Nonparametric Multiple Comparison Research Articles

Nonparametric Stepwise Multiple Comparison Procedures

Abstract Nonparametric multiple comparisons are discussed, with particular emphasis given to stepwise procedures. Nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc nonparametric analog of the Newman—Keuls procedure. These new procedures are compared among themselves and with nonstepwise procedures based on Type I error levels and comparisonwise power. It is shown that these stepwise nonparametric procedures control Type I error levels, and that they have superior pairwise power compared to the commonly used nonstepwise procedures.

Field Evaluation of An Aqueous Formulation of Carbaryl for Rangeland Grasshopper Control, 1983

Abstract A small plot study (see J. A. Onsager and P. C. Mazuranich, 1983, Insecticide and Acaricide Tests 8:204) indicated the potential of reduced rates of carbaryl in an aqueous formulation for control of rangeland grasshoppers. The objective of this study was to determine if lower rates of carbaryl would be effective when used in an aqueous formulation on larger plots. The Sevin FR formulation of carbaryl was applied at dosages of 0.250 and 0.375 lb (AI)/acre (8 and 12 fluid oz) to 320 acres (0.5 X 1 mile) plots near Big Timber, Montana, on 23 Jul and 24 Jul ‘83. Both treatments were applied in 20 fluid oz of mix/acre, each containing 4 oz of water plus either 8 oz or 4 oz respectively, of PA3 (an antidrift additive containing molasses). These treatments were compared to standard rangeland treatments of 0.5 lb (AI) carbaryl/acre (16 fluid oz of Sevin-4-Oil diluted with 4 oz of diesel/acre) and 0.58 lb (AI) malathion/acre (8 fluid oz of Cythion) applied to adjacent 320-acre plots (0.5 x 1 mile and 0.25 x 2 miles, respectively) on 24 and 26 Jul, respectively. All treatments were applied from a Cessna Ag Truck aircraft operating at 120 mph. All treatments were applied through flat fan stainless steel jet nozzle tips from an altitude of 50 to 75 ft with a swath of 100 ft. Seven 8006 tips directed 45° down and aft were used for the 0.250 and 0.375 lb (AI)/acre Sevin FR treatments (43 psi and 41 psi, respectively). Ten 8004 tips directed straight down and operating at 35 psi were used for delivering the Sevin-4-oil treatment and eleven 80015 tips directed straight down at 40 psi were used for applying the Cythion. Pre and postapplication grasshopper densities were ascertained by counting grasshoppers in forty 0.1 m2 rings, 5 m apart, arranged for the duration of the study in circles or diagonal transects at 8 sites within each block (1 transect contained only 29 rings). Pre-treatment counts were taken 1 to 2 days prior to treatment and posttreatment counts were conducted 5 times during a period of 21 days following treatment. Grasshopper densities from 59 counts between 20 Jul to 16 Aug ‘83, at 9 untreated sites adjacent to the treatment area were used to determine the natural change in the grasshopper population during the study. Data expressed as a percentage survival based on pretreatment counts in the same plot were adjusted for the natural population change by Abbott’s formula. Sums of the ranks of the percentage control at 19 to 21 days postapplication for each of the treatments were compared by a nonparametric multiple comparison procedure. (See J. H. Zar, 1974, Biostatistical Analysis, pp 156–157.) Mean daily percentage control values from 2 to 19 days after application for each of the treatments were also ranked and the treatment sums compared as above. The above species were mostly fourth (36%) and fifth (38%) instars and respectively comprised 43.1, 21.2, 14.1, 4.1, and 4.0 of the grasshopper population in the treatment plots before application. Pretreatment densities ranged from 2.3 to 25.3 and averaged 11.4 grasshoppers/m2 in the treated plots.

Nonparametric approaches to testing and multiple comparisons in a one-way anova

Two questions of interest involving nonparametric multiple comparisons are considered. The first question concerns whether it is appropriate to use a multiple comparison procedure as a test of the equality of k treatments, and if it is, which procedure performs best as a test. Our results show that for smaller k values some multiple comparison procedures perform well as tests. The second question concerns whether a joint ranking or a separate ranking multiple comparison procedure performs better as a test and as a device for treatment separation. We find that the joint ranking procedure does slightly better as a test, but for treatment separation the answer depends on the situation.

