of X and Y, and where N is the number of pairs of values (X, Y) in the data.
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The sign test 10.1. Referring to Table 10-1, test the hypothesis H0 that there is no difference between machines I and II against the alternative hypothesis H1 that there is a difference at the 0.05 significance level.
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Figure 10-1 is a graph of the binomial distribution (and a normal approximation to it) that gives the probabilities of x heads in 12 tosses of a fair coin, where x 0, 1, 2, c, 12. From 4 the probability of x heads is Pr5x6 whereby Pr{0} 0.00024, Pr{l} a 12 1 x 1 12 ba b a b 2 2 x
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12 1 12 ba b 2 x 0.05371.
0.00293, Pr{2}
0.01611, and Pr{3}
Fig. 10-1
Since H1 is the hypothesis that there is a difference between the machines, rather than the hypothesis that machine I is better than machine II, we use a two-tailed test. For the 0.05 significance level, each tail has the associated probability 1(0.05) 0.025. We now add the probabilities in the left-hand tail until the sum exceeds 2 0.025. Thus Pr{0, 1, or 2 heads} Pr{0, 1, 2, or 3 heads} 0.00024 0.00293 0.01611 0.01928 0.07299
Since 0.025 is greater than 0.01928 but less than 0.07299, we can reject hypothesis H0 if the number of heads is 2 or less (or, by symmetry, if the number of heads is 10 or more); however, the number of heads [the signs in sequence (1) of this chapter] is 3. Thus we cannot reject H0 at the 0.05 level and must conclude that there is no difference between the machines at this level.
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