对应用到COVID-19临床特征的量子值进行非参数模糊假设测试

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance,...

The Kruskal-Wallis test, also known as the Kruskal-Wallis H test, serves as a nonparametric alternative to the one-way ANOVA, offering a solution for analyzing the differences across three or more independent groups based on a single, ordinal-dependent variable. This statistical test is particularly valuable in scenarios where the data does not meet the normal distribution assumption required by its parametric counterparts. Kruskal-Wallis test is designed typically to handle ordinal data or...

The Wilcoxon rank-sum test, also known as the Mann-Whitney U test, is a nonparametric test used to determine if there is a significant difference between the distributions of two independent samples. This test is designed specifically for two independent populations and has the following key requirements:

When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the...

Nonparametric statistics offer a powerful alternative to traditional parametric methods, useful when assumptions about the population distribution cannot be made. Unlike parametric tests, which require data to follow a specific distribution with well-defined parameters (such as the mean and standard deviation), nonparametric tests do not require such constraints. This makes them particularly valuable when dealing with small sample sizes, skewed data, or ordinal and categorical variables.
One of...