M. Hollander and D. A. Wolfe. Nonparametric Statistical Methods. John Wiley & Sons, 1973.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....shows object pairs. The ordinate is the number of times subjects confirmed there was no difference between the objects presented. The maximum is 28 subjects multiplied by 3 repetitions for each pair. In this preliminary study, we undertook a nonparametric approach. Using Friedman s test [20] [21], 22] significant treatment (here treatment refers to the particular pairing, e.g. h 3 h 8 ) effects were found (S=72.67, p 0.005) Since in each object pair we compare an object with h 8 , the pairing of h 8 and h 8 acts as a control treatment. We next compare each treatment with the control ....

....and h 8 acts as a control treatment. We next compare each treatment with the control treatment to see which objects when paired with h 8 tend to objects haptic model graphic model 0 20 40 60 80 100 12345678 be identified as different. A simultaneous multiple comparisons test [21] based on Friedman s test was conducted at a significance level of 0.05, yielding the grouping shown in Table 2. Table 2: Grouping of objects in experiment 1, using Friedman s test. h 1 , h 2 , h 3 , h 4 h 5 , h 6 , h 7 , h 8 The grouping indicates that when any of the first four objects are ....

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Hollander, M. and Wolfe, D.A., Nonparametric Statistical Methods, published by John Wiley & Sons.

....on the relative performance within each query. While using ranks reduces the power of the test, it requires less restrictive assumptions about the error distribution. Only one nonparametric test, the Friedman test, will be described here. Others can be found in Conover [13] or Hollander and Wolfe [39]. All of these tests assume that the query effect and the effect of the evaluation methods are independent and additive. An initial test is performed to determine whether there is any difference between methods. If a difference is detected, a subsequent multiple comparison test determines which ....

M. Hollander and D. Wolfe. Nonparametric Statistical Methods, chapter 3, 7, pages 27--49, 138--184. John Wiley and Sons, 1973.

....which has since been found to be false in certain cases. In addition, we utilised many pairs of t tests, opening up the possibility of an erroneous conclusion occurring due to the sheer number of comparisons being made. This paper verifies the previous results with distribution free ANOVA analyses [7] in sections 4.3 and 4.4. We also look at the use of different complexities of sensory anticipation model and the resulting differences in landmark alignment in section 4.5. We compare the perceptual novelty method of landmark detection to the sensory anticipation method in terms of landmark ....

....or external cameras available. The best possible evaluation of the alignments in these circumstances is the success rate of using the alignments to find a goal location, as shown in section 4.7. These scores are evaluated using distribution free statistical tests of param eters, see for example [7]. In particular, we use a Kruskal Wallis ANOVA, which tests if the null hypothesis that all choices of treatments (i.e. experimental parameters) are equal is false. We also use a Freidman ANOVA, which does the same thing, but also seeks to cancel out the effects of other systematic ....

Myles Hollander and Douglas Wolfe. Nonparametric Statistical Methods. Wiley, New York, 1973.

....for all a. To verify this hypothesis, the cumulative distribution function, cdf, of two samples are compared. To achieve this, the N observations from the two samples are ordered to form the set Z (i) i = 1, N , where Z (1) # Z (2) # . # Z (N) The statistic J is defined as follows [7]: d mn i =1, N # F m (Z (i) G n (Z (i) # (1) 2 where m and n are as before, d is the greatest common divisor of m and n, and F m (a) m number of X s # a and G n (a) n number of Y s # a are considered to be the empirical ....

.... J (i) i = 1, 4 , where J (1) # . # J (4) Therefore, for the two sided Kolmogorov Smirnov # level test (viz H 0 versus the broad alternatives that H 0 is not true) reject H 0 if J (4) # j (#,m,n) accept H 0 if J (4) j (#,m,n) where j (#,m,n) is extracted from the Table A 23 in [7]. Due to the nondecreasing nature of the cumulative distribution function, noise and speckle are suppressed significantly. However, for further improved noise suppression, the first and second greatest of the Kolmogorov Smirnov statistics may be tested against desired thresholds. 3. Hardware ....

