S. Siegal and N. J. Castellan. Non-Parametric statistics for the behavioural sciences. McGraw Hill, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....determine the degree of association between two sets of rank ordered data. It is defined as: ae s = P K i=1 (r i Gamma r) s i Gamma s) q P K i=1 (r i Gamma r) 2 P K i=1 (s i Gamma s) 2 (5) where r i and s i are the two sets of rankings being compared, and K is the number of ranks [29]. If there are no ties in the rankings, then Equation 5 can be simplified to give: ae s = 1 Gamma 6 P K i=1 (r i Gamma s i ) 2 K(K 2 Gamma 1) 6) The ae s statistic will be 1 if the two rankings are identical (complete agreement) and Gamma1 if the rankings are opposite (complete ....

....may be kept separate to allow the fuzzy system to be trained to certain experts. Note that if the average correlation between all pairs is denoted ave(ae s ) then ave(ae s ) can only range from Gamma1= k Gamma 1) to 1, as it is not possible for k experts to all totally disagree with each other [29]. In this case the significance of ave(ae s ) must be tested by: 2 = K Gamma 1) i (k Gamma 1) ave(ae s ) 1 j ; with df = K Gamma 1: III. Application to Umbilical Acid Base Interpretation A. Medical Background In many areas of medicine, such as obstetrics, advances in technology ....

S. Siegel and N.J. Castellan, Nonparametric Statistics for the Behavioural Sciences (2nd edn), McGraw-Hill, New York, 1988.

....duplicate pair 1 . Assume also that there exists a set of pairs of requirements that are identified as actual duplicate pairs. The similarity measure hence provides an approximation of this set of actual duplicate pairs, and the quality of the estimation may be defined according to Table 1 [16]. The resulting pairs that have a similarity value above or equal to the threshold level are regarded as duplicate pairs suggested by the analyser. Matches between actual duplicate pairs and those suggested by the analyser are denoted true positives.The 1. The term duplicate is here used in a ....

....reported 70 similar pairs on a 0 threshold (9, 18, 21, 10, and 12 pairs in each set respectively) of which 25 were true positives. Table 4 shows the frequencies of actual dependencies in relation to the similarity measure using the assessment scheme presented in Table 1. A chi square test [16] gives a p value 0.0001, which shows that the similarity measure vary significantly with actual dependencies. Thus, by checking for lexical similarity on a slogan level, this particular case demonstrates that it is possible to support the interdependency identification process by automatic ....

Siegel, S., Castellan, N. J., Nonparametric Statistics for the Behavioural Sciences. Second Edition. McGraw-Hill, 1988.

....the degree of association between two sets of rank ordered data. It is defined as: r s K i ; 1 r i r s i s F K i ; 1 r i r 2 K i ; 1 s i s 2 (5. 6) 169 where r i and s i are the two sets of rankings being compared, and K is the number of ranks [113]. If there are no ties in the rankings, then Equation 5.6 can be simplified to give: r s 1 6 K i ; 1 r i s i 2 K K 2 1 (5.7) The r s statistic will be 6 1 if the two rankings are identical (complete agreement) and 1 if the rankings are opposite (complete ....

....be kept separate to allow the fuzzy system to be trained to certain experts. Note that if the average correlation between all pairs is denoted ave r s , then ave r s can only range from 1 7 k 1 to 6 1, as it is not possible for k experts to all totally disagree with each other [113]. In this case the significance of ave r s must be tested by: c 2 K 1 k 1 ave r s H6 1 with df K 1 170 5.4.5 Aside: Rank Order Statistics in MATLAB Rank order statistics, such as the Spearman rank order correlation coefficient described above, require ....

S. Siegel and N.J. Castellan. Nonparametric Statistics for the Behavioural Sciences (2nd edn). McGraw-Hill, New York, 1988.

....of Chi square tests, to find any significant degree of association between turnover growth and employment growth and age, size, turnover and legal form of business. In the absence of these, therefore, a bivariate correlation analysis was performed using a Spearman correlation coefficient (Siegel, 1956). These revealed, as Table 3 shows, that there was, at the 0.05 level, a high statistical association for both employment change and turnover change with size, turnover and between turnover change and employment change. Other variables, such as age and legal form, were less associative, although ....

Siegel, S. (1956) Nonparametric Statistics for the Behavioural Sciences, McGrawHill: New York.

