Nonparametric Statistics
Daryl S. Paulson in Applied Statistical Designs for the Researcher, 2003
Up to this point, Chaps. 1 through 11, we have discussed parametric statistics and have become quite knowledgeable in their applications. Now, we will focus on nonparametric statistical methods. Parametric statistics, although generally more powerful, require that more assumptions be met than do non-parametric methods. For example, in situations in which the experimenter has no previous understanding of the data (e.g., has not worked in this area before), it is not known whether the data are normally distributed or fall under another distribution. Although increasing the sample size tends to normalize any distribution, an experimenter is often restrained by a budget to a small sample size. Nonparametric statistics can be useful here, for they do not require a normal distribution. Nonparametric statistics are so termed because they do not utilize parameters, e.g., the mean, the variance, or the standard deviation.* Instead, the median—midpoint of the data—is generally utilized. The biggest advantage of using nonparametric statistics is that they remain valid under very general and limited assumptions [40,41].
Approaches to quantitative data analysis
Louis Cohen, Lawrence Manion, Keith Morrison in Research Methods in Education, 2017
Non-parametric data are those which make no assumptions about the population, usually because the characteristics (numerical parameters) of the population are unknown. Parametric data assume knowledge of the characteristics of the population, in order for inferences to be able to be made securely; inferential statistics are premised on a normal, Gaussian curve of distribution, as, for example, in reading scores, in order to be able to generalize to the wider population (though Wright (2003, p. 128) suggests that normal distributions are actually rare). In practice this distinction means the following: nominal and ordinal data are often considered to be non-parametric, whilst interval and ratio data are often considered to be parametric data (unless, for example, the data are skewed). The distinction is important, as, for the four scales of data, the consideration of which statistical test to use is dependent on the kinds of data: it is often incorrect to apply parametric statistics to non-parametric data, though it is possible to apply non-parametric statistics to parametric data if those data do not conform to the curve of distribution, being skewed or unevenly distributed. Statistics for parametric data tend to be more powerful than those for non-parametric data, though such power is bought at the price of, for example, conformity to the normal curve of distribution and random samples. Non-parametric data are often derived from questionnaires and surveys (though these can also include parametric data), whilst parametric data tend to be derived from experiments and tests (e.g. examination scores).
Evaluation of Associated Behavioral and Cognitive Deficits in Anticonvulsant Drug Testing
Steven L. Peterson, Timothy E. Albertson in Neuropharmacology Methods in Epilepsy Research, 2019
During the acquisition trial an animal is placed into the white, illuminated box facing the wall opposite to the door and then, after a certain time interval (e.g., 10 s) the door is opened. Once the animal enters the dark compartment with all four paws, the door is closed and a footshock is delivered. Usually animals enter the dark compartment within 10 to 30 s. Animals that enter the dark box with a considerably longer latency should be excluded from further testing. Because a footshock is used as a reinforcer for this task, the shock parameters are critical. The footshock duration is usually 1 to 5 s and the current intensities vary between 0.1 and 0.8 mA for mice and 0.4 and 1.0 mA for rats. The stimulus duration is relatively easy to determine, while the current intensity is not. The footshock strength depends on the sex and strain of the animals, as well as on the cleanliness of the grid floor (feces block and urine facilitates current passage). Therefore, several preliminary trials have to be performed using some reference drugs that are known to produce memory impairment, like the anticholinergic drug scopolamine, in order to find the current intensity best suited for the purpose. Current intensities that are too high will likely result in no influence of test substances on memory (“ceiling” effect). With weak current intensities even low doses of antiepileptic drugs will produce memory impairment (“floor” effect). In either case it will not be possible to construct a dose-response curve. The time that each animal spends in the illuminated box before entering the dark box is measured using a stopwatch. Twenty-four hours later (retention or retrieval trial), each animal is placed again in the illuminated box in the same way as during the acquisition trial and the latency to enter the dark box is noted. The time the animal is allowed to stay in the illuminated box without entering the dark box or the cut-off time is arbitrary and usually is set at 120 to 300 s. The measure of long-term memory in this test is the time spent by an animal in the illuminated box during the acquisition trial subtracted from that spent during the retention trial (the greater the difference, the better the task was remembered). Usually, the data obtained do not conform to the requirements imposed by the theory for parametric data because of high variability (e.g., lack of normal distribution) and an a priori setting of cut-off time. Accordingly, nonparametric statistics should be used. Also, the aforementioned high dispersion of experimental data forces the researcher to use larger groups of animals (10 to 15 per group).