M. Hollander and D.A. Wolfe, Nonparametric statistical methods, Jhon-Wiely (1973).

.... values computed by the analyzer based on the profile record specification for problem i and algorithm j (see below for the discussion of the methods used to compute the X ij ) The process for ranking the algorithms uses multiple comparisons and contrast estimators based on Friedman rank sums [HW73] The two way layout associated with distribution free testing is shown in Table 2, which assumes nk data values from each of k algorithms for n 7 problems. This assumption is not strictly necessary; the analyzer can fill in missing values using various methods, for example, averaging values ....

M. Hollander and D.A. Wolfe. Nonparametric statistical methods. John Wiley and Sons, 1973. 17 No. PDE First Method First Method Second Method Second Method (from [HR82]) (from PYTHIA-II) (from [HR82]) (from PYTHIA-II)

....power of the test, it requires less restrictive assumptions about the error distribution. Of the various non parametric tests, only the Friedman test, a generalization of the sign test, will be described here. For descriptions of other non parametric tests, see Conover [4] or Hollander and Wolfe [7]. All of these tests assume that the query effect and the effect of the evaluation methods are independent and additive. An initial test is performed to determine whether there is any difference between methods. If a difference is detected, a subsequent multiple comparison test determines which ....

M. Hollander and D. Wolfe. Nonparametric Statistical Methods, chapter 3, 7, pages 27--49, 138--184. John Wiley and Sons, 1973.

....we have borrowed the approach presented in [38] where a non parametric statistical technique is considered for the ranking of methods with respect to a given set of problem instances. The process for ranking the methods uses multiple comparisons and contrast estimators based on Friedman rank sums [13]. Pattern Extraction Algorithms A variety of induction algorithms have been incorporated into MyPYTHIA; in this section we outline some of the more important categories of induction algorithms. Clustering: An area where tremendous progress has been made in inductive learning is clustering a ....

M. Hollander and D.A. Wolfe. Nonparametric Statistical Methods. John Wiley and Sons, 1973.

....of bias. External validity relates to the extent to which the hypotheses capture the objectives of the research and the extent to which any conclusions can be generalized. 22 It is encouraging that recent software research papers have included discussion of threats to validity (see for example,[19], 26] However, studies still report that some projects were omitted from the analysis because they did not collect all the required data , but do not consider the implication of those projects on their conclusions. If the authors were looking for quality differences among projects, it would be ....

....Software Engineering Conference, Sitges, Spain, September 25 28, 1995, Proceedings. Lecture Notes in Computer Science, Vol. 989, pp. 124 136, Springer, 1995, ISBN 3 540 60406 5. 18] Hoaglin, D.C. Mosteller, F. and Tukey, J.W. Understanding robust and exploratory data analysis, John Wiley, 1983 [19] M. Host and C. Wohlin. A subjective effort estimation experiment, Information and Software Technology, 39, 1997, pp.755 762. 20] P. Johnson and D. Tjahjono, Does every inspection really need a meeting Empirical Software Engineering, vol. 3, 1998, pp. 9 35. 21] G. Keppel. Design and ....

M. Hollander and D. Wolfe, Nonparametric Statistical Methods, John Wiley and Sons, 1999.

....downloaded from the PTAGIS database. We pooled run timing data for all six streams at Lower Granite dam, and then compiled run timing data for individual streams at all four dams. Run timing at Lower Granite Dam was compared using the Kruskal Wallis test,followed by a multiple comparison test (Hollander and Wolfe 1973; SAS Institute 1988) Run timing data to all dams during this report period is from actual first time observations of individual tagcodes expanded for spillway flow. This expansion factor was: Powerhouse Flow Spillway Flow) Powerhouse Flow This expansion factor (Appendix Table 7) accounts ....

....Fish Passage Center. 1987. Smolt monitoring program annual report 1986 Volume I: Migrational characteristics and survival of Columbia Basin salmon and steelhead trout. Annual Report to the Bonneville Power Administration, Agreement No.DE AI79 86BP61747, Project No. 86 60, Portland. Hollander, M. and D.A. Wolfe. 1973. Nonparametric statistical methods. John Wiley and Sons, New York. Matthews, G.M. J.R. Harmon, S. Achord, O.W. Johnson, and L.A. Kubin. 1990. Evaluation of transportation of juvenile salmonids and related research on the Columbia and Snake Rivers, 1989. Report to the U.S. Army Corps of ....

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Hollander, M., and D.A. Wolfe. 1973. Nonparametric statistical methods.

....the sample from one half of the window by the vector x drawn from the random variable X, and the sample from the other half by y drawn from Y. A very well known test for comparing cumulative distribution functions is the Kolmogorov Smirnov test, which is discussed in Conover (1980, Chapter 6) and Hollander and Wolfe (1973, Chapter 10) The cumulative distribution function (cdf) is a mapping which assigns the probability that a random variable Z is less than or equal to some specific value z for all possible z values, in other words FZ (z) P Z # z . The test statistic is K =sup # z # F X (z) FY (z) 9) ....

....signal, while the 4 minute window appears to catch it. Many similar detection strategies are discussed in Gibson and Melsa (1975) One of these strategies is called the Spearman Rho Detector. This detector is based on the Spearman Rho test which is discussed in Conover (1980, Chapter 5) and Hollander and Wolfe (1973, Chapter 8) In the context of the current problem this detector computes a correlation coe#cient between the two window halves and then tests to determine whether these two samples are correlated or not. Intuitively one would think that in the present situation the correlation between window ....

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Hollander, M., & Wolfe, D. (1973). Nonparametric Statistical Methods. Applied Probability and Statistics Series.

....sizes of up to ten pixels. For PRESTO (Fig. 8) the proportions of clusters with one or two pixels obtained by the spatial detection method greatly exceeded those obtained by the wavelet detection method. Equality of the two distributions was clearly rejected by the Kolmogorov Smirnov test [56], with median cluster sizes for the spatial and wavelet methods of one and six, and maximum detected cluster sizes of seven and 28, respectively. A cor Fig. 9. Cluster size distributions within ROI for EPI. Filled bars, regions detected by wavelet analysis and subsequent thresholding at 0.5 of ....

M. Hollander and D. A. Wolfe, Nonparametric Statistical Methods. New York: Wiley, 1973.

....shaded area above k is (1 #) 2. Thus the required bound is the solution of the following equation: I # (k, m k 1) 1 #) 2 (2) Equation (2) can be solved numerically using standard techniques. Press et al. 1992) explain how to efficiently calculate the incomplete beta function. Hollander and Wolfe (1999) discusses exact and asymptotic approximations for confidence intervals for the binomial parameter #. 4 Confidence intervals for the odds ratio The previous two sections described how to estimate confidence intervals for binomial distributions. Sometimes it is necessary to compare two different ....

....the general strategy for trading recall for precision proposed in this paper, we use the lower bound # of a confidence interval for the odds ratio as a discounted estimator for the odds ratio #. There are several ways in which this can be done, and the reader is referred to Agresti (1992) Hollander and Wolfe (1999) and Lloyd (1999) for details of asymptotic approximations and exact methods for calculating confidence intervals for the odds ratio. The exact method, which is used to produce the results shown in Table 2, involves conditional inference. That is, it involves conditioning not only on the row ....

Hollander, Myles and Douglas A. Wolfe. 1999. Nonparametric statistical methods. J. Wiley, New York.

....are also mutually independent. However, as can be seen in the next section, the error distributions for the algorithms can be quite di erent, both in mean and variance. Therefore, to compare the accuracy of the algorithms, we test if there is any stochastic di erence between the algorithms (Hollander and Wolfe, 1999), which means that we test if the probability that an error resulting from one algorithm is smaller than an error resulting from another algorithm is signi cantly di erent from # # . First, wecheck if there is any signi cantoverall stochastic di erence between the algorithms, by applying the ....

Hollander, M., D.A. Wolfe. 1999. Nonparametric Statistical Methods. John Wiley & Sons, New York.

....and procesess them within the problem execution environment to generate performance data. The statistical data analysis and pattern extraction modules comprise the data mining subsystem. The statistical analysis module uses a non parametric statistical method to rank the generated performance data [Hollander and Wolfe 1973]. PYTHIA II integrates a variety of publicly available pattern extraction tools such as relational learning, attribute value based learning, and instance based learning techniques [Bratko and Muggleton 1995; Kohavi 1996] These tools and our integration methods are discussed in Section 5.2. Our ....

....II illustrates the predicate s profile matrix; its columns represent algorithms and its rows represent problems as specified by a profile record. The X ij are performance values (see below) computed by the analyzer. PYTHIA II currently ranks the preformance of algorithms with Friedman rank sums [Hollander and Wolfe 1973]. This distribution free ranking assumes nk data values from each of k algorithms for n problems. The analyzer can fill in missing values using various methods. The Friedman ranking proceeds as follows: For each problem i rank the algorithms performances. Let r ij denote the rank of X ij in ....

Hollander, M. and Wolfe, D. 1973. Non-parametric Statistical Methods. John Wiley and Sons.

....s profile matrix. The X ij are performance values (see below) computed by the analyzer based on the profile record specification for problem i and algorithm j. The process for ranking the algorithms uses an analysis for multiple comparisons and contrast estimators based on Friedman rank sums [Hollander and Wolfe 1973]. The two way layout associated with distribution free testing is shown in Table II, which assumes nk data values from each of k algorithms for n problems. This assumption is not strictly necessary; the analyzer can fill in missing values using various methods, for example, averaging values in ....

Hollander, M. and Wolfe, D. 1973. Non-parametric Statistical Methods. John Wiley and Sons.

....determine whether there is evidence from two independent samples that H 1 #= H 2 ,whereH i is the cumulative distribution function (cdf) of a univariate outcome from sample i =1,2. Each outcome is not observed directly, but is recorded as belonging to one of k ordered categories. Siegel (1956) Hollander Wolfe (1973), and others recommend the Mann Whitney U test (Mann Whitney 1 1947, also called the Wilcoxon rank sum test) This is questioned in Edwardes (1997a) where random cut points theory for the distribution free analysis of ordinal (i.e. ordered categorical) data is given, and a modification of ....

M. Hollander & D. A. Wolfe (1973). Nonparametric Statistical Methods. Wiley, New York.

.... 0.909 Synthetic 0.758 0.0219 0.922 0.0156 Tab l e 2 : A comparison of the median absolute error between the actual data and synthetic data drawn from a Poisson distribution. of the means for the synthetic data. We conducted a Wilcoxon test, described for instance in Conover (1980) and Hollander and Wolfe (1973), of the hypothesis that the value of E med x for the actual data was drawn from a distribution having the same mean as the one for the synthetic data. We conducted a similar hypothesis test for the statistic E med y . These hypothesis tests gave p values of 0.0006 and 0.0003 for E med x ....

Hollander, M., & Wolfe, D. (1973). Nonparametric Statistical Methods. Applied Probability and Statistics Series. John Wiley & Sons, Inc., New York, NY.

....cycle is present, with higher values for DOD when O 3 concentrations are low. 3. 5 TREND ANALYSIS Trend statistics was calculated using percentiles of the measured mixing ratios for every year between 1985 and 1997 and applying the non parametric Mann Kendall test for the presence of trends (HOLLANDER and WOLFE, 1973; GILBERT, 1987) and Sen s method (GILBERT, 1987) for determining the slopes of the trends. The results are summarized in Figure 5. We found decreasing trends of the SO 2 mixing ratios at the forest sites. All trends are highly significant (a 0.05) and we note that the highest percentiles ....

HOLLANDER, M., and WOLFE, D.A. 1973. Nonparametric Statistical Methods. John Wiley & Sons. New York.

....The questionnaire contained four sets of statements to determine whether or not the users enjoyment and frustration levels were affected by the different interaction conditions. We used the Freeman Rank Sum two way layout distribution free test (with large sample approximation, S ) described in [9] to ascertain if there was a difference between the responses in each condition. The results for two of the questions indicated that the conditions had an effect on the response from the users, thus we could not average all of the responses. The users responses to these statements are shown in ....

Hollander, M., and Wolfe, D. Nonparametric Statistical Methods. John Wiley and Sons, New York, 1973.

....di erences of mean ranks. For our experiment, it gives a signi cance probability less than 10 4 . Therefore the null hypothesis that the algorithms are equally accurate on average is again rejected. Further, a di erence in mean ranks greater than 8. 7 is statistically signi cant at the 10 level [24]. Thus POL is not statistically signi cantly di erent from the twenty other algorithms that have mean rank less than or equal to 17.0. Figure 2(a) shows a plot of median training time versus mean rank. Those algorithms that lie to the left of the vertical line are not statistically signi cantly ....

M. Hollander and D. A. Wolfe. Nonparametric Statistical Methods. John Wiley & Sons, New York, NY, 2nd edition, 1999.

....of mean ranks. For our experiment, it gives a significance probability less than 10 Gamma4 . Therefore the null hypothesis that the algorithms are equally accurate on average is again rejected. Further, a difference in mean ranks greater than 8. 7 is statistically significant at the 10 level (Hollander and Wolfe, 1999, p. 296) Thus POL is not statistically significantly different from the twenty other algorithms that have mean rank less than or equal to 17.0. Figure 2(a) shows a plot of the median training time versus the mean ranks of the algorithms. Those algorithms that lie to the left of the vertical line ....

Hollander, M. and Wolfe, D. A. (1999). Nonparametric Statistical Methods, 2nd edn, John Wiley & Sons, New York, NY.

....if the underlying density is the uniform density on (0; 1) Thus the proposed test is theoretically designed for the specified class of density functions. An interesting problem is how to combine the proposed testing procedure with the EDF based tests or conventional nonparametric tests (see Hollander and Wolfe 1973) to yield an omnibus test for a broader class of distributions. This article is organized as follows. In Section 2 the test statistic 1 , which is a modified version of a kernel based estimate of Hall and Marron (1987, 1991) is introduced. The asymptotic distribution of 1 is derived and ....

Hollander, M., and Wolfe, D.A. (1973), Nonparametric Statistical Methods, New York: Wiley.

....in Figure 3 we present a ranking of the methods in Figure 2 with respect to dofs vs. time profiles for a certain class and for the accuracy level of 0:05 . The rank of a method for a class of problems is generated using a non parametric ranking scheme (Friedman, Kendall, Babbington Smith test [Hollander and Wolfe 1973]) The values in the other columns relate to the time taken by a method to solve problems in the given class. 4. THE PYTHIA KNOWLEDGE BASES The PYTHIA knowledge bases consist of 1) a priori rules specified by a (human) expert, 2) facts, and 3) rules generated from the performance knowledge for ....

Hollander, M. and Wolfe, D. 1973. Nonparametric Statistical Methods. John Wiley and Sons.

....a) for all a. To verify this hypothesis, the cumulative distribution function, cdf, of two samples are compared. To achieve this, the N observations from the two samples are ordered to form the set Z (i) i = 1, N , where Z (1) Z (2) Z (N) The statistic J is defined as follows [7]: J = d mn i =1, N max # # # F m (Z (i) G n (Z (i) # # # (1) where m and n are as before, d is the greatest common divisor of m and n, and F m (a) m number of X s a and G n (a) n number of Y s a are considered to be the empirical ....

.... set J (i) i = 1, 4 , where J (1) J (4) Therefore, for the two sided Kolmogorov Smirnov a level test (viz H 0 versus the broad alternatives that H 0 is not true) reject H 0 if J (4) j (a,m,n) accept H 0 if J (4) j (a,m,n) where j (a,m,n) is extracted from the Table A 23 in [7]. Due to the nondecreasing nature of the cumulative distribution function, noise and speckle are suppressed significantly. However, for further improved noise suppression, the first and second greatest of the Kolmogorov Smirnov statistics may be tested against desired thresholds. 3. Hardware ....

M. Hollander and D.A. Wolfe, Nonparametric statistical methods, Jhon-Wiely (1973).

....8, and estimated the mean classification accuracies and standard error of the means in five runs (Fig. 3) The statistical significance of the results was evaluated by the Wilcoxon rank sum test (a nonparametric test for comparing the medians of two independent samples of cardinal or ordinal data [HW73]) p values are shown at each point. On the original waveform data (noise oe 2 = 1) C4.5 performed similarly to the 72 accuracy reported for CART in [BFOS84] Calchas improved this accuracy to 77 (p = 0:01) Discussion It has been shown elsewhere that in domains where instances are governed ....

M. Hollander and D. Wolfe. Nonparametric Statistical Methods. Wiley, New York, 1973.

....significantly better than MRSH; the probability that it finds a candidate design with a fitness value larger than the one found by MRSH is between 80 and 90 . Figure 8 confirms that this difference in performance is statistically significant as indicated by the non parametric Fisher sign test [5]. In conclusion, three hours into the experiment, the agent based genetic algorithm performs significantly better than the MRSH algorithm: there is a chance of more than 80 that the GA achieves a higher fitness value than MRSH. Moreover, after six hours, the agent based genetic algorithm finds a ....

Hollander, M. and Wolfe, D. A. 1973. Nonparametric Statistical Methods. Wiley Series in Probability and Mathematical Statistics. New York, NY: John Wiley & Sons.

....rank sum test. NS denotes differences not statistically significant. the differences in accuracy between Calchas and C4.5 with feature extraction was evaluated by a Wilcoxon rank sum test (a nonparametric test for comparing the medians of two independent samples of cardinal or ordinal data [HW73]) p values are shown at each point. Calchas performance gains showed under moderate noise levels; these gains were all found to be statistically significant. Under low or high noise levels Calchas performed no worse than C4.5 (at noise level 8.0, Calchas performed slightly worse, but this ....

M. Hollander and D. Wolfe. Nonparametric Statistical Methods. Wiley, New York, 1973.

.... (d1 )i Y (b1 )j ) If q = p and D opt = d 1 ; d 1 , the null distribution of UDimp (q, p)isthesameasthe null distribution of the simple random sample Mann Whitney Wilcoxon rank sum statistic based on nX s and mY s, which is available in standard nonparametric text books (cf. e.g. Hollander Wolfe 1998). On the other hand, if the set sizes q and p are not equal, then the null distribution of UDopt (q, p) is not easily accessible. Di#culty arises from the fact that even though the number of order statistics is reduced to one in each sample, the sequences of order statistics are still not ....

Hollander, M., & Wolfe, D. A. (1998). Nonparametric Statistical Methods. 2nd edition, John Wiley, New York.

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M. Hollander and D. A. Wolfe. Nonparametric Statistical Methods. John Wiley & Sons, 1973.

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Hollander, Myles; and Douglas A. Wolfe. (1998) Nonparametric Statistical Methods, Second Edition, New York, NY: John Wiley and Sons, ISBN 0--471--19045--4.

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Hollander M, Wolfe DA. Nonparametric Statistical Methods. John Wiley & Sons, 1973.

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M. Hollander and D. A. Wolfe. Nonparametric Statistical Methods. John Wiley and Sons, 1973.

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M. Hollander, D. A. Wolfe, Nonparametric statistical methods, John Wiley and Sons, Inc., New York,1999.

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Myles Hollander and Douglas A. Wolfe. Nonparametric Statistical Methods. Second Edition, 1999. John Wiley & Sons.

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M. Hollander, and D.A. Wolfe. Nonparametric Statistical Methods (2nd ed.). Wiley, New York, 1999.

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Myles Hollander and Douglas A. Wolfe, Nonparametric Statistical Methods, 2nd Edition, Wiley-Interscience, 1999.

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H. Wolfe, Nonparametric Statistical Methods, Wiley, 1973. 30

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Hollander, M. and Wolfe, D.A. (1973). Nonparametric Statistical Methods. New York: Wiley

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HOLLANDER,M.AND WOLFE, D. 1973. Nonparametric Statistical Methods. John Wiley and Sons, Inc., New York, NY.

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M. Hollander and D.A. Wolfe, Nonparametric Statistical Methods, John Wiley & Sons, New York, 1973.

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Hollander, M. and D. Wolfe, Nonparametric Statistical Methods, New York: Wiley, 1973. Journal of Financial and Strategic Decisions 72

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Hollander, M. and Wolfe, D. A. 1973. Nonparametric Statistical Methods. Wiley Series in Probability and Mathematical Statistics. New York, NY: John Wiley & Sons.

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