....a linguistic task and that which would be expected by chance. It is calculated according to formula 1, where Pr(A) is the proportion of times the annotators agree and Pr(E) the proportion which would be expected by chance. Detailed instructions on calculating these probabilities are described by Siegel and Castellan (1988). Pr(A) Gamma Pr(E) 1 Gamma Pr(E) 1) The value of the kappa statistic ranges between 1 (perfect agreement) and 0 (the level which would be expected by chance) It has been claimed that content analysis researchers usually regard :8 to demonstrate good reliability and :67 :8 al ....

....could compare the subjects annotations who had not agreed on any sentence boundaries but find that they agreed most word boundaries were not sentence boundaries. The same problem will effect other standard measures of inter annotator agreement such as the Cramer, Phi and Kendall coefficients (see Siegel and Castellan (1988)) Carletta mentions this problem, asking what the difference would be if the kappa statistic were computed across clause boundaries, transcribed word boundaries, and transcribed phoneme boundaries (Carletta, 1996, p. 252) rather than the sentence boundaries she suggested. It seems likely that ....

S. Siegel and N. Castellan. 1988. Nonparametric Statistics for the Behavioural Sciences. McGrawHill, second edition.

....that which would be expected by chance. It is calculated according to formula 1, where Pr(A) is the proportion of times the annotators agree and Pr(E) the proportion which would be expected by chance. Detailed instructions on calculating these probabilities are described by Siegel and Castellan [15]. Pr(A) Gamma Pr(E) 1 Gamma Pr(E) 1) The value of the kappa statistic ranges between 1 (perfect agreement) and 0 (the level which would be expected by chance) It has been claimed that content analysis researchers usually regard :8 to demonstrate good reliability and :67 :8 allows ....

....annotations who had not agreed on any sentence boundaries but find that 4 they agreed most word boundaries were not sentence boundaries. The same problem will effect other standard measures of inter annotator agreement such as the Cramer, Phi and Kendall coefficients (see Siegel and Castellan [15]) Carletta mentions this problem, asking what the difference would be if the kappa statistic were computed across clause boundaries, transcribed word boundaries, and transcribed phoneme boundaries (p. 252) 4] rather than the sentence boundaries she suggested. It seems likely that more ....

S. Siegel and N. Castellan. Nonparametric Statistics for the Behavioural Sciences. McGraw-Hill, second edition, 1988.

....However, some authors note that the choice of an level is arbitrary [39] 29] and it is clear that null hypothesis testing at fixed alpha levels is controversial [15] 82] More relevant for our endeavours, it is noted that typical statistical texts provide critical value tables for =0. 1 [77][78], indicating that this choice of level is appropriate in some instances. As we explain in the text, our choice of level was driven by power considerations. 16 We used one sided hypothesis tests since we posit a directional difference between the two reading techniques. 16 H 1 H 2 H 3 H 4 ....

....to investigate whether a difference in the defect detection effectiveness or the cost per defect ratio is due to chance. Although the t test is robust against violation of certain assumptions (i.e. the normality 22 and homogeneity of the data) we also performed the Wilcoxon signed ranks test [78], which is the non parametric counterpart of the matchedpair t test. The Wilcoxon signed rank test corroborated the findings of the t test in all cases. Hence, we do not present the detailed results of this test. We run the statistical tests for the quasi experiment and the two replications ....

S. Siegel and J. Castellan. Nonparametric Statistics For The Behavioural Sciences. McGraw Hill, Inc., 2 nd edition, 1988.

.... the data analysed here is measured on a ratio scale (evenly spaced success scores from 0 [perfect] to in nity [bad] and the U test only requires an ordinal scale, the U test avoids the assumption of normal distribution and equal variance between the populations that is required by the t test [Siegel, 1956]. The same test will be used in all the following analyses. Since H 1 predicts the direction of the hypothesised di erence, the region of rejection is onetailed. Any computed value for U that has a probability of occurring under H 0 equal to or less than = 0:05 will reject H 0 . The data sets ....

....distance to goal scores found for randomly generated points within the arena. The table shows the ranking of the scores and the total of the ranks for both sample types, used to determine the U score. The sample sizes are n 1 = 12 (m1s) and n 2 = 12 (rnd) Following the algorithm for the U test [Siegel, 1956, pp116 127] it is found that the U value for these data sets is 7. From the Mann Whitney U test tables it is found that the critical U for a one tailed test at = 0:05 is 42. Any value of U less than or equal to 42 indicates that the probability of the two data sets being drawn from the same ....

