Non-parametric method analysis is an important part of statistical analysis methods, and the basic content of statistical inference together with parameter test. The parameter test is a method to infer the parameters such as mean, variance, etc. of the general distribution in the case of a known general distribution. However, in the process of data analysis, because of various reasons, people often cannot make a simple assumption about the overall distribution pattern. At this time, the method of parameter test is no longer applicable. Non-parametric testing is a kind of method based on this consideration, in which the total variance is unknown or little known, and the sample data is used to infer the overall distribution pattern. Since non-parametric test methods do not involve the parameters of the general distribution in the inference process, they are named as "Non-parametric" tests. In practical application, because non-parametric test does not need to pre-set the specific form and error distribution of the model, it can obtain a wide nonlinear change. At the same time, in the overall evaluation of the sample, non-parametric test is not necessary to rely on the overall distribution of the sample. It can be widely used in different types of the general, which is conducive to reduce the deviation and improve the understanding of the dynamic structure of a sample sequence.
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Our statistical experts will choose the most appropriate non-parametric analysis method based on the cost, time, validity, total available data, form of available data, sampling method and overall attributes for you.Chi-square test
When it is necessary to statistically determine the degree of deviation between the actual observed value of the sample and the theoretically inferred value, we recommend a chi-square test. To analyze the relationship between two variables X and Y, you can use an independence test to examine whether the two variables are related and can get a more accurate degree of reliability of this judgment. The specific method is to establish an independent sample four-grid table and calculate the value of the test statistic from the data in the table. The degree of deviation between the actual observed value and the theoretically inferred value determines the magnitude of the chi-square value.
Binomial distribution test
The binomial distribution test belongs to the goodness-of-fit test, which is applicable to data populations that can only be divided into two categories. The binomial distribution test is to test whether the two types of proportional values observed from the sample are from a population with the established P value.
Kruskal-Wallis test
The essence of Kruskal-Wallis test is the generalization of the Mann-Whitney U test for two independent samples under multiple samples, and it is also used to test whether there is a significant difference in the distribution of multiple populations. The null hypothesis is that there is no significant difference in the distribution of multiple populations from multiple independent samples.
Signature test
The symbol test is also a non-parametric method used to test whether there is a significant difference in the overall distribution of two paired samples. The null hypothesis is that there is no significant difference in the distribution of the two populations in the two paired samples.
Wilcoxon
The Wilcoxon signed rank test also determines whether there is a difference in the distribution of the two populations by analyzing two paired samples to which they belong. The null hypothesis is that there is no significant difference in the distribution of the two groups. The basic idea is: first, according to the method of symbol testing, we subtract the observation values of the first set of corresponding samples from the corresponding observation values of the second set of samples. The difference is positive for positive sign, negative for negative sign, and the difference data is saved at the same time; then, the difference variables are sorted in ascending order to get the level of the difference variable; finally, the positive rank and W + and the negative rank and W- are calculated.
Non-parametric tests of multi-paired samples are based on the analysis of multiple sets of paired sample data to infer whether there is a significant difference in the median or distribution of multiple populations from which the sample is derived.
Friedman test
The Friedman test is a non-parametric test method that uses rank to achieve significant differences between multiple population distributions. The null hypothesis is that there is no significant difference in the multiple population distributions from multiple paired samples. Based on the above basic idea, in the Friedman test of multi-paired samples, the data is first sorted in ascending order in units of rows, and the ranks of the variables in their respective rows are obtained; then, the rank sum and average rank under each group of samples are calculated separately. The Friedman test of multi-paired samples is suitable for the analysis of distance-type data.
Cochran Q test
By analyzing multiple paired samples, it can be inferred whether there is a significant difference in the distribution of multiple populations from which the sample is derived. The null hypothesis is that there is no significant difference in the distribution of multiple populations from multiple paired samples.
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References:
1. Bagdonavicius, V. B., & Nikulin, M. S. (2011) ‘Chi-squared goodness-of-fit test for right censored data’, The International Journal of Applied Mathematics and Statistics, 24 (Suppl I-11A), 30-50.
2. Kessler, D. C., Hoff, P. D., & Dunson, D. B. (2015) ‘Marginally specified priors for non-parametric Bayesian estimation’, J R Stat Soc Series B Stat Methodol, 77(1), 35-58.
3. Oliver-Rodríguez, J. C., & Wang, X. T. (2013). ‘Non-parametric three-way mixed ANAVO with aligned rank tests’, British Journal of Mathematical & Statistical Psychology, 68(1), 23-42.