### Table 7. Advantages of non- parametric statistics for use in health science research

"... In PAGE 5: ... For each of the main parametric techniques there is a non-parametric counterpart; Experiment with the data to determine which test provides the best power, and the greatest level of signif_icance. There are a number of advantages to using non-parametric techniques in health science research ( Table7 ). The most important of these advantages are the generality and wide scope of non-parametric techniques.... ..."

### Table 8. Common nonparametric statistics

"... In PAGE 6: ... This study demonstrated that the use of non- parametric techniques is implicated whenever there is doubt regarding the fulf_illment of parametric assumptions, such as normality or sample size. Which non-parametric test should we use? The most common non-parametric tests can be found in Table8 . Please refer to the following statistical texts for the derivation and calculation of these statistics, as this is beyond the scope or intention of this paper: Nonparametric Statistics for the Behavioural Science (Siegel Sand Castellan NJ, 1988) (6), Applied Nonparametric Statistical Methods (Sprent P and Smeeton NC, 2001) (9), Nonparametric Statistical Inference (Gibbons JD, 1985) (8), Nonparametrics: Statistical Methods Based On Ranks (Lehmann EL, 1975) (18), Practical Nonparametric Statistics (Conover WJ, 1980) (19), Fundamentals of Nonparametric Statistics (Pierce A, 1970) (15), and Essentials of Research Methods in Health, Physical Education, Exercise Science and Recreation (Berg KE and Latin RW, 2003) (10).... ..."

### Table 3. ANOVA for Model choice

"... In PAGE 12: ...0344 compare the results in Table 2 with a nonparametric technique based on Gen- eralized addittive models. Table3 show the outcome from generalized additive model. In our application we use the splines.... ..."

### Table 3. Nonparametric Test Results under Various Weighting Schemes.

"... In PAGE 16: ... Results Specific programming problems as defined in equations (5) and (7) for the cigarette manufacturing industry are reported in Table 2. Test results for cases where monopsony power is allowed in the domestic tobacco market (single input case) and where monopsony power is allowed in both the domestic tobacco market and international tobacco market (two input case) are presented in Table3 . In general, the results indicate that cigarette manufacturers exert economically significant monopsony market power in the domestic tobacco market.... ..."

### Table 5: Performance impact of the Generalized Induction technique.

"... In PAGE 12: ... In #5BBE94a#5D, wehave described a new analysis technique that can handle such nonlinear subscripts. The e#0Bect of the Generalized Induction Variable transformation is shown in Table5 . The table shows the same type of information as Tables 3 and 4.... ..."

### Table 4: Generalization Lower bound technique

### Table 7: Nonparametric Model Tests Percent of population not rejecting each hypothesis at the 95% confidence level

2006

"... In PAGE 18: ... Gasoline demand itself has almost the same own price elasticity as in the aggregate data, and shows many similar cross price effects (again including a small positive cross effect on other transportation), though these nonparametric cross price effects are not estimated with enough precision to be statistically significant. Table7 lists results of various tests of rationality restrictions. We evaluate the estimated nonparametric demand functions and their derivatives at each data point, and for each ob- servation we test whether the demand functions at that point satisfy homogeneity, negative semidefiniteness, and Slutsky symmetry.... In PAGE 18: ... We evaluate the estimated nonparametric demand functions and their derivatives at each data point, and for each ob- servation we test whether the demand functions at that point satisfy homogeneity, negative semidefiniteness, and Slutsky symmetry. For each hypothesis, Table7 lists the percent of observations at which the hypothesis is not rejected at the 0.95 confidence level.... In PAGE 18: ...95 confidence level. Table7 shows that homogeneity (the absence of money illusion) is generally accepted, with a rejection rate of 11% of the data when we allow for endogenous regressors. We test symmetry and negative semidefiniteness of the composite commodity Slutsky matrix tildewide S(r, y, z) both with and without imposing homogeneity.... ..."

### Table 7: Nonparametric Model Tests Percent of population not rejecting each hypothesis at the 95% confldence level

2006

"... In PAGE 19: ... Gasoline demand itself has almost the same own price elasticity as in the aggregate data, and shows many similar cross price efiects (again including a small positive cross efiect on other transportation), though these nonparametric cross price efiects are not estimated with enough precision to be statistically signiflcant. Table7 lists results of various tests of rationality restrictions. We evaluate the estimated nonparametric demand functions and their derivatives at each data point, and for each ob- servation we test whether the demand functions at that point satisfy homogeneity, negative semideflniteness, and Slutsky symmetry.... In PAGE 19: ... We evaluate the estimated nonparametric demand functions and their derivatives at each data point, and for each ob- servation we test whether the demand functions at that point satisfy homogeneity, negative semideflniteness, and Slutsky symmetry. For each hypothesis, Table7 lists the percent of observations at which the hypothesis is not rejected at the 0.95 confldence level.... In PAGE 19: ...95 confldence level. Table7 shows that homogeneity (the absence of money illusion) is generally accepted, with a rejection rate of 11% of the data when we allow for endogenous regressors. We test symmetry and negative semideflniteness of the composite commodity Slutsky matrix e S(r; y; z) both with and without imposing homogeneity.... ..."

### Table 3. Results of parametric and nonparametric tests for between-shape differences in fencerow and intersection characteristics.

"... In PAGE 9: ... Regression analyses indicated that none of the fencerow characteristics were related to the richness variables, implying that this control technique was effective and that we therefore obtained a clear assessment of the effect of inter- section shape on plant richness. Differences in intersection area among intersec- tion shapes ( Table3 ) were probably just a physical result of the number of intersecting fencerows comprising L, T and X intersections. One could argue, however, that vertebrate-dispersed richness may have been higher in intersections with more avenues for influx simply because such intersec- tions happened to be larger and therefore more structurally diverse (c$ Gutzwiller and Anderson 1987), which could have attracted a greater variety ... ..."

### Table 1: Quadratic or Nonparametric?

2001

"... In PAGE 8: ... The squared L2 risks of the estimators are computed based on 100 replications. The numbers in the parentheses in Table1 are the corresponding standard errors. Quadratic regression works much better than the nonparametric alternatives for the rst two cases, but becomes much worse for the latter two due to lack of exibility.... ..."

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