Kneeling for nonparametric statistical methods and applications 50

The differences are as follows:

1. The applicable data types are different.

Parametric statistics are often used for fixed-distance or fixed-ratio data, while non-parametric statistics are often used for data consisting of only some grades, or the data to be analyzed does not meet the assumptions required by the parametric test, so the parametric test cannot be applied.

2. The assumptions about the parameters are different.

Parametric statistics requires people to estimate or test the parameters in the question; The questions asked by non-parametric statistics do not contain parameters and cannot be tested with parameters.

3. The degree of dependence on the whole is different.

In parameter statistics, the distribution form or distribution family of the population needs to be given in order to estimate and test the parameters. In non-parametric statistics, no assumptions are made about the population distribution or only very general assumptions, and the dependence on the population is low, but the characteristic distribution of the population is inferred from the sample is not a parameter value.

4. The scope of application is different.

Since each specific parameter statistics method is based on a specific theoretical distribution, the parameter statistics have certain requirements and limitations on the data to be analyzed and processed. Because non-parametric statistics do not rely on a specific theoretical distribution, the requirements for data conditions are relatively loose and have a wide range of applications.

In statistics, the two most basic forms of statistical inference are: parameter estimation and hypothesis testing, most of which are related to normal theory, which is called parametric statistics. In parametric statistics, the form of distribution or family of distributions of a population is often given, while parameters such as mean and variance are unknown.

The task is to estimate or test these parameters. When the distribution is assumed, the inference has a high precision.

Non-ginseng bai

Mathematics is one of the important branches of applied statistics. Non-parametric statistics are different from traditional ones.

The basic characteristics of DAO parametric statistics are that the modular weight type of non-parametric statistical analysis is usually more lenient in the assumptions of the model and data. Generally speaking, non-parametric statistics is a method that does not make detailed assumptions about the specific form of data distribution, tries to obtain the structural relationship of data from the data itself, and gradually establishes a mathematical model and statistical model of the research object.

The conditions for the application of non-parametric statistics include:

First, the basic characteristics.

The assumptions of the population distribution in the nonparametric statistical problem require a wide range of conditions, so the nonparametric statistical method constructed for this problem will not lead to major errors due to the improper assumption of the population distribution, so it tends to have good robustness (see robust statistics), which is an important feature.

However, because nonparametric statistical methods need to take care of a wide range of distributions, they can lead to a decrease in their efficiency in some cases. However, the near-** theory proves that some important nonparametric statistical methods, when compared with their counterparts, have little loss in efficiency, even in the case that is most favorable to the latter.

2. Scope of application.

1. The data to be analyzed does not meet the assumptions required by the parameter test, so the parameter test cannot be applied. For example, when we have encountered a small sample of a non-normal population, the t-test is not suitable, and a nonparametric test can be used as an alternative.

2. The data that is only composed of some grades cannot be applied to the parameter test. For example, consumers may be asked how much they like beverages under several different trademarks, and while they cannot assign a number to each trademark to indicate their liking for the trademark, they can rank several trademarks in order of like. In this case, it is also advisable to use a non-parametric test.

3. The questions raised do not contain parameters, nor can they be tested by parameters. For example, if we want to determine whether a sample is random, a nonparametric test is appropriate.

4. When we need to get results quickly, we can also use non-parametric statistical methods instead of parametric statistical methods to achieve the goal. In general, the calculations required by non-parametric statistical methods are faster and easier to complete than parametric statistical methods. Some non-parametric statistical methods can be calculated in a timely manner even for people who are not familiar with statistics.

In the statistical test, it is important to consider whether the non-parametric statistical method is used ( ).

a.The decision should be made based on the purpose of the study and the characteristics of the data.

b.The choice can be made after several statistics have been calculated and preliminary conclusions have been drawn.

c.It depends on which statistical conclusion conforms to the professional theory.

d.It depends on which value is smaller.

e.Since non-parametric statistics do not have strict requirements for data, they can be used directly in any case.

Answer analysis aThe decision should be made based on the purpose of the study and the characteristics of the data.

Statistical testing (the process of rejecting or not rejecting a null hypothesis of one or more population distributions based on the results of sampling) is generally referred to as hypothesis testing.

Hypothesis testing, also known as statistical hypothesis testing, is a statistical inference method used to determine whether the differences between samples and samples and populations are caused by sampling errors or essential differences.

Significance testing is one of the most commonly used methods of hypothesis testing, and it is also the most basic form of statistical inference, which is based on the basic principle of making some kind of assumption about the characteristics of the population, and then making inferences about whether the hypothesis should be rejected or accepted through statistical reasoning from sampling studies. Commonly used hypothesis testing methods include z-test, t-test, chi-square test, f-test, etc.

The basic idea of hypothesis testing is the principle of "small probability events", and its statistical inference method is a counterproof method with a certain probabilistic nature. The idea of low probability is that a small probability event will not occur in a single trial. The idea of the counter-evidence method is to first put forward a test hypothesis, and then use appropriate statistical methods to determine whether the hypothesis is true by using the principle of small probability.

That is, in order to test whether a hypothesis h0 is correct, the hypothesis h0 is first assumed to be correct, and then a decision to accept or reject hypothesis h0 is made based on the sample. If the sample observations cause a "small probability event" to occur, hypothesis h0 should be rejected, otherwise hypothesis h0 should be accepted.

The so-called "small probability event" in hypothesis testing is not an absolute contradiction in logic, but is based on the principle widely adopted in practice, that is, small probability events almost never occur in an experiment;

Obviously, the smaller the probability of a "small probability event", the more convincing it is to reject the null hypothesis h0, and this probability value is often remembered as (0< <1), which is called the significance level of the test.

The significance level of the test is not necessarily the same for different problems, and it is generally accepted that the probability of an event occurring is less than05 or so on, i.e. "small probability event".