The sign test

The sign test is among the simplest of all non-parametric statistical methods, and was first discussed in the early eighteenth century. It can be used in a number of ways, the simplest of which is demonstrated by the following example. 

A pharmaceutical preparation is claimed to contain 8% of a particular component. Successive batches were found in practice to contain 7.3, 7.1, 7.9, 9.1, 8.0, 7.1, 6.8 and 7.3% of the constituent. Are these results consistent with the 

It is apparent from this example that the sign test will involve the frequent use of the binomial distribution with p = q =. So common is this approach to non-parametric statistics that most sets of statistical tables include the necessary data, allowing such calculations to be made instantly (see Table A.9). Moreover, in many practical situations, an analyst will always take the same number of readings or samples, and will be able to memorize easily the probabilities corresponding to the various numbers of -t or - signs. 

A further use of the sign test is to indicate a trend. This application is illustrated by the following example. 

The level of a hormone in a patient s blood plasma is measured at the same time each day for 10 days. The resulting data are  

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The p-value for the sign test or Wilcoxon signed rank test can be found in the pValue variable in the pvalue data set. If the variable is from a symmetric distribution, you can get the p-value from the Wilcoxon signed rank test, where the Test variable in the pvalue data set is Signed Rank. If the variable is from a skewed distribution, you can get the p-value from the sign test, where the Test variable in the pvalue data set is Sign. ... 

Of the 38 subjects tested, 27 showed the predicted shift (13 of 19 in the Decrease condition and 14 of 19 in the Increase condition), and 11 did not,/> <. 01 by the sign test. Five subjects in each condition showed no shift, whereas one subject in the Decrease condition, a suicidal type, showed a shift opposite from prediction. 

For both DSL and ASL, nominals that do not have inherent temporal meaning can be associated with the deictic time line and thereby take on temporal meaning. Figure 6.8 provides an example in which the sign test is associated with a location on the deictic time line, test is not a time expression, but it takes on temporal meaning ( next Friday s test ) by virtue of its spatial location. 

The sign test to compare two treatments. We assume that there are several independent pairs of observations on the two treatments. The hypothesis to be tested states that each difference has a probability distribution having mean equal to zero. For each difference the algebraic sign is noted and then the number of times the less frequent sign is considered as the test statistic. There are speciahzed tables for the critical value of this quantity once a level of significance is chosen. 

The price paid for the extreme simplicity of the sign test is some loss of statistical power. The test does not utilize all the information offered by the data, so it is not surprising to find that it also provides less discriminating information. In later sections, non-parametric methods that do use the magnitudes of the individual results as well as their signs will be discussed. 

Section 6.3 described the use of the sign test. Its value lies in the minimal assumptions it makes about the experimental data. The population from which the sample is taken is not assumed to be normal, or even to be s)mimetrical. On the other hand a disadvantage of the sign test is that it uses so little of the information provided. The only material point is whether an individual measurement is greater than or less than the median - the size of this deviation is not used at all. 

A titration was performed four times, with the results 9.84, 9.91, 9.89 and 10.20 ml. Calculate and comment on the median and the mean of these results. The level of sulphur in batches of an aircraft fuel is claimed by the manufacturer to be symmetrically distributed with a median value of 0.10%. Successive batches are found to have sulphur concentrations of 0.09, 0.12, 0.10, 0.11, 0.08, 0.17, 0.12. 0.14 and 0.11%. Use the sign test and the signed rank test to check the manufacturer s claim. 

The FOEX ranges from -50% to +50%, with an optimum value of 0. The EAn ranges from an optimum value of 100% to 0. The factor of 2 (FA2) is most often referred to in dense gas evaluation studies (Hanna et al, 1991). The sign tests have the advantage of being distribution-free. 

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