Siegel, S. (1956). Nonparametric statistics for the behavioural sciences. McGraw-Hill.

.... the data analysed here is measured on a ratio scale (evenly spaced success scores from 0 [perfect] to in nity [bad] and the U test only requires an ordinal scale, the U test avoids the assumption of normal distribution and equal variance between the populations that is required by the t test [Siegel, 1956]. The same test will be used in all the following analyses. Since H 1 predicts the direction of the hypothesised di erence, the region of rejection is onetailed. Any computed value for U that has a probability of occurring under H 0 equal to or less than = 0:05 will reject H 0 . The data sets ....

....(Table 2 of 2) scores found for randomly generated points within the arena. The table shows the ranking of the scores and the total of the ranks for both sample types, used to determine the U score. The sample sizes are n 1 = 12 (m1s) and n 2 = 12 (rnd) Following the algorithm for the U test [Siegel, 1956, pp116 127] it is found that the U value for these data sets is 7. From the Mann Whitney U test tables it is found that the critical U for a one tailed test at = 0:05 is 42. Any value of U less than or equal to 42 indicates that the probability of the two data sets being drawn from the same ....

Siegel, S. (1956). Nonparametric statistics for the behavioural sciences. McGraw-Hill.

....r, the Spearman rank order correlation coefficient rs , and the Kendall rank order correlation coefficient T . Detailed information on these correlation coefficients can be found in many standard statistics books (see, for example, 3] for the Pearson product moment correlation coefficient and [11] for the Spearman and Kendall rank order correlation coefficients) The language model evaluation schemes which will be described in this paper are evaluated with respect to the reference transcription of the broadcast news shows upon which the WER scores are based, rather than the much larger ....

S. Siegel and N. Castellan. Nonparametric Statistics for the Behavioural Sciences. McGraw Hill, 2nd edition, 1988.

....so, again, any performance difference is invisible. The statistical comparisons between the data took this into account by only considering trials whose mean lifetime was greater than, an arbitrarily chosen, 10000. The non parametric nature of the lifetime data led to choosing Mood s median test (Siegel and Castellan, 1988) to determine if two trends were statistically different. This was performed by testing pairs of points recorded under the same loss per cycle parameter, thus generating a series of statistical tests indicating when the performance of the strategies differed within a parameter range. Unless ....

Siegel, S. and Castellan, N.J. (1988). Nonparametric statistics for the behavioural sciences.

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S. Siegal and N. J. Castellan. Non-Parametric statistics for the behavioural sciences. McGraw Hill, 1988.

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S. Siegel and N. J. Castellan. Nonparametric Statistics for the Behavioural Sciences. McGraw-Hill, 2nd edition, 1988.

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Sidney, S., Castellan, N. J.: Non parametric statistics for the behavioural sciences. McGraw Hill, Boston, MA. (1988)

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S. Siegal and N. J. Castellan. Non-Parametric statistics for the behavioural sciences. McGraw Hill, 1988.

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Siegal, S. and N. Castellan (1988). Nonparametric Statistics for the Behavioural Sciences. McGraw Hill.

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S. Siegel and N.J. Castellan (1988). Nonparametric Statistics for the Behavioural Sciences (2nd edn). McGraw-Hill, New York, 1988.

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S. Siegel and N.J. Castellan. Nonparametric Statistics for the Behavioural Sciences (2nd edn). McGraw-Hill, New York, 1988.

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S. Siegal and N. J. Castellan. Non-Parametric statistics for the behavioural sciences. McGraw Hill, 1988.

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S. Siegel and N.J. Castellan, Nonparametric Statistics for the Behavioural Sciences (2nd edn), McGraw-Hill, New York, 1988.

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S. Siegel and N.J. Castellan. Nonparametric Statistics for the Behavioural Sciences (2nd edn). McGraw-Hill, New York, 1988.

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SIEGEL, S., Nonparametric Statistics for the Behavioural Sciences, McGraw-Hill, New York (1956).

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Urbana, Ill. Siegel, S. and Castellan, N. (1988). Nonparametric Statistics for the Behavioural Sciences. McGraw Hill, 2nd edition.

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