Experimental comparison of functional and multivariate spectral-based supervised classification methods in hyperspectral image
Published in Journal of Applied Statistics, 2018
Anthony Zullo, Mathieu Fauvel, Frédéric Ferraty
Nonparametric statistics refers to a set of distribution free data-driven methods, in the sense of methods which do not rely on any parametric assumption nor any given probability distribution. The use of nonparametric models leads to more general, robust, flexible and adaptable models, while allowing the exploration of nonlinear relationships. In this high-dimensional context, nonparametric classification methods can be built in several ways, as in Greenshtein and Park [39] where a Nonparametric Empirical Bayes Estimation is proposed. This approach combines many weakly informative variables using naive Bayes classifiers. In a hyperspectral classification context, several recent articles report the use of nonparametric methods, as in Delalieux et al. [23] for the detection of biotic stress in apple trees. The use of nonparametric functional methods on hyperspectral datasets have only been recently investigated, as in Ordóñez et al. [66] for vine-leaf composition characterization.
Social attainment in physically well-functioning long-term survivors of pediatric brain tumour; the role of executive dysfunction, fatigue, and psychological and emotional symptoms
Published in Neuropsychological Rehabilitation, 2021
Anita Puhr, Ellen Ruud, Vicki Anderson, Bernt Johan Due-Tønnessen, Anne-Britt Skarbø, Arnstein Finset, Stein Andersson
Statistical analyses were conducted using the statistical package SPSS for Windows, version 25.0 (SPSS, Inc., Chicago, Illinois). Missing item scores were replaced by the participant’s average subscale score where at least 2/3 of the items were completed (Tabachnick & Fidell, 2007). Due to non-normal distributions, non-parametric statistics were conducted. Between group and subgroup differences were tested by Pearson Chi Square and Mann–Whitney U test. Bonferroni corrections for multiple comparisons were employed; only differences surviving corrections are reported. Effect size (ES) is reported as r for continuous data, and as ϕ for categorical data, in both cases defining small ES as = .1–.3; medium ES as = .3–.5; and large ES as >.5 (Field, 2009).
A non-parametric statistic for testing conditional heteroscedasticity for unobserved component models
Published in Journal of Applied Statistics, 2021
Alejandro Rodriguez, Gabriel Pino, Rodrigo Herrera
In order to overcome the problem of serial correlation in the series tested, we propose testing the presence of heteroscedasticity using a nonparametric statistic for testing changes in the mean. It is well known that the use of nonparametric statistics requires less restrictive assumptions than parametric ones. Indeed, using the ideas of Broto and Ruiz [15], the nonparametric statistic can be used to indicate the presence of heteroscedasticity if it detects changes from zero in the differences in the correlations of the auxiliary residuals. Wang [76] and Dehling et al. [25] studied the asymptotic properties of Wilcoxon's rank statistic for long memory-dependent data. They find that the asymptotic distribution of the statistics and the critical values can be obtained through simulation. In the case of short memory, these authors' results can be extended to analyze processes in which the difference between the correlations of the square auxiliary residuals and the squared correlation of the auxiliary residuals.
Related Knowledge Centers
- Power of A Test
- Statistical Inference
- Parametric Statistics
- Ranking
- Power of A Test
- Histogram
- Kernel Density Estimation
- Semiparametric Regression
- Kernel
- K-Nearest Neighbors Algorithm
- Sign Test