The Effect of Violating the Assumption of Equal Item Means in Estimating the Livingston Coefficient

The validity of five methods of estimating the reliability of criterion-referenced tests was evaluated: one method based on the binomial expansion; two based on Kuder and Richardson's formulae 20 and 21; and two methods based on the analysis of variance. The methods were compared across nine conditions of variability among item means. Within each condition the number of test items, number of testees, the value of the criterion, the population mean, and variance of true scores were varied to form 1024 cases. The results were analyzed by means of a conditions-by-methods analysis of variance, the Newman-Keuls test, and a nonparametric multiple comparison procedure. There was a tendency for all of the methods to be conservative. The KR-21 method tended to be more valid given low variability among item means, and the KR-20 method given high variability.

A note on multiple comparisons for randomized complete blocks with a binary response

AbstractIn the present paper a nonparametric multiple comparison procedure is studied asymptotically. It is applicable in randomized complete block designs when the responses are dichotomous and the sample size is large.

An evaluation of some nonparametric multiple comparison procedures by Monte Carlo methods

Computer simulation techniques were employed to investigate the Type I and Type II error rates (experiment-wise and comparison-wise) of three nonparametric multiple comparison procedures. Three different underlying distributions were considered. It was found that the nonparametric analog to Fisher’s LSD (a Kruskal-Wallis test, followed by pairwise Mann-Whitney U tests if a significant overall effect is detected) appeared to be superior to the Nemenyi-Dunn and Steel-Dwass procedures, because of the extreme conservatism of these latter methods.

On multiple comparisons among k populations differing by scale parameters

Two nonparametric multiple comparisons procedures for determining which of Kpopulations differ from each other by scale shifts are described. Both procedures are based upon K-sample generalizations of the two sample test proposed by Savage:one method utilizes a pairwise and the other a joint ranking scheme. It is shown that the two procedures have equivalent asymptotic properties

Further Comments on Nonparametric Multiple-Comparison Tests

A Monte Carlo study of four nonparametric multiple-comparison tests (the Ryan, Nemenyi, Steel, and Wilcoxon) for k independent groups indicated that the Wilcoxon rank-sum test performed optimally when it was used after a significant over-all Kruskal-Wallis H test.

A One-Sided Nonparametric Multiple Comparison Control Percentile Tests: Treatments Versus Control

A One-Sided Nonparametric Multiple Comparison Control Percentile Tests: Treatments Versus Control

A one-sided nonparametric multiple comparison control percentile test: treatments versus control

SUMMARY The control median test studied by Gart (1963) is generalized to a control percentile test in which there may be more than one treatment. Exact and asymptotic null distributions are obtained, the latter being that of the minimum of normal variates having a common correlation. Tables for the control median test are provided for small sample sizes. In applied research it is common to be confronted with the problem of deciding which, if any, of several treatments are better than a standard or control treatment on the basis of observations from groups of items to which each of the treatments will be applied. For example, in drug screening for a type of cancer an experimenter desires to know whether any of several doses of a drug is suited to alleviating the disease by prolonging survival. The dose levels to be examined, together with a standard treatment, are all assigned to different groups of test animals, and the observations consist of the survival times of the animals after tumour implantation and subsequent drug application. Hence, the ordered observations are obtained sequentially, and, since an inordinately long period of time may pass before all observations are recorded, an analysis is desired based on those in hand when a preselected number of control animals have died. For a situation such as this, the easily computed nonparametric test described below permits a rapid assessment of the null hypothesis that there is no difference among all the populations considered, relative to the alternative that the percentile of interest of at least one of the treatment populations is greater than that of the control. The statistic on which this test is based is the minimum of the numbers of observations in each treatment sample which do not exceed the preselected ordered observation in the control sample. Clearly, small values of the statistic militate against the null hypothesis in favour of the alternative. For the application cited above, suppose that the percentile of interest were the median and that the experimenter placed nO = 13 animals under standard treatment and n = 9 animals under each of p = 4 different doses of the drug. Then, having found x = 0 dead animals under some dose level when the seventh control animal died, he could, by means of Table 3 below, assert with a significance level of 3 67 % that that dose level is effective in prolonging median survival relative to the control treatment. Dunnett (1955) provided a one-sided experimentwise test for means in complete samples when the distributions involved are normal. In the realm of nonparametric many-to-one tests which permit early analysis of data, P. Nemenyi in an unpublished thesis mentioned by Miller (1966, p. 185), studied the joint, rather than control, median